## Abstract

Pool boiling heat transfer offers high-performance cooling opportunities for thermal problems of electronics limited with high heat fluxes. Therefore, many researchers have been extensively studying over the last six decades. This paper presents a critical literature review of various parametric effects on pool boiling heat transfer and critical heat flux (CHF) such as pressure, subcooling, surface topography, surface orientation, working fluid, and combined effects. To achieve an optimal heat removal solution for a particular problem, each of these parameters must be understood. The governing mechanisms are discussed separately, and various options related to the selection of appropriate working fluids are highlighted. A broad summary of correlations developed until now for predicting CHF is presented with their ranges of validity. While proposed correlations for predicting CHF have been quite promising, they still have a considerable uncertainty (±25%). Finally, a correlation proposed by Professor Avram Bar-Cohen and his team (thermal management of electronics (TME) correlation) is compared with the experimental dataset published in previous studies. It shows that the uncertainty band can be further narrowed down to ±12.5% for dielectric liquids by using TME correlation. Furthermore, this correlation has been enhanced to predict CHF values underwater above 50 W/cm2 by applying a genetic algorithm, and new perspectives for possible future research activities are proposed.

## 1 Introduction

Reducing the amount of waste energy during system operations has been one of the major challenges in engineering, especially in areas where an excessive amount of heat is dissipated such as power plants and electronic systems [1]. Concerning latter devices, working speed, and technical functionality have increased remarkably over the last few decades, while the systems are further required to occupy small spaces. Simultaneously, material selection as well as overall configuration can lead locally to high temperatures when the cooling performance of thermal management is not sufficient. This phenomenon can either cause a malfunction or even damage system components. Therefore, having small chips generating high heat fluxes can affect the device's performance, reliability, and safety [2]. It is well-known that current thermal management systems using single-phase natural or forced convection have reached their heat removal limits. Thus, some technologies working with the principle of latent heat, such as phase-change materials, heat pipes, or miniature/mini chambers must replace single phase cooling mechanisms. Especially, regarding the latter cooling solution, a number of pool boiling experiments have been conducted in the past to understand the interdependence between material compatibility, operating parameters, and process dynamics [3,4]. Throughout the past six decades, many papers have been published proposing correlations to predict bubble frequency, bubble departure diameter, overall heat transfer coefficient, and critical heat flux (CHF) for various operating conditions. Particularly, exact forecasting methods of CHF has been one of the most popular objectives since it represents a junction at which an instant change in the state of boiling can occur. This metastable condition significantly limits the operation at large temperature differences obtained between the working liquid and the heated wall. The so-called wall superheat can rise two orders of magnitude and lead to a burn out of solid material.

From the thermohydrodynamic viewpoint, a rise in surface temperature accompanies a large number of active nucleation sites and increase in bubble frequency where stronger liability to bubble coalescence. In terms of intensified bubble merge effects, the wetted area fraction can decrease, resulting in a dry-out of the surface. Thus, CHF is also mostly correlated with wetted area fraction which in turn relies on the lifetime and scale of the dry patches, for instance, Eq. (1.13) in Table 1 [57].

Table 1

Critical heat flux correlations

Critical heat flux
Correlation numberReferenceTitleCorrelationYear
1.1[8]Rohsenow and Griffith$qCHF=143Ahlνρv(ρl−ρνρν)0.6$1956
1.2[9]Vishnev$qCHF=z(190−ϕ)0.5hlν[ηgσ(ρl−ρν)ρν2]1/4$1973
1.3[10]Zuber$qCHF=0.131[σg(ρl−ρv)ρν2]1/4+2kl(Tsat−Tl)(παlτ)$1993
1.4[11]Theofanous and Syri$qCHF=0.5+0.0133ϕ$ for $0 deg≤ϕ≤15 deg$1997
$qCHF=0.54+0.0107ϕ$ for $15 deg≤ϕ≤90 deg$
1.5[12]Haddad$qCHF=0.4+0.0084ϕ−(1.96×10−5)ϕ2$1997
1.6[13]Chang and You$qCHF=20.26+3.11ln(Dp)−0.25(ln(Dp))2−0.016(ln(Dp))3$1997
1.7[14]Chang et al.$qCHF=ρνhlν(sL)(gL sin ϕ(ρlρν−2)1+fsl2s)$2000
1.8[15]Dizon et al.$qCHF=0.4312+(6.807×10−3)ϕ$2003
1.9[16]Guan et al.$qCHF=0.2445ρνhlν[σg(ρl−ρv)ρν2]1/4(ρνρl)1/10$2011
1.10[17]Kaviany$qCHF=π8hlν(σρνλm)1/2$2012
$qCHF=Khlνρν1/2(σg(ρl−ρv))1/4$
1.11[18]Kutateladze$K=0.13−0.19$1951
1.12[19]ZuberK =0.1311959
1.13[7]Ivey$K=0.131[1+0.1(ρνρl)1/4[cplρl(Tsat−Tl)hlvρν]]$1973
1.14[20]Linehard and DhirK =0.1491973
1.15[21]Katto and Kosho$K=0.181+0.00918(ρl/ρν)0.14[g(ρl−ρν)Dsσ]1/2(Dss)$1979
1.16[22]Monde et al.$K=0.161+(6.7×10−4)(ρl/ρν)0.6(L/s)$1982
1.17[23]Guo and El-Genk$K=(0.034+0.0037(180−ϕ)0.656)$1993
1.18[24]Chang and You$K=0.131[1−0.0012ϕ tan(0.414ϕ)−0.122 sin(0.318−ϕ)]$1996
1.19[25]Brusstar and Merte$K=0.131(1+0.102ρvρl1/4Ja)$1997
1.20[26]Inoue et al.$K=1.03[1+0.70ρνρl1/4JaPe1/4]$ for plain1998
$K=1.78[1+1.20(ρνρl)1/4JaPe1/4]$ for microporous
1.21[27]Kandlikar$K=(1+cos θ16)[2π+π4(1+cos θ)cos ϕ]1/2$2001
1.22[28]Arik and Bar-Cohen$K=0.131[1−0.001117ϕ+(7.79401×10−6)ϕ2−(1.37678×10−7)ϕ3]$2001
1.23[29]Liter and Kaviany$K=0.131[3(σ(ρl−ρν)/g)1/4λm1/2]$2001
1.24[30]El-Genk and Bostanci$K=0.131[1(1−0.00127ϕ)4+1(3.03−0.016ϕ)4]−0.25$2003
1.25[31]Kim and Suh$K=0.171+6.8×10−4(ρl/ρν)0.62(Dh/s)$2003
1.26[32]Priarone$K=Cf,w,sat[1−0.0011(180−ϕ)+7.794×10−6(180−ϕ)2−1.377×10−7(180−ϕ)3]$2005
1.27[4]Theofanous et al.$K=(1− sin θ2−π/2−θ2 cos θ)−0.5$2006
1.28[33]Liao et al.$K=0.131[−0.73+1.731+10−0.021(185.4−ϕ)]×[1+55−θ100(0.56−0.0013ϕ)]$2008
1.29Liao et al.$K=0.131[1+0.56ϕbefore−ϕafter100]$
1.30[34]Chu et al.$K=(1+cos θ16)[2(1+r cos θrec)π(1+cos θ)+π4(1+cos θ)cos ϕ]1/2$2012
1.31[35]You et al.$K=SA(1+cos θ16)[2π+π4(1+cos θ)+4C cos θ1+cos θRaSm]1/2$2016
1.32[36]Zhao et al.$K=0.131~0.151[cos(ϕ−90deg)]1/4$2021
1.33[37]Kim et al.$qCHF=(1+cos θ16)[2π+π4(1+cos θ)cos ϕ]1/2hlνρν1/2(σg(ρl−ρv))1/4+CwhlνρνW2(1−fls)λd2$2014
Critical heat flux
Correlation numberReferenceTitleCorrelationYear
1.1[8]Rohsenow and Griffith$qCHF=143Ahlνρv(ρl−ρνρν)0.6$1956
1.2[9]Vishnev$qCHF=z(190−ϕ)0.5hlν[ηgσ(ρl−ρν)ρν2]1/4$1973
1.3[10]Zuber$qCHF=0.131[σg(ρl−ρv)ρν2]1/4+2kl(Tsat−Tl)(παlτ)$1993
1.4[11]Theofanous and Syri$qCHF=0.5+0.0133ϕ$ for $0 deg≤ϕ≤15 deg$1997
$qCHF=0.54+0.0107ϕ$ for $15 deg≤ϕ≤90 deg$
1.5[12]Haddad$qCHF=0.4+0.0084ϕ−(1.96×10−5)ϕ2$1997
1.6[13]Chang and You$qCHF=20.26+3.11ln(Dp)−0.25(ln(Dp))2−0.016(ln(Dp))3$1997
1.7[14]Chang et al.$qCHF=ρνhlν(sL)(gL sin ϕ(ρlρν−2)1+fsl2s)$2000
1.8[15]Dizon et al.$qCHF=0.4312+(6.807×10−3)ϕ$2003
1.9[16]Guan et al.$qCHF=0.2445ρνhlν[σg(ρl−ρv)ρν2]1/4(ρνρl)1/10$2011
1.10[17]Kaviany$qCHF=π8hlν(σρνλm)1/2$2012
$qCHF=Khlνρν1/2(σg(ρl−ρv))1/4$
1.11[18]Kutateladze$K=0.13−0.19$1951
1.12[19]ZuberK =0.1311959
1.13[7]Ivey$K=0.131[1+0.1(ρνρl)1/4[cplρl(Tsat−Tl)hlvρν]]$1973
1.14[20]Linehard and DhirK =0.1491973
1.15[21]Katto and Kosho$K=0.181+0.00918(ρl/ρν)0.14[g(ρl−ρν)Dsσ]1/2(Dss)$1979
1.16[22]Monde et al.$K=0.161+(6.7×10−4)(ρl/ρν)0.6(L/s)$1982
1.17[23]Guo and El-Genk$K=(0.034+0.0037(180−ϕ)0.656)$1993
1.18[24]Chang and You$K=0.131[1−0.0012ϕ tan(0.414ϕ)−0.122 sin(0.318−ϕ)]$1996
1.19[25]Brusstar and Merte$K=0.131(1+0.102ρvρl1/4Ja)$1997
1.20[26]Inoue et al.$K=1.03[1+0.70ρνρl1/4JaPe1/4]$ for plain1998
$K=1.78[1+1.20(ρνρl)1/4JaPe1/4]$ for microporous
1.21[27]Kandlikar$K=(1+cos θ16)[2π+π4(1+cos θ)cos ϕ]1/2$2001
1.22[28]Arik and Bar-Cohen$K=0.131[1−0.001117ϕ+(7.79401×10−6)ϕ2−(1.37678×10−7)ϕ3]$2001
1.23[29]Liter and Kaviany$K=0.131[3(σ(ρl−ρν)/g)1/4λm1/2]$2001
1.24[30]El-Genk and Bostanci$K=0.131[1(1−0.00127ϕ)4+1(3.03−0.016ϕ)4]−0.25$2003
1.25[31]Kim and Suh$K=0.171+6.8×10−4(ρl/ρν)0.62(Dh/s)$2003
1.26[32]Priarone$K=Cf,w,sat[1−0.0011(180−ϕ)+7.794×10−6(180−ϕ)2−1.377×10−7(180−ϕ)3]$2005
1.27[4]Theofanous et al.$K=(1− sin θ2−π/2−θ2 cos θ)−0.5$2006
1.28[33]Liao et al.$K=0.131[−0.73+1.731+10−0.021(185.4−ϕ)]×[1+55−θ100(0.56−0.0013ϕ)]$2008
1.29Liao et al.$K=0.131[1+0.56ϕbefore−ϕafter100]$
1.30[34]Chu et al.$K=(1+cos θ16)[2(1+r cos θrec)π(1+cos θ)+π4(1+cos θ)cos ϕ]1/2$2012
1.31[35]You et al.$K=SA(1+cos θ16)[2π+π4(1+cos θ)+4C cos θ1+cos θRaSm]1/2$2016
1.32[36]Zhao et al.$K=0.131~0.151[cos(ϕ−90deg)]1/4$2021
1.33[37]Kim et al.$qCHF=(1+cos θ16)[2π+π4(1+cos θ)cos ϕ]1/2hlνρν1/2(σg(ρl−ρv))1/4+CwhlνρνW2(1−fls)λd2$2014

Comprehensive discussions are presented regarding the optimization of the relationship between CHF and heat transfer coefficient by covering the parametric effects of pressure, wall superheat, subcooling, surface topography, and surface orientation. In addition to these parameters, the bubble geometry and bubble frequency have been defined as key parameters, which were referred to the working fluids' thermophysical properties owing to different chemical compositions. When going through the literature, one can recognize that there is no general technique for the optimal adjustment of previously mentioned governing parameters to achieve the best boiling performance, since the investigations on boiling are mainly based on certain working fluids used at a particular range of operating conditions. Consequently, this highly dynamic liquid-to-vapor phase-change process is still not fully understood in detail and the developed correlations contain several assumptions usually at a confined spectrum of validity.

The present work exhibits a summary of large number of investigations done on pool boiling and gives a broad discussion about the influences of each relevant parameter. Correlations to predict CHF were recapitulated in Table 1 while their range of validity and operating conditions are summarized in Table 2 available in the Appendix. Finally, some novel or overarching insights to up-to-date methods concerning pool boiling enhancement are introduced. These methods are explained for a wide range of parameters.

Table 2

Validation range table

Validation ranges
Correlation numberReferenced bySurface treatmentWorking fluidPressure rangeCHF $W/cm2$, HTC $W/cm2K$Subcooling temperatureExtra notesHeat flux range $W/cm2$
1.12[96]Plain copper Microporous copperFC-721 atm21.6, N/A0 KAlternative surface sizes 0–180 deg orientation0–21.7
1.20[64]Machine-roughened Copper surface Microporous enhanced surfaceFC-7230–150 kPaN/A0–50 KN/A0–30
1.11[143]Porous graphite Smooth copperHFE-710085 kPa66.4, N/A0–30 KNo temperature excursion0–70
1.1[122]Copper chipsWater1 atm244, 26.90 KMicrochanneled surfaces0–250
1.2–1.22 1.28–1.29[33]Copper surfaceDe-ionized (DI) water1 atm$∼145$, N/A0 K0–180 deg orientation Superydrophilic surfaces30–150
1.2–1.3–1.6 1.17–1.18 1.19–1.20[189]Printed circuit boardWater1 atm161, N/A0 K0–180 deg orientation0–165
1.2–1.17 1.25–1.26[132]Copper surfaceDI water1 atm126, 350 K0–90 deg orientation Alternative cavities50–350
1.4[11]Copper surfaceWater1 atm161.7, N/A0 K0–180 deg orientation Reactor pressure vessel46.1–157.9
1.6[13]Microporous copper surface Porous copper surfaceWater1 atm$∼28, ∼2.05$0 KFive different sizes of diamond particles0–28
1.7[14]Stainless steel tube Copper tubeWater1 atm$∼100$, N/A0 K0–90 deg orientation Alternative tube sizes0–100
1.8[15]Stainless steel tube Copper tubeWater2.5 bar188, N/A0 KDownward-facing boiling Durability and adhesion tests0–190
1.9[16]Stainless steel tube Copper tubePentane Hexane FC-72150–450 kPa47.5, N/A0 KReduced pressure range of $2×10−5−2×10−1$0–157.8
1.11[200]AluminumWater FC-720.176 bar 1 bar71, $∼2.7$0 KJet impingement1–190
1.12 1.9[55]NichromeWater0.1–7 MPaN/A, N/A0 KMassive pressure High heat flux rates2.5–721
1.12[85]Plain Sanded Microfinned Microporous copper surfacePF50601 atm$∼28$, N/A0–10 K0–90 deg orientation diamond/omegabond/methyl–ethyl–ketone coating0–300
1.12[88]Chrome–aluminum –iron alloy wireDI water1 atm$∼350, ∼65$0–20 KVoltage apply 1 s–1000 s0–450
1.12[136]Untreated Hydrophobized Laser pretreated and hydrophobized Stainless steel surfaceFC-721 atm$∼34.5$, N/A0–20 KX type texturing Parallel texturing Circular texturing0–35
1.12[159]Bare zircaloy-4 Anodized zircaloy-4DI water1 atm192.4, N/A0 K0.15–0.32 μm surface roughness respect to 0–600 s anodization0–200
1.12[139]Plain Microporous Microporous-vapor channeled copper surfaceDI water1 atm354.75, $∼5.5$0 KSintered copper powder Vapor jet creation0–355
1.12[123]Plain Microporous Microporous-vapor channeled copper surfaceDI water1 atm398.93, $∼16$0 KHole type channel coating 0.3–1.2 mm channel depth 1.5–4.0 mm channel pitch 0.35–1.0 mm channel width0–400
1.12[212]Polished copper surface$Al2O3$-distilled DI water0.2 bar168, N/A0 KNanoparticle ranges of 0 g/l–0.05 g/l0–170
1.12–1.3 1.15–1.31[56]Flat copper surface Roughed copper surfacesWater1–10 bar$∼300, ∼23$0 K0.106–4.03 μm surface roughness0–300
1.13[7]18/8 steel tubeWater1 atm$∼85$, N/A0 KDimensionless acceleration of $1−160 ft/ sec 2$N/A
1.15[21]Platinum wireWater Methanol1 atmN/A, N/A0 KLow gravityN/A
1.16[22]Copper surfaceWater Ethanol Freon 113 Benzene1 atm$∼127.5$, N/A0 KVarious surface sizes0–130
1.17[23]Copper surfaceWater1 atm$∼80$, N/A0 K90–180 deg orientation0–85
1.18[24]Plain copper Microporous copperFC-721 atm26.8, N/A0 K0–180 deg orientation Cu and Al coating particles0–26.8
1.19[25]Copper surface Quartz surfaceN/A1 atmN/A, N/A2.8–22.2 K0–360 deg orientation Low velocity fluidsN/A
1.20[26]Stainless steel wire Platinum wireWater R-1130.1–3 MPa128.5, N/A0–220 K0–360 deg orientation0–130
1.21[49]Smoothed copper surfaceWater0–413.7 kPa142, $∼12$0–40 K0–90 deg orientation0–145
1.22[28]ATC2.6 chip packagesHFE-7100 HFE-7200101.3–303.9 kPa60, N/A2–80 KReal electornic chips figure of merit comparison of liquids0–60
1.23[29]Plain copper surface Porous copper surfacePentane1 atm76.2, N/A0 KConical macrostructures1–80
1.23 1.29[153]Polished-plain copper Flat-nanostructured copper Flat-porous copper Modulated-porous copper Nanostructured-flat-porous copper Nanostructured-modulated-porous copperWater1 atm384.12, 1.870 KMacroscale, microscale and nanoscale coating combination0–385
1.24[30]Smooth copper surfaceHFE-71000.085 MPa24.45, N/A0 K0–180 deg orientation0–250
1.25[31]Copper surfaceWater1 atm$∼120$, N/A0 K0–180 deg orientation0–120
1.27[4]Fresh copper Aged copper Heavily aged copperHigh-purity water DI water1 atm171, N/A0 KX-ray radiographic imaging0–175
1.30[116]Bare silicon Microstructured siliconDI water1 atm216.5, 5.030 K12 different microstructured surfacesN/A
1.31[35]Flat copper Scratched copperWater1 atm162.5, N/A0 KSandpapers for starching0–165
1.32[36]Plain copper Nanograss (NG) copper NG-sparse microflower copper NG-middle microflower copperDI water1 atm210, 12.60 K0–180 deg orientation nano/micrograss/flowers0–210
Validation ranges
Correlation numberReferenced bySurface treatmentWorking fluidPressure rangeCHF $W/cm2$, HTC $W/cm2K$Subcooling temperatureExtra notesHeat flux range $W/cm2$
1.12[96]Plain copper Microporous copperFC-721 atm21.6, N/A0 KAlternative surface sizes 0–180 deg orientation0–21.7
1.20[64]Machine-roughened Copper surface Microporous enhanced surfaceFC-7230–150 kPaN/A0–50 KN/A0–30
1.11[143]Porous graphite Smooth copperHFE-710085 kPa66.4, N/A0–30 KNo temperature excursion0–70
1.1[122]Copper chipsWater1 atm244, 26.90 KMicrochanneled surfaces0–250
1.2–1.22 1.28–1.29[33]Copper surfaceDe-ionized (DI) water1 atm$∼145$, N/A0 K0–180 deg orientation Superydrophilic surfaces30–150
1.2–1.3–1.6 1.17–1.18 1.19–1.20[189]Printed circuit boardWater1 atm161, N/A0 K0–180 deg orientation0–165
1.2–1.17 1.25–1.26[132]Copper surfaceDI water1 atm126, 350 K0–90 deg orientation Alternative cavities50–350
1.4[11]Copper surfaceWater1 atm161.7, N/A0 K0–180 deg orientation Reactor pressure vessel46.1–157.9
1.6[13]Microporous copper surface Porous copper surfaceWater1 atm$∼28, ∼2.05$0 KFive different sizes of diamond particles0–28
1.7[14]Stainless steel tube Copper tubeWater1 atm$∼100$, N/A0 K0–90 deg orientation Alternative tube sizes0–100
1.8[15]Stainless steel tube Copper tubeWater2.5 bar188, N/A0 KDownward-facing boiling Durability and adhesion tests0–190
1.9[16]Stainless steel tube Copper tubePentane Hexane FC-72150–450 kPa47.5, N/A0 KReduced pressure range of $2×10−5−2×10−1$0–157.8
1.11[200]AluminumWater FC-720.176 bar 1 bar71, $∼2.7$0 KJet impingement1–190
1.12 1.9[55]NichromeWater0.1–7 MPaN/A, N/A0 KMassive pressure High heat flux rates2.5–721
1.12[85]Plain Sanded Microfinned Microporous copper surfacePF50601 atm$∼28$, N/A0–10 K0–90 deg orientation diamond/omegabond/methyl–ethyl–ketone coating0–300
1.12[88]Chrome–aluminum –iron alloy wireDI water1 atm$∼350, ∼65$0–20 KVoltage apply 1 s–1000 s0–450
1.12[136]Untreated Hydrophobized Laser pretreated and hydrophobized Stainless steel surfaceFC-721 atm$∼34.5$, N/A0–20 KX type texturing Parallel texturing Circular texturing0–35
1.12[159]Bare zircaloy-4 Anodized zircaloy-4DI water1 atm192.4, N/A0 K0.15–0.32 μm surface roughness respect to 0–600 s anodization0–200
1.12[139]Plain Microporous Microporous-vapor channeled copper surfaceDI water1 atm354.75, $∼5.5$0 KSintered copper powder Vapor jet creation0–355
1.12[123]Plain Microporous Microporous-vapor channeled copper surfaceDI water1 atm398.93, $∼16$0 KHole type channel coating 0.3–1.2 mm channel depth 1.5–4.0 mm channel pitch 0.35–1.0 mm channel width0–400
1.12[212]Polished copper surface$Al2O3$-distilled DI water0.2 bar168, N/A0 KNanoparticle ranges of 0 g/l–0.05 g/l0–170
1.12–1.3 1.15–1.31[56]Flat copper surface Roughed copper surfacesWater1–10 bar$∼300, ∼23$0 K0.106–4.03 μm surface roughness0–300
1.13[7]18/8 steel tubeWater1 atm$∼85$, N/A0 KDimensionless acceleration of $1−160 ft/ sec 2$N/A
1.15[21]Platinum wireWater Methanol1 atmN/A, N/A0 KLow gravityN/A
1.16[22]Copper surfaceWater Ethanol Freon 113 Benzene1 atm$∼127.5$, N/A0 KVarious surface sizes0–130
1.17[23]Copper surfaceWater1 atm$∼80$, N/A0 K90–180 deg orientation0–85
1.18[24]Plain copper Microporous copperFC-721 atm26.8, N/A0 K0–180 deg orientation Cu and Al coating particles0–26.8
1.19[25]Copper surface Quartz surfaceN/A1 atmN/A, N/A2.8–22.2 K0–360 deg orientation Low velocity fluidsN/A
1.20[26]Stainless steel wire Platinum wireWater R-1130.1–3 MPa128.5, N/A0–220 K0–360 deg orientation0–130
1.21[49]Smoothed copper surfaceWater0–413.7 kPa142, $∼12$0–40 K0–90 deg orientation0–145
1.22[28]ATC2.6 chip packagesHFE-7100 HFE-7200101.3–303.9 kPa60, N/A2–80 KReal electornic chips figure of merit comparison of liquids0–60
1.23[29]Plain copper surface Porous copper surfacePentane1 atm76.2, N/A0 KConical macrostructures1–80
1.23 1.29[153]Polished-plain copper Flat-nanostructured copper Flat-porous copper Modulated-porous copper Nanostructured-flat-porous copper Nanostructured-modulated-porous copperWater1 atm384.12, 1.870 KMacroscale, microscale and nanoscale coating combination0–385
1.24[30]Smooth copper surfaceHFE-71000.085 MPa24.45, N/A0 K0–180 deg orientation0–250
1.25[31]Copper surfaceWater1 atm$∼120$, N/A0 K0–180 deg orientation0–120
1.27[4]Fresh copper Aged copper Heavily aged copperHigh-purity water DI water1 atm171, N/A0 KX-ray radiographic imaging0–175
1.30[116]Bare silicon Microstructured siliconDI water1 atm216.5, 5.030 K12 different microstructured surfacesN/A
1.31[35]Flat copper Scratched copperWater1 atm162.5, N/A0 KSandpapers for starching0–165
1.32[36]Plain copper Nanograss (NG) copper NG-sparse microflower copper NG-middle microflower copperDI water1 atm210, 12.60 K0–180 deg orientation nano/micrograss/flowers0–210

### 1.1 A Brief Overview of Professor Avram Bar-Cohen's Critical Heat Flux Research.

This section is dedicated to a brief glimpse of Prof. Bar Cohen's remarkable work in the field of pool boiling heat transfer and CHF. He has authored more than 60 academic papers, many refereed proceedings papers, and chapters in books with more than 10 graduate and undergraduate students regarding pool boiling heat transfer enhancement methods. These enhancement methods cover different areas including various working liquids, a large pressure spectrum, subcooling effects over a wide range of chips, and surface treatments. His first-ever work on pool boiling was back in 1987, involving saturated pool boiling characteristics of commercially available perfluorinated liquids [38]. At that time, pool boiling was not extensively studied, and a number of fundamental questions were present; thus, he started with publishing a journal paper regarding the thermal design of immersion cooling modules for electronic components and theoretical aspects of nucleate pool boiling with dielectric liquids. Cooling of electronic systems using dielectric liquid was still a potential to be used due to the high-efficiency rate and simplicity as well. His motivation was to clearly indicate the characteristics of vapor bubbles and nucleate pool boiling of these liquids and their ability to be utilized in extending limits on electronics cooling [39]. His first experimental results were published in 1995 comprising the investigation on the effects of dissolved gas content on pool boiling of FC-72, which is a high-wetting liquid. It was found that having gas dissolved in FC-72 influences positively by shifting the boiling curve to the left and increasing CHF when the gas concentration is high (>0.005 moles/mole). It was also observed that a large superheat is required to start boiling when the gas concentrations are low-to-moderate [40]. His group then tested the effects of both pressures ranging from 1 to 3 bar and subcooling levels ranging from 0 to 67.5 K on a plastic pin grid array.

A correlation was proposed that predicts CHF under combined effects of pressure and subcooling [41]. Later, on the same experimental setup, pool boiling heat transfer was performed using a multi-element array of thin-film flush-mounted square heaters immersed in an FC-72 bath [42]. Thermal management of electronics (TME) correlation was first proposed in 2001 [43]. The results have shown that the correlation is applicable for dielectric liquids with a thermal effusivity range of between 0.2 and 120 J/m2$Ks1/2$ under pressures ranging from 1 to 4.5 bar, and subcooling levels from 0 to 75 K, with a standard deviation of 12.5%. At that time, there were limited experimental results and correlations for predicting confinement-driven boiling heat transfer enhancement; thus, an experimental study has been performed on vertical, rectangular parallel-plate channels immersed in FC-72. A modified correlation to predict CHF under these conditions was presented and demonstrated a good agreement with the experimental results [44]. The TME correlation, which is explained in Sec. 4 was compared with the CHF values obtained from microporous coated surfaces in a dielectric fluid. High CHF values in excess of 47 W/cm2 were obtained. The research was mainly focused on testing the effects of both pressure and subcooling. It was aimed to determine how accurate the TME correlation can predict CHF over a range of 1 to 3 bar and subcooling levels from 0 to 75 K [45]. Then, another paper was published regarding pool and flow boiling in narrow gaps, as it was crucial to study these applications in three-dimensional chip stacks [46]. Later, a theoretical study on the optimization of pool boiling heat sinks was conducted. The study includes the effect of confinement at the inner fin spaces [47]. The setup was operating under a pressure range from 1 to 3 bar at high subcooling conditions in a FC-72/FC-40 mixture. The binary mixture showed no enhancement in CHF beyond mixing more than 10% of the secondary liquid. The chips were ATC2.6 packages and what was believed that there was a great contribution of increasing the latent heat of evaporation and surface tension of the mixture to enhance the CHF performance of binary mixtures [48]. As a conclusion to be drawn from all these studies, Prof. Bar-Cohen and his team have presented inspiring and groundbreaking results on CHF. Moreover, one of the most dedicated scientific contributions of Bar-Cohen was to establish a TME correlation with a highly accurate prediction capability.

## 2 Parametric Effects on Pool Boiling

### 2.1 Pressure Effect.

In the nucleate pool boiling process, pressure has a significant impact on heat transfer performance. It directly determines the inception of CHF, the trend of heat transfer coefficient, the departure diameter of bubbles and their frequency, as well as surface activation [49]. Three different pressure regimes, which are high-pressure, atmospheric pressure, and subatmospheric pressure, have been applied in more than 79 experimental studies as shown in Fig. 1. More than half of the experiments are done under atmospheric pressure, while about 20% of the papers focused on subatmospheric conditions.

Fig. 1
Fig. 1
Close modal

#### 2.1.1 High Pressure.

During high pressure, above atmospheric pressure, there are two main parameters for bubble formation, bubble size, and bubble growth rate. At these levels, volumetric ratios for both liquid and vapor can be lower by two orders of magnitude, whereas the surface tension is also lower. In that condition, the status of the interface between the heated surface and the liquid–vapor phase can show a variety of heat capacities on the heated material and power increase rates in this transient mechanism. However, the thermophysical conditions under high pressure reveal a decrease in bubble growth rate and result in small radii for bubble detachment [50,51]. Labunstov [52] has developed a correlation for predicting bubble growth rate at high pressure levels up to 100 bar in 1964 [11]
$R=f(Ja)×αl1/2×tnf(Ja)=2.1077Ja0.7902n=1.0012×e(−P/0.3257)−0.9624×e(−P/0.6161)+0.5$
(1)
In 2016, Du et al. [53] proposed an improved correlation (see Eq. (1)) for the bubble growth rate at a similar pressure range of 0–95.7 bar, where f(Ja) is bubble growth coefficient, α is the contact angle, n is the bubble growth exponent, P is the pressure, and t is the time needed. Concerning bubble dynamics, a higher pressure level leads to a lower bubble growth rate, which is strongly supported by the experimental data collected by Duta et al. [53]. The authors further noticed that an increase in pressure led to a remarkably larger number of active nucleation sites. Sakashita [54] has reported that the nucleation site density increases by a factor of 1.5 of the pressure at constant heat flux. However, neither the heat flux nor the pressure has shown a considerable effect on the rate of bubble detachment on the surface. In another study, a reliable correlation has been developed to accurately predict CHF for different pressure ranges [55]. The study revealed the bubble departure frequency increased when the pressure rose (see Fig. 2), in contrast to the correlation for bubble frequency recommended by Zuber [49] with Eq. (2). The authors attributed this finding to the lower surface tension of the liquid
$fDd=0.59(σg(ρl−ρv)ρl2)1/4$
(2)
Fig. 2
Fig. 2
Close modal

In addition to the trend of boiling curves having large CHF values at high-pressure levels and high heat flux levels, there is no difference observed on the curves at lower heat fluxes as illustrated in Fig. 3. This enhancement is also proven for different liquids such as pentane, hexane, and FC-72. Additionally, at the end of this study, Guan [16] developed a correlation (see Eq. (1.9) in Table 1) by utilizing these fluids. In pool boiling, the lower surface tension on the heater surface causes tiny bubbles departing from the surface and concluding that the bubble departure diameter decreases as the pressure increases [56]. Moreover, both bubble departure diameter and dimensionless bubble Re number illustrate that Nu number and ebullition frequency are pressure dependent. At higher pressures, the bubble generation frequency on the surface doubles, whereas the bubble departure diameter diminishes approximately 1.7 times along the process [57]. Mass velocity and stream quality of the departure bubbles show effective variances. In conclusion, having high pressure affects both bubble and surface properties by improving heat transfer. In addition, pressure has an almost similar behavior for all plain surfaces, chemically treated, and mechanically treated surfaces since it mainly affects the nucleation density [58].

Fig. 3
Fig. 3
Close modal

#### 2.1.2 Subatmospheric Pressure.

A group of researchers have focused their work on bubble nucleation under subatmospheric pressure conditions. In one of these studies, an increase in the vapor bubble growth rate and the departure diameter of the bubbles were demonstrated when the boiling pressure was lowered below atmospheric conditions. The bubbles had an axisymmetric mushroom-like geometry while the bubble growth process was relatively slow in a time scale of seconds [59]. Furthermore, the researchers have observed three main stages of the bubble growth process based on the equivalent bubble radius $(Req)$ and time (t). These stages were declared as the inertia-controlled stage $(Req(t)∼t)$, the heat diffused inertial stage $(Req(t)∼t0.75)$, and heat diffusion-controlled stage $(Req(t)∼t0.75)$, respectively [60,61]. The overall mechanism can be further intensified at subatmospheric pressures along surface modifications, and it is suggested as an appropriate solution for electronics cooling with the goal of very high heat fluxes of more than 100 W/cm2 [62]. Pressure reduction at a given heat flux density also leads to a considerable enhancement in the nucleation site activation and the growth rate of vapor bubbles [6365]; hence, an increase in the Jakob number, $Ja=cpl(Tw−Tsat)hfg$, where Tw is the surface temperature. Thus, at low-pressure levels, the heat transfer coefficient is mainly governed by the nucleation site density, while at the same time, the bubble generation frequency decreases. In that case, the pressure at values below 1 bar shifts the boiling curve to the right, leading to a higher superheat with consequently lower heat transfer as shown in Fig. 3 [49,60,66,67]
$HTC/HTC0=f(Fq,Fp,Fw)$
(3)
$A=A0(0.88+0.12P)h/hid=(11+A(y−x))$
(4)
The relationship between the pressure and heat transfer coefficient (HTC) at a given heat flux can be, for instance, approximated by Gorenflo correlation (see Eq. (3)). However, this prediction is valid for smooth surfaces solely and could be inappropriate for microstructured surfaces [68]. Nonetheless, the overall boiling mechanism can also be intensified at subatmospheric pressures, which are suggested as an appropriate solution for electronics cooling with the goal of very high heat fluxes of over 100 W/cm2 with the advantage of low surface temperatures under lower saturation temperate of any liquid [62]. Peyghambarzadeh et al. [69] have developed a new correlation in 2009 on the basis of Stephan and Körner [70] findings in 1964 to predict nucleate boiling HTC in binary mixtures (see Eq. (4)). The parameter A named as pressure-dependent term in the Stephan and Körner correlation is highly dependent on not only the composition and thermophysical properties of the binary mixture, but also on the pressure. The parameter can be improved as a function of heat flux for better predictions as well. This modification can improve the performance of the Stephan and Körner correlation [69]. Besides, the experimental results have shown a good agreement with correlations predicted by Kutateladze–Zuber and Rohsenow correlations at intermediate pressures [71]. However, for low pressures, there is a great deviation from the experimental results that can be inherited from unreliability in data; therefore, it can be the reason of prediction incompatibility [72]. In addition to the deviation in results, the steady-state CHF data for subatmospheric pressures are also not in good agreement with conventional correlations whereas illustrating higher CHF values with a decrease in pressure. Therefore, transient CHF values under subatmospheric pressures could be divided into two major exponential groups in regions of short period and long period [73]. It can be concluded that many correlations are accounting for pressure effects. Gupta et al. [74] have developed a correlation (see Eq. (5)) using least squares method for both, atmospheric and subatmospheric pressures as
$h=C1q0.7p0.32$
(5)

In this equation, C1 is a constant and depends on the circumferential surface position on a tube, while it yields a maximum error of 10%. Another factor of reduced pressure ($p*$), the ratio of the actual pressure to the critical pressure, is important for the physical performance of pool boiling especially during multiphase change. The reduced pressures $p*≤$ 0.35 at all heat fluxes and at low values of q for higher $p*$ where the upper limit is $p*$ = 0.9 can reflect very well for the VDI-Heat Atlas [75] calculation method based on the principle of the corresponding states found by Gorenflo and Kenning [76]. Experimental deviations may happen athigh levels of HTC above a threshold value of heat flux at $p*>$ 0.65. This can be attributed to increasing surface roughness.

### 2.2 Subcooling Effect.

Out of various effects that can alter the thermal performance of pool boiling, subcooling is another factor influencing the phase-change process. The bulk liquid temperature lower than the saturation temperature has been shown different behaviors for the bubble growths and boiling curves. In Fig. 4, more than 79 experimental studies which investigated different ranges of subcooling are summarized.

Fig. 4
Fig. 4
Close modal

Liquid subcooling rate increases at a constant heat flux by increasing the temperature difference between the surface and coolant. Those results are obtained naturally from a temperature difference between the liquid near the wall and the boiling surface. The sensitivity of HTC to subcooling decreases at low heat flux, whereas average surface temperature decreases with the increase of subcooling [26,77]. Performing pool boiling heat transfer under different subcooling levels has been studied by researchers to increase the CHF [26,64,73,7884]. This enhancement on CHF has been performed at several pressure levels, liquids, and surface topographies. Different surface treatments were performed to create a microporous layer. When the subcooled pool increases by 10 K, the boiling curve shifts to a higher wall superheat region for this specific surface type. As discussed in Refs. [80] and [85], the trend of CHF followed the increase in subcooling effect (see Fig. 5). One can conclude that boiling takes longer time to occur, while bubbles are growing on the surface more slowly and are smaller as liquid subcooling was increasing [86]. Increased subcooling can be beneficial in terms of heat transfer, but when it comes to bubble visualization, it has a clear disadvantage, since subcooling is a factor that inhibit bubble growth by condensing bubbles [85]. On a heated surface, the superheated layer occurring during subcooled boiling is remarkably thinner than the layer present at saturation condition. The nucleate boiling process is significantly facilitated by the rapid activation of nucleation sites. The inability of a bubble to exceed the thin superheated layer results due to local cooling, which can be seen up to heat fluxes of 1000 W/cm2 at 75 K subcooling level. This phenomenon would also happen without undergoing the boiling crisis [87]. The superheat temperature of the surface is highly dependent on the characteristics of the material. In the period of 1 to 1000 s and under subcooled temperatures of 10–20 K, the nucleate boiling mechanism may have a transient boiling heat transfer at a rate of 28% and 53%, whereas CHF increases 68% and 86% in the period of 1 s, respectively. This CHF increase was also observed at 257% and 436% for saturation temperatures of 283 K and 293 K, respectively. The temperature of the surface at CHF for subcooled temperatures decreases corresponding to this improvement [28,88]. Sathyamurthi et al. [89] had a similar conclusion when the experiment was done on multiwalled carbon nanotubes (MWCNT)-coated silicon surfaces with different thicknesses and liquid subcooling ranged from 273 to 303 K. As the subcooling rate is increased, CHF decreases dramatically. This event perhaps happens due to a change in the bubble departure frequency. Under a 10 K subcooling, no bubble columns were observed, unlikely, the bubble columns were noticeable for higher subcooling. In conclusion, the nanotube-coated substrate shows a reduction in heat flux enhancement as the subcooling increases. Therefore, the experiments strongly demonstrated that CHF is dependent on the subcooling level [90]. Nucleate boiling heat transfer may not be strongly affected by subcooling; however, CHF linearly increased with increasing subcooling at a fixed surface orientation. One reason for this effect may be that the surrounding subcooled liquid in the pool flows to the heated surface to cool down the vapor on the heated wall. Therefore, this generation may have caused a delay in the formation of vapor film and CHF due to temporal dry out [64,79,80]. However, the vapor film prevention and CHF increase could be enhanced with high heat fluxes leading to an increment in both, departure frequency and bubble departure diameter as well [91]. In another study, large vapor structures were formed on the heating surfaces at subcooling greater than 20 K [92]. At those conditions, a liquid layer was formed on the heating surface that was not able to dry out even if the heat flux range was much higher than CHF for saturated boiling. In subcooling conditions, vapor masses become discontinuous, and their forms changed to an aggregation of narrow pulses by intensive vapor mass oscillation. The thickness of the macrolayer formed at low heat flux in the vapor region in subcooling condition is comparable to those formed at high heat fluxes in saturated boiling [92]. Moreover, high CHF values up to 47 W/cm2 are obtained by Arik [45] over on a microporous coated silicon chip in FC-72. The research was mainly focused on testing the effects of both pressure and subcooling. It was aimed to see how accurate the TME correlation is for a pressure range of up to 3 bar and subcooling rate of up to 75 K. Zhou [93] illustrated CHF on micropin fins over a surface under subcooling. The effect of subcooling on bubble behavior is discussed under subcooling of 15 K and 25 K in FC-72. As the subcooling increases, the bubble diameter decreases; thus, the liquid can supply more pathways to elevate the CHF.

Fig. 5
Fig. 5
Close modal

### 2.3 Heater Surface Effect.

Heater size and surface characteristics affect CHF, HTC, and bubble dynamics. Therefore, m any experimental studies regarding pool boiling heat transfer were conducted to investigate different geometries and properties of the heater surface. The thermophysical properties, as well as the size of the heat transfer surface, have remarkable influence on CHF.

#### 2.3.1 Surface Size.

The heater dimensions and boundary conditions have a considerable impact on the pool boiling CHF. Usually, in small surfaces, the homogeneity of the test conditions is easier to preserve, and the measurement results may be more accurate if axial heat transfer is prevented [94]. In pool boiling, the boiling curve is heater size-independent where heater size is considerably larger than the capillary length to be buoyancy dominated ($Lh/Lc>2.8$), where Lh is heater size and Lc is capillary length. The research by Raj and Kim has demonstrated this phenomenon on square platinum microheaters whose sizes range from 0.7 × 0.7 to 7 × 7 mm2 in an array format [95]. The CHF data from several experiments with the same heater size agree very well, and this stability can be confirmed with empirical correlations for different heater sizes [96]. Moreover, this study illustrates that surface size has a serious impact (see Fig. 6) on CHF, especially at different surface inclinations [96]. For upward-facing heater plates, the heater size effect might be small or negligible based on operating conditions. However, some experimental investigations demonstrate that the size effect has a more considerable influence on boiling heat transfer for the inclined surfaces, especially for downward plates [97]. The heater size combined with the magnitude of gravity also created a great impact on boiling phenomena. The experiments performed under microgravity illustrated that reduction of heater size from 7 × 7 to 2.7 × 2.7 mm2 decreases satellite bubble formation and has a strong effect on thermocapillarity and hence on the heat transfer before CHF. At high gravity, on the other hand, heater size can positively influence bubble departure and boiling heat transfer [98,99]. CHF demonstrates a gradual reduction for both coated and uncoated surfaces with heater size increase from 7.5 × 7.5 to 20 × 20 mm2. You et al. [100] explained this phenomenon by longer resistive path to the cooler bulk on large surface sizes. Indeed, this method is effective on boiling performance by extending effective surface area, regulating wettability and instability, increasing nucleation site density and capillary suction [61,101]. The modified surface enhancements regarding size and geometry influence bubble formation, release mechanisms, and convective heat transport by decreasing the wall superheat significantly [102]. In addition to heater's size that can show an effective impact on CHF as shown in Fig. 6, a study based on a general regression neural network was done to investigate the sensitivity of boiling based on heater size and material property on a square heat transfer surface. It is concluded out that CHF becomes independent of the surface area when the side length is sufficiently large. Apart from previous statements, heater side length has been explained by Rayleigh–Taylor Instability Wavelength. In that case, the stability at the liquid interface is reached at high wave numbers and low wavelength; thus, the heater side length of 8 mm resulted as half of the Rayleigh–Taylor Instability Wavelength, and it produced maximum CHF values for all materials. Thus, optimizing CHF depends on far-field fluid properties rather than near field surface properties [103].

Fig. 6
Fig. 6
Close modal

#### 2.3.2 Surface Treatment.

The boiling mechanism also depends on the interaction between liquid and heated walls' surface condition; hence, the surface topography is another strong parameter affecting the overall heat transfer performance.

The surface textures vary between macro- and microstructures. Microscale structures are constituted by microscale or macroscale channels, grooves, fins, or pillar arrays that are able to increase surface roughness, effective area, nucleation site density, and influence bubbles growth and departure. In nanoscale enhancement techniques, nanoparticles provide a surface coating with nanotubes, nanowires, nanofibers, nanoporous, and nanofilm layers by creating a simple and cost-efficient process [22,101,104]. Surface roughness increases nucleation sites and the size of cavities resulting in an enhancement of boiling heat transfer. Roughness is defined as average roughness $(Ra)$ in common owing to the presence of surface roughness irregularity on the overall surface [35,105]. Kim et al. [35] developed a model to predict CHF on rough surfaces (see Eq. (1.31) in Table 1), which performs with a standard deviation of 10% for a range of $(Ra)$ between 0.041 and 2.359. Generally, researchers believe that at a given superheat, a rough surface has a better boiling performance than a smooth surface because of a large number of active nucleation sites. However, studies are supporting the hypothesis stating that by using a smooth surface, better wettability is achieved, and hence the boiling curve shifts to a larger wall superheat.

The effect of surface roughness is still not clear for scientists and engineers. Moreover, when changing the substrate material such as switching from aluminum to copper, for instance, CHF on the latter material is much lower than the prior one, even though they are both experiencing the same roughness [106108]. This means that the thermal properties of the base material are also an influencing aspect, which should be considered.

Heating surfaces can be classified into two main categories in terms of wettability: hydrophilic and hydrophobic. As it can be seen in Fig. 7, several surfaces are present with different wettabilities and clearly illustrate how bubbles can attach to surfaces in different ways by modifying the surface topography and chemistry.

Fig. 7
Fig. 7
Close modal

Hydrophilic surfaces are known to have a strong affinity for water, while hydrophobic ones are nonpolar which makes them water-repelling [109]. While a uniform super hydrophilic surface can increase wettability by reducing the contact angles of the bubbles departing from the surface, the hydrophobic areas lead to a higher density of active nucleation sites and delay the dry-out. For horizontal surfaces, the structured surfaces, especially hydrophilic surfaces show better performance in boiling heat transfer rather than superhydrophobic surfaces. Because, in high heat fluxes, dry-outs, and heat transfer reduction appear with the vapor film initiation [36,110]. Besides, capillary action supplying the liquid has a dominant effect on pool boiling heat transfer. This enhancement is demonstrated by a CHF increase in the high heat flux region. In recent studies, the capillary wicking models illustrated better agreement than roughness-based models on CHF. This phenomenon can also be explained with capillary wicking-based models leading to capillary-induced momentum [111,112]. As an example of this phenomenon, horizontal rectangular fin arrays over a copper block provide different fin-to-fin spacing. As a result of this variation, it is concluded that closer and taller fins provide more heat transfer. As the heat flux increases, the center of the fin array is dried out. The maximum CHF value, which is five times greater than that of a plain surface was observed on the specimen having a fin spacing of 0.5 mm and a length of 4.0 mm, in the variation of fin spacing from 0.5 mm to 2.0 mm and fin lengths from 0.5 mm to 4.0 mm. On the other hand, as the fin spacing decreases, or the fin length increases, the HTC decay rapidly [113115].

This phenomenon could be explained by the improved capillary wicking rate that is responsible for the improvement of bubble departure frequency as shown in Fig. 8 [113,116]. Capillary wicking is the liquid inflow rate, and the reduced permeable liquid inflow becomes more observable in rewetting situations while the gap size is decreasing. To provide better boiling heat transfer and delay in CHF, the experimental results show that the critical gap size, which provides a good capillary induced moment, can be obtained between 10 and 20 μm [116]. Another study also illustrated that as the distance between cavities decreases from 800 μm down to 300 μm on a heating surface, the maximum heat transfer was found with the cavity distance of 300 μm [117].

Fig. 8
Fig. 8
Close modal
##### 2.3.2.1 Microscale surface treatment.

The theory of the microstructure influence on the heterogeneous onset of nucleation boiling is based on Gibbs free energy and availability in a uniform temperature. Microstructures influence boiling heat transfer where the curvature radius of these structures is in the range of 5100 times less than the bubble radius. Unless this effect is negligible, the wettability effect dominates the heat transfer system [118]. As an example, the selective laser melting technique was used on AlSi10Mg based powder using a Gaussian distribution to obtain a defined surface texture [119]. The surfaces had improvements up to 70% and 76% in terms of average HTC and CHF, respectively. These enhancements are due to the presence of inherent surface grooves and cavities resulting from the selective laser melting process. One of the experiments applied on microgrooved brass and copper surfaces as shown in Fig. 9 demonstrated that microgrooved surfaces have higher HTC, more nucleation sites, lower bubble departure frequency, and larger bubble diameter for boiling with the same external conditions [120]. Therefore, microchannels have been widely used in pool boiling enhancements where higher heat dissipation for confined spaces could be achieved [81]. Vapor bubbles enable the three-phase contact line to oscillate periodically. This period reduces the equivalent diameter of each bubble by the heat flux increment. The smaller microgroove sizes may cause a reduction in the equivalent diameter of bubble-burst at the same microgroove depth and width. The bubble equivalent diameter of the micronano hybrid surface is significantly smaller compared to the microgroove surface; therefore, the modification of microconfiguration dimensions has more impact on the equivalent diameter of bubble burst for micronano hybrid surface [121]. Moreover, optimizing the fin spacing/geometry leads to a significant enhancement in heat transfer performance.

Fig. 9
Fig. 9
Close modal

The CHF is delayed due to the interruption of the vapor bubble coalescences and fluid replenishment paths, which are caused by the microstructure surface features [115,119,122125]. The enhancement in CHF is further explained by pointing out the reason behind it, which is the roughness amplifying capillary forces. These capillary forces determine the hydrophobicity of the surface. To demonstrate the effect of capillary forces on CHF, Chu et al. [34] developed a correlation (see Eq. (1.30) in Table 1). Corresponding to experimental results, it has been concluded that by alternating the surfaces with water, better heat removal can be achieved [34]. Decreasing the microcavity diameter of the surface nanostructures creates only a slight increase in nucleation site density in microstructures compared to smooth surfaces [91]. Therefore, the microgrooved surfaces with reentrant cavities were fabricated by employing the orthogonal plowing/extrusion method to enhance the formation of micropores and capillary force. Cavity bubbles developing on these surfaces are almost unchanged with the increase in heat flux due to the restriction of cavity diameter. In addition to heat flux variation, the subcooling range has also a little influence on the cavity bubbles [126,127]. Furthermore, it was shown that CHF on the microchannel surface reached up to 3.4 times that of the plain silicon chip. Another microchanneled copper chip showed significant enhancement for both HTC and CHF up to 5 times and 3.7 times, respectively. Thus, it may be observed clearly that the microchannels are more efficient for boiling heat transfer due to their better heat removal regardless of the surface material. The depth of the channels has a significant effect on the performance as well as the width of the channels [122,128].

In addition, microchannels were etched on a silicon chip and then tested with water. The silicon chips were etched using the deep reactive ion etching method. Deep reactive ion etching method is an anisotropic dry-etching process developed when deep penetration is needed, creating cavities with a high aspect ratio [129]. Surface modification stability and durability are critical for extending the boiling duration on the surfaces [101,130]. Further studies done by Dewangan et al. [131] on a copper wire coated with copper powder using a flame spraying technique showed that the coated wire has 90% enhancement in HTC than the bare wire in R134a and R-410A. Six different tests were performed, and a coated surface of 151 μm thick had the highest enhancement factor of 1.92 among all the other surfaces varying from 42 μm to 423 μm. You [132] had a pool boiling setup with water as the working fluid on super hydrophilic aluminum surfaces. Using sandpapers, the roughness of these surfaces was altered by varying from 0.11 μm to 2.93 μm.

As the roughness increased, the boiling HTCs also increased since the number of cavities that lead to bubble generation increased. It has been reported that a silicon chip with submicron scale roughness can show a significant enhancement in boiling heat transfer due to the number of nucleation sites [133]. The surface roughness may also be achieved by a sandblasting. The rough sandblasted surfaces could consist of considerable irregular large cavities for bubble nucleation requiring lower superheat compared to medium and fine sandblasted surfaces. Therefore, a larger HTC is found compared to fine sandblasted surfaces at low heat fluxes [134]. In the study, different surface roughness in the range between 0.032 and 0.544 μm were realized on the copper tube as a specimen. It is shown that small increments in the surface roughness with some hydrophobic patterns significantly lower the wall superheat temperature and increase the HTC by 1.5 times.

The hydrophobic patterns provide bubbles to be more uniformly distributed over the entire surface; thus, the temperature along the tube is more evenly distributed. This shows that HTC is dependent on the density of nucleation sites [135]. Some laser textured stainless-steel ribbon heaters were tested with a working fluid of FC-72. Three main surfaces were tested, one was untreated, second sample was hydrophobic, and the other was laser-treated hydrophobic. Enhancement in CHF was noticed at both saturation and 12 K subcooling shown in Fig. 10 [136].

Fig. 10
Fig. 10
Close modal

Smooth and laser-textured surfaces were experienced under pure ethanol and ethanol-water mixtures. The laser-textured surface had an HTC enhancement of 280%. The enhancement was explained by the dependency on the width done by a laser pattern. Thus, these studies proved that for laser-texturing applications, there is an increment in both CHF and HTC. These enhancements can be explained with the cavities existing on the heating surface, which leads to early action of nucleation sites. This structure ultimately decreases the surface temperature [137,138].

Microporous structures are also one of the effective methods for the enhancement of surface quality. These structures enable a smaller size of vapor-jet than that of the flat and microgroove surfaces. As a result of this enhancement, hydrodynamic instability is delayed and an enhancement in the CHF and HTC is observed. It is concluded that controlling the growth and distribution of the vapor layer is one of the key factors for the enhancement of pool boiling. It has been observed that a hydrodynamic-instability limit has been reached; hence, CHF cannot be further enhanced by utilizing channel optimization, and viscous-capillary limit [123,139]. Microporous surfaces have the potential to lead approximately 50–270% enhancement on the HTC with the direct benefits on larger nucleate site density compared to plain surfaces. CHF may increase by 33%–60% for the usage of microporous surfaces instead of plain surfaces at the same time. Aside from the observed improvement in CHF and HTC, the bubble site density and frequency are enhanced while the departure diameter stays relatively insensitive with temperature increase [140]. One of the earliest studies regarding microporous and porous coatings on five different sizes of diamond particles showed enhancement in nucleate boiling and CHF due to the increased active nucleation site density within the superheated liquid layer. As the particles get larger, the boiling performance decreases due to the greater thermal resistance associated with the increase in wall thickness [13]. In another study, two aluminum foams with low pore densities are tested and compared with the flat plate. The foam densities were 5 and 10 pores per inch. Best results were obtained for the surface with 5 pores per inch since further increasing the pore density led to higher vapor release resistance, having significant effects on heat removal at high heat fluxes above 20 W/cm2 [141]. When compared to plain copper surfaces, sintered microporous coating with an average particle size of 67 m demonstrated an eight-fold improvement in nucleate boiling heat transfer coefficient and a double CHF. Increasing the coating thickness after an optimized number showed that the nucleate boiling heat transfer decreases sharply, and this is because the thermal conduction resistance of the vapor in the porous layer seems to rise, but the CHF keeps on slightly increasing [29,142]. Liter [29] has been modeled this CHF behavior with Eq. (1.23) in Table 1. A comparison of the plain surface, the sandpaper treated surface, the microfinned surface, and the microporous surface together for the same material has been done [85]. The microporous surface causes the most decrease in the wall to superheat yet recorded the highest heat transfer enhancement with the help of a smaller vapor-jet, delaying hydrodynamic instability [85].

In general, coatings need to be applied on surfaces as thin as possible and their thermal conductivity should be very high to avoid thermal resistance. The presence of porous graphite surfaces helps to achieve high HTC. Porous graphite surfaces have a 60% enhancement in CHF values when compared to the smooth copper surface, also showing 25% lower surface superheat when compared. The reasons behind this enhancement are the high density of the active nucleation sites and the highly wetting HFE-7100 liquid that lowers the wall superheat compared to smooth copper [143]. Surfaces with microstructures with semiclosed pores showed four times higher heat transfer. A decrease in the static contact angle value was reported between the low viscosity liquids used (R114, R21) and the microstructures; thus, more liquid was absorbed and transferred to the hot spot regions underneath the growing bubbles, which showed CHF enhancements [144]. Polytetrafluoroethylene (PTFE) hydrophobic circle spot is an available methodology to induce preferred bubble formations at the edges of the spots that present higher roughness than the central regions of the spots. Increasing the roughness of a surface contributes to nucleation sites in defined areas; thus, the edges of the spots enhance boiling heat transfer at saturated and subcooled conditions. However, in subcooled conditions, the enhancement was observed at a certain heat flux range on a TiO2 coated copper block with a PTFE hydrophobic circle spot by varying the diameter but keeping the overall PTFE area constant [145]. TiO2-coated surface has advantages on heat transfer in nucleate pool boiling due to micro- and nanoscale structured surfaces. SiO2-coated surface is also defined as a nonhydrophilic surface that presents similar surface roughness to the surface that is modified by TiO2. The TiO2 coating alone can improve CHF by 50.4% and 38.2% in saturated water and FC-72, respectively. TiO2-coated surface may give a chance for nucleate boiling enhancement and CHF increase because of the bubble growth in reduced dry patches and more effective liquid–solid interaction.

SiO2 coating that creates similar roughness was compared with and the results demonstrate that TiO2 has additional benefits for boiling enhancement compared with SiO2 coating [146]. Electrical discharge machining (EDM) is another technique for microstructuring to obtain systematically fabricated surfaces. The roughness on the surface constructed by EDM performs better heat transfer compared to a bare surface. The roughest EDM surface (10 μm) demonstrated a 210% enhancement in HTC for FC-77 whereas there was a 100% increment for water in the range of surface roughness from 1.08 μm to 10.0 μm [105]. The surface modification on the microscale can also be achieved with the help of Cr-Cu seed layers, which are applied by a double-layered hollow structure. The fabrication methodology of this uncommon process can be seen in Fig. 11. The all-metal structure contributes a highly efficient heat transfer path between the heat source and the working fluid leading to more nucleation sites. This construction also prevents bubble combinations with each other during the departure of the bubbles. Instead of bubble merges, the structure provides a capillary-driven liquid-imported mechanism fully supplying water so that it can accelerate the bubbles to their escape from the surface. As a result of these advantages, the heat flux is dissipated with a 400% enhancement compared to a bare silicon surface, whereas HTC reaches 50 kW/m2K [147].

Fig. 11
Fig. 11
Close modal
##### 2.3.2.2 Nanoscale surface treatment.

The most motivating part of nanostructured surface treatment studies is perhaps the industrial trend toward producing the systems in compact sizes. Nanostructures are capable of triggering bubble formation. This incident promotes an energy transfer from a solid surface to a liquid by controlling the nucleation site and postponing the formation of the vapor film. The nanostructured surface bubble formation is also smaller than flat surface formation requiring lower activation temperature compared to plain surfaces [148]. The surface wettability increases with the nanostructure leading rewetting process to enhance CHF [149]. Nanocoating technology can be divided into several methods such as nanoporous coating, electrospun nanofibers, nanoparticles, and crystalline nanostructure coating [150]. Nanocoated surfaces show better performance compared to smooth surfaces without deposition [151]. As presented by Hendricks [152], pool boiling was enhanced using nanostructured surfaces on aluminum and copper in water. It was demonstrated that CHF is enhanced about 4 times on nanostructured surfaces compared to plain surfaces. Wall superheat was reduced as well, ranging from 25 to 38 K. It was found that the reason behind this improvement is the nucleation site density due to ZnO nanoparticles. These nucleation sites facilitated bubble growth and increased the critical heat flux at the same time. On these nanostructured surfaces, an optimum balance between the bubble frequency, nucleation site density, and bubble diameter was found. A nanostructured surface created by the acid etching method supported this methodology for CHF enhancement by 27%, whereas creating a 25% degradation on surface temperature. It was also proven that the porous surface with nanostructures had more advantages on both, CHF with an increment of 30% and on surface temperature with a reduction of 27% compared to a flat porous surface without any nanostructured morphology [153]. In an experimental study, the heat flux concentration was grouped as the varying heat flux ranged from 10 to 80 W/cm2 and the fixed heat flux at 50 W/cm2 [151]. The wall superheats of fixed heat flux nanoparticle deposition were lower than varying heat flux. Therefore, this led to higher heat fluxes at relatively lower wall superheat. On the other hand, the nanocoated surfaces indicate a fair amount of decrease in HTC compared to the rough surfaces without deposition [151]. The carbon nanotubes, which have recently been included in the literature, are very efficient compositions for nucleate pool boiling. MWCNT barely experience a heat flux enhancement. As a result, there was an obvious increment in CHF for different MWCNT thicknesses on the two samples, and they showed an enhancement of 62% and 58%, respectively, compared to a plain silicon chip [89].

Fully covering the silicon chip with carbon nanotubes (CNTs) has observable CHF enhancement, as the substrate coverage increases from zero (bare surface) to 5% (“island” pattern), 60% (“grid” pattern), and ultimately to 100% (fully coated). The results obtained are highly desirable in electronic cooling as they illustrate the ability of a chip to maintain a constant temperature while having large fluctuations in heat dissipation [154]. The densification of CNT bundles caused arbitrary and either more or less regular structuration. This structuration enabled the efficient initiation of nucleation in hydrophobic sites formed by the CNT bundles at the surface. The microcavities cause new nucleation sites resulting in microbubbles. The cavity dimensions increase with CNT length, and it leads to heat transfer enhancement up to 100% [155].

The enhanced surfaces with copper nanowires have a considerable effect on CHF as well. The number of cavities and their sizes in scales of microns may be revealed as a conclusion of the coagulation of increased nanowires with a rise in the diameter of nanowires. The proximity of nanowires reduces the cavity sizes by producing shielding during the initial stages of the boiling. Therefore, this phenomenon is very significant for surface temperature decrease avoiding excessive heating of the surfaces before boiling [156]. Nanowires of different heights mounted on a silicon substrate by electrochemical deposition were tested. It is observed that the surface with the tallest silicon nanowire structure (35 μm tall) has CHF 300% higher than a plain silicon surface at same wall superheats. Active nucleation sites are obtained when increasing the nanowire height, thus heat transfer may be enhanced leading to better CHF values [157]. On the other hand, generating separate liquid–vapor pathways by coating different areas on the microchannels can significantly enhance the pool boiling performance. For a surface with open microchannels in it, some porous coatings were deposited on different areas as shown in Fig. 12 to control the bubble departure [158].

Fig. 12
Fig. 12
Close modal
##### 2.3.2.3 Hybrid surface treatment.

Hybrid surface treatment is a microreactor technique providing high-density nucleation sites, and this technique sufficiently adaptable to fabricated surfaces. This methodology is implemented with ZnO on Al and Cu substrates. This application can lead to an extraordinary 4x enhancement in CHF [152]. Graphene oxide nanocoating surfaces on copper have relatively high wettability and thermal conductivity as compared to plain copper surfaces. Therefore, these surfaces have an enhancement of 78% in CHF and 41% in CHF when operated under atmospheric pressure in distilled water [86]. Working on micro/nanoscale modification of the zincaloy-4 surface under atmospheric pressure and saturated conditions can also contribute to enhancement of CHF due to better wettability. Strong water spreadability on the surface can happen when the contact angle reaches below 10 deg [159].

The boiling HTC may vary according to manufacturing parameters of sintering process. The biggest contribution goes to particle size with more than 30% and the least due to sintering pressure with less than 10%. Moreover, sintering time, sintering temperature, and heating rate are influencing manufacturing parameters but it seems that the particle size is to be the strongest parameter to the overall surface performance [160]. As a result of effective bubble nucleation sites on the heated surface, an increase in heat transfer is observed [121].

Trends in surface modification are summarized as micro/nanoporous [161167] and nanowire surfaces [68,168,169] enhancing nucleation site tremendously. Applying the laser texturing process [138,170] and microgroove/-channel formations [171,172] onto the heating surfaces are the most preferred methods to rapidly achieve controlled and enhanced surfaces. Moreover, with the enhancement of laser manufacturing, three-dimensional grid structures are developed to be used in boiling mechanisms [173,174]. Some refrigerants [175177] and dielectric liquids [68,172] are commonly used in many research groups. Moreover, ultrasonic waves [178,179] and magnetic fields [180,181] are used in boiling mechanisms to control both liquid and particle behavior.

### 2.4 Surface Orientation Effect.

The orientation of the surfaces during the boiling process has a substantial role in the heat transfer mechanism by affecting bubble departure physics. The buoyancy forces remove the vapor vertically from the heater surface in the upward-facing region whereas the wavy liquid–vapor interface sweeps along the heater surface. The surface orientations may be classified as upward-facing (0–60 deg), near vertical (60–165 deg), and downward-facing (>165 deg) or can be separated into two levels of upward-facing (0–90 deg) and downward-facing (90–180 deg). The surface orientation has a significant impact on CHF trigger mechanism associated with orientation in both nanofluids and DI water. Thus, El-Genk and Bostanci [30] have been contributed a great correlation (see Eq. (1.24) in Table 1) to predict CHF at different surface orientations. Vapor repeatedly stratifies on the surface leading to a decrease in CHF in the downward-facing configuration [30,31,182,183]. The increase in surface inclination benefits the boiling heat flux at lower surface superheats less than 15 K while negatively impacting at higher superheats [184]. The superheat decreases by 15–25% as the inclination angle changes from 0 to 165 deg, respectively.

These modifications could increase the heat flux by a factor of two when compared to a plain surface during the surface orientation from 0 to 90 deg, while decreasing from 90 to 180 deg, especially from 170 to 180 deg. The detriment of downward-facing boiling is reflected on CHF, which falls 4.5 times on a plain surface and almost two times on the structured surface. Therefore, this may be explained by some surface modifications such as high-temperature thermally conductive microporous coating [185]. Moreover, for high heat fluxes, the HTC diminishes remarkably as the orientation angle increases above 90 deg, whereas it increases from 0 to 90 deg. However, at low heat flux levels, HTC values continuously increase from 0 to 175 deg [32]. The surface orientation in a vertical direction (90 deg) increases the nucleation site density and average bubble departure diameter remarkably. During the movement of position from horizontal (0 deg) to vertical (90 deg), the thermal boundary layer induces isolated bubbles to slide on the surface and coalesce with each other by merging [186188].

As a result of this phenomenon, especially at 90 deg inclination as shown in Fig. 13, larger bubble generation is observed with lower bubble departure frequency. These formations result in higher onset of nucleate boiling heat flux values but lower CHF [189]. Moreover, Priarone has observed a decrease in CHF as orientation angle increases from 0 to 90 deg upward facing, whereas it decreases drastically from 90 to 180 deg at downward facing [32]. Also, if low flow velocities (0.08 m/s) are considered as pool boiling models, it can be noted that downward facing position has a considerable impact on CHF with high precision [15,25]. The bubble generation on fully inclined surfaces such as tubes, sticks, or slim long prisms attached horizontally to the ground can face mostly with bubble breakages and coalescences at high heat flux levels as shown in Fig. 14 [190].

Fig. 13
Fig. 13
Close modal
Fig. 14
Fig. 14
Close modal

The contact angle also increases from 41 deg to 60 deg [191]. At upward-facing orientations, a decrease in contact angle will significantly improve CHF, whereas as the inclination increases, the enhancement ratio weakens [14,33]. Furthermore, due to certain bubble dynamics, it has been observed that the horizontally downward facing configuration has the lowest HTC. This process has been explained by the fact that bubbles nucleate mostly on the surfaces, and particles have a smaller tendency to deactivate nucleation sites on the bottom. The larger the bubble diameter, the more time it will take to depart from the surface. The reason behind this was attributed to the vapor trapped on the heated surface that caused an obstacle between the contact of the liquid and the heated surface [36,189,192]. The continuity and stability increase of the vapor film on the surface has a significant effect on the heat transfer rate [193]. The heater surface inclination and size have small or negligible impacts on plates oriented upward compared to plates that are positioned with their heat transfer surface in the direction of gravity. In other words, CHF values can be nearly steady at the upward aligned surface depending on the underlying thermophysical properties of the bubble generated, but a sharp decrease was observed in CHF values at the downward facing surface [97]. The microporous surfaces on copper and aluminum showed an 80% reduction in incipience superheat, and 100% enhancement in CHF compared with plain surfaces (copper/aluminum) [24]. In contrast to DI water, CHF enhances with inclination angle in nanofluids, whereas it decreases in DI water. This difference between the two liquids was caused by the deposition of the nanoparticles occurring during the boiling process. Nanoparticles become more profound and this construction benefits surface wettability and CHF accordingly [194]. Until now, both bare silicon and carbon nanotube surfaces have not been implemented by considering surface orientation with no clear dependence on boiling incipience. In the case of carbon nanotube covered surfaces, a significant reduction in average HTC by changing the inclination angles from 30 to 60 deg has been recorded [195].

### 2.5 Working Fluid Effect.

Heat transfer coefficients, CHF, active surface area, bubble frequency, bubble size, and bubble growth rate are also dependent on the fluid properties [196]. Working liquids being utilized include dielectric fluids, nanofluids, binary mixtures, and graphene solvents.

#### 2.5.1 Dielectric Liquids.

With the recent evolution in the electronics industry and the high rate of heat dissipation approaching 100 W/cm2, an efficient way of heat removal requires compatible liquids. This is usually carried out by using dielectric fluorocarbon liquids (FC-72, HFE-7100, or HFE-7200, etc.) [134,197]. These highly wetting dielectric liquids with efficient heat transfer mechanisms have been identified as one of the most effective thermal control methods [198,199]. Similar to FC-72, HFE-7100 also shows relatively high enhancements in CHF and boiling heat flux on porous graphite compared to smooth copper [143]. In another investigation using FC-77, it has been demonstrated that large heat transfer enhancement can be achieved when the surface roughness value is increased due to EDM surface texturing [105]. Contrary to these studies, one of the investigations illustrated that pure liquid may show better performances under unexpected conditions. DI water is compared with FC-72 under the same temperature. Thus, saturation temperature of the water is lowered to reach the same saturation temperature of FC-72 at ambient temperature. Water has clearly shown some advantages over FC-72. There is a significant 3.6× enhancement in CHF more than FC-72. Regardless of water being more cost effective, environmentally friendly, and nonhazardous, FC-72 and similar liquids are used due to their compatibility with electrical components [200].

In common, involving dielectric liquids, the bubble departure diameter is much smaller than nondielectric liquids such as water due to the tiny surface tension of dielectric liquids. While dielectric liquid bubble diameters are 400–600 μm, nondielectric fluid bubble diameters are approximately 2.5 mm in a nucleate pool boiling at or near atmospheric pressure level [201]. Due to the high wettability of these liquids, they lack undeveloped bubbles leading to the prevention of heterogeneous nucleation and allowing the liquid superheat to rise and reach spontaneous high-energy molecules in the formation of a stable vapor bubble [202].

#### 2.5.2 Nanofluids.

Over the last three decades, a rich family of nanofluids has been investigated. Nanoparticles are spread in base fluids such as water, oil, dielectric fluids, methanol, ethylene glycol, and refrigerants. For high thermal performance in boiling, nanoparticles exhibiting high thermal conductivity must be mixed with conventional liquids in certain concentrations [203205]. A study [206] has illustrated the availability ratio of common nanoparticles presented in Fig. 15.

Fig. 15
Fig. 15
Close modal

One of the most cited papers regarding nanofluids first suggested that an excessive increase of nanoparticles in a pure liquid presents an increase of wall superheat at given heat fluxes likewise other researches in the literature [204]. On the other hand, Mohamadifard et al. [207] demonstrated the strange behavior of a nanofluid by shifting the boiling curve to the left when the nanoparticle increases. Also, Ding and Wen [208] showed that the nanoparticle concentration in liquids reduces the surface temperature while heat flux increasing in Fig. 16.

Fig. 16
Fig. 16
Close modal

A nanoparticle concentration increase by 1.25% in weight reveals a considerable enhancement on HTC with a ratio of 40% on high heat fluxes. When nanoparticle deposition of the surface occurs, nanofluids can have a positive effect on CHF by leading to an increase in surface wettability. The enhancement factor for most nanofluids based on water with TiO2, Al2O3, and Cu decreases in the case of higher heat fluxes [209,210]. It has been reported that some nanofluids can lead to better bubble visualization and a significant increase in CHF compared to DI water. When nanofluids boil, they deposit some particles on the heater surface [211]. This collection of nanoparticles on the surface leads to more nucleation sites and better surface wettability that enhances CHF [212,213]. The same nanofluid effect was observed but on Ni-Chrome wire, which is used for better optical visualization. It has been observed that intense nanoparticles were deposited on the wire leaving a layer of Al2O3 on the surface [214]. Kim [215] has diluted dispersions of alumina, zirconia, and silica nanoparticles in water with volumetric concentrations lower than < 0.1% (see Fig. 17).

Fig. 17
Fig. 17
Close modal

He observed superior bubble formation compared to pure water experiments. They reported that an evaporating microlayer for bubbles developing on a heated surface that achieves stability from the presence of the nanoparticle layer could be one reason for this improvement. The increment of nanoparticle density in pure substances such as water can cause degradation on CHF. The preparation of the nanoparticles is one of the examples negatively affecting CHF in pure water with a decrease of 75%, 68%, and 62% where copper nanoparticle dispersion of 0.25%, 0.5%, and 1.0% in water was used, respectively. This event is strongly dependent on the surface tension reduction of the surfactant and the high bubble dynamic [216]. Nanofluid dilution in water shows promising results but should be performed on a clear surface to obtain more reliable results.

Additionally, the paper by Sarafraz [217] only focused on zirconia dissolved in a water–glycerol mixture of different volumes. In general, when a liquid has impurities, the boiling point decreases; thus, due to the presence of these solid particles the thermal conductivity of nanofluids is relatively higher. This also improves the thermal conduction mechanism inside the base fluid (see Fig. 18). Except for the Water-Cu, nanofluid enhancement factor of keff, the HTC for distilled water decreases with heat flux density increase at the same wall superheat [218].

Fig. 18
Fig. 18
Close modal

#### 2.5.3 Binary Mixtures.

In different molar rates, binary mixtures show exceptional thermophysical properties. However, using single component pure liquids cannot be suitable; hence, binary mixtures such as water–ethanol, water–methanol, water–glycerin, ethanol–butanol, and ethanol–benzene in regulated concentrations are preferred in common. The binary mixtures can increase the growth of vapor bubbles while it can decrease the bubble departure diameters, nucleation site density, and heat flux. The boiling incipience on superheat can be observed at low values of heat flux (30 $≤$ W/cm2) in simple liquids compared to binary mixtures due to physical properties and wetting characteristics [219223].

On the other hand, adding surfactant into the liquid shifts the surface superheat curve to lower values by creating an earlier boiling incipience and increasing the nucleate boiling HTC. In that case, CHF is characterized by irreversible dry patches on the surface caused by the failure of the rewetting [224]. Ethylene–glycol–water mixtures are typically preferred as antifreeze solutions in the field of electronic cooling and automotive. With the knowledge of Al2O3 nanoparticle deposition, an Al2O3/ethylene–glycol/water mixture was produced that has considerable impact on nucleate pool boiling heat transfer as well. CHF shows 64% enhancement with 11.3 W/cm2 and the boiling heat transfer enhancement sustains during the particle concentration increases naturally [207]. Less-volatile components provide a sharp CHF increase and heating surface temperature is dropped by optimizing the volume ratio of mixtures [225]. The bubble temperature increases at this interface due to the generated layer, and HTC diminishes as well [85]. More volatile component at low concentrations in binary systems, domination of mass diffusion is demonstrated by several factors such as substantial slowdown of asymptotic bubble growth, the prevention of the dry area formations beneath bubbles, contraction of the lower part of the bubble, and omission of the evaporation microlayer contribution at either atmospheric or elevated pressures [226]. Besides, amine solutions enhance HTC with reduced surface energy bringing more nucleation sites. In this condition, the bubble detachment diameter is larger, and the bubble frequency is increased; consequently, HTC shifts to higher levels [69]. Therefore, the well-known Schlünder model (see Eq. (6)) may be preferred as the most available method with its excellent theoretical basis that is based on the analogy of mass, heat, and momentum transfer to predict HTC [227]. The glow-plasma water treatment is one of the potential methods to improve the HTC during boiling by breaking down the water molecules grouped into smaller structured nanoclusters. Glow-plasma water treatment in near vacuum conditions with 0.075 bar may have a reduced ability to transfer heat compared with demineralized water due to fewer nucleation sites occurring in subatmospheric conditions [228]
$HTCHTC0=11+(y−x)[1−exp(−B0qβlρlhlv)](Ts1−Ts2)ΔTid$
(6)

#### 2.5.4 Graphene Solvents.

Graphene is another excellent material with a well-structured atomic layer similar to honeycomb and superb thermal conduction property. Graphene's thermal conductivity may be more than almost 2000 W/m-K when it is grown on, or attached to a substrate or embedded within a material. It can also potentially reach up to 6600 W/m-K in suspended form. However, the usage of graphene is limited due to its weak dispersity in solvents, which is caused by strong van der Waals forces among the particles [229232]. Therefore, the conductivity of the graphene decreases dramatically in any solvent, but it significantly increases the HTC of the liquid solved in. The increase of graphene concentration and temperature improves thermal conductivity with the capacity of 9 and 19% for graphene nanofluid and polyethylene glycol (PEG) graphene nanofluid, respectively, with the mass percentage of 0.1% at 60 °C [233]. On the other hand, with the hydrophobicity of graphene in nature, the wetting characteristic of the surface can be altered by activating a carboxyl group on the reduced graphene oxide flakes so that the layer can absorb water well and this phenomenon is one of the possible mechanisms for CHF enhancement that able to reach 179% [229,234]. Increasing the concentration of nanofluids beyond 0.01 wt.% leads to a reduction in HTC whereas the HTC of the graphene nanoplate (GNP) and GNP with PEG nanofluids is relatively enhanced.

Graphene nanoplate-PEG with 0.1 wt.% is the best sample in terms of stability over 90 days, CHF and thermal conductivity which has been experienced with an increase of 72% and 20%, respectively, compared to DI water [235]. The cured GNP, which is has a good ability to wet surfaces (see Fig. 19), performs much better than the hydrophobic uncured GNP and the uncoated copper surface. Simultaneously, the mass flowrate can increase by 151% and 154%, respectively, when compared to bare surfaces at 150 °C. This dramatic increase is inherited from the cured GNP performance on the amount of vapor bubbles, despite the smaller vapor bubble size in the case of surface activation. GNP enhances the pool boiling efficiency and leads to a delay in transition boiling [236].

Fig. 19
Fig. 19
Close modal

## 3 Critical Heat Flux and Correlations

Critical heat flux is perhaps the most important engineering aspect of pool boiling since pool boiling heat transfer has been taken into consideration over the last six decades. To summarize maximum CHF values, Fig. 20 was generated in chronological order. The studies were divided by the surface material and the liquid, which influence the surface energy of the heater and heat transfer coefficient, respectively. This graph briefly illustrates that there were good enhancements as high as 425 W/cm2 on metal surfaces. On the other hand, other studies done with applicable surface materials under different liquids demonstrated low CHF values dramatically. However, these studies show CHF increases individually compared to either bare surfaces or pure liquids with brilliant methods. The low-set may have originated from the distinctness of the experimental methods, conditions, and measurement techniques as preferred liquids and surface modifications are sufficient.

Fig. 20
Fig. 20
Close modal

The importance of CHF has been to promote the studies that accurately predict the effects of different parameters concerning the heat transfer mechanism. Therefore, Table 1 has been constructed to gather all the developed correlations for pool boiling and introduced in preliminary sections. More than 30 correlations have been proposed in the past, accounting for a number of parameters. Besides, one more table, Table 2, that indicates their range of validity and operating conditions was inserted into the Appendix. Those more than 30 prediction methods to expect CHF of the unstable pool boiling process were correlated under dissimilar parameters but most of them are in agreement with experimental results from different sources. One of the well-known mathematical formulations has been developed by Kutateladze [18] (see Eq. (1.11) in Table 1), while for the same equation more than 20 different improvements (see Eqs. (1.12)–(1.32) in Table 1) have been proposed, mostly with a modified K value in order to improve predictions. Then, Rohsenow and Griffith, in 1956, Ref. [8] developed a different equation based on the surface area. Then, in 1959, Zuber [19] developed another model mostly preferred for predicting the CHF by altering the K value from 0.13 to 0.19. Different researchers are still developing various values for the parameter K to make the original equations accurate in predicting CHF with their experimental data [79]. K values can be affected by different independent dimensions/numbers such as surface diameter (Ds), equivalent heated surface diameter (Dh), channel gap size (s), Jakob number (Ja), effective Peclet number (Pe), vapor escape length (λm), and some other factors or coefficients. In addition to the angle of the surface inclination, the liquid-surface contact angle has an impact on CHF and is added into prediction models. In about 20 models, one common model is Zuber's CHF equation [49] and is used in the studies [55,56,85,123,136,139,159,212] with a K value of 0.131. Zuber's correlation is very suitable for modifications on corresponding to different operating conditions. Therefore, this correlation can provide the most suitable prediction on different surfaces (plain, microstructured, microporous), fluids (water, FC-72, PF-5060, Al2O3–water nanofluid), pressure, and subcooling levels. In general, the correlations to predict CHF have evolved from the simple correlations based on merely natural parameters such as Jakob number, densities of both liquid phases, and sizes based on liquid–solid contact angle and surface orientation.

## 4 Thermal Management of Electronics Correlation

A pool boiling correlation developed by Prof. Cohen and his team proposed as the Thermal Management of Electronics correlation (see Eq. 7) predicts pool boiling CHF [43]. The correlation considers the thermal properties of the heater by including the length, thickness, and thermal conductivity, making the correlation valid for thermal effusivity between 0.2 and 120, pressure from 1 to 4.5 bar, and subcooling from 0 to 75 K
$qCHF,TME=π24hlvρv[σlg(ρl−ρv)]1/4(SS+0.1)×[1+〈a−b×L′(P)〉]×(1+B×[(ρlρv)0.75cplhlv]ΔTsub)$
(7)

This correlation was revisited in this work by using additional data points extracted from the recent literature and given in Fig. 21. The additional data illustrated that TME correlation has a good prediction capability with an error of ±12.5% where it shows a shortage for CHF values in water (CHF > 50 W/cm2) on several treated surfaces. A further study has been performed to improve the prediction capability. The parameters a, b, and B have been optimized by using a genetic algorithm resulting in 0.031, 0.0024, and 0.1, respectively. In conclusion of this improvement, the modified TME correlation (TME′) reached a better capability for predicting CHF on a plain surface within ±7.5% for water as working fluid operated at different subcooling levels. The new extracted data were also used in different correlations to compare the results with TME correlation [237] for its predictive capability and have a closer look at where it stands. In this comprehensive graph (see Fig. 21), the TME correlation was mainly compared with the prediction methods by Kutateladze [18], Zuber [19], Ivey [7], Guan [16], and Linehard et al. [20]. TME correlation has superiority in taking the heater's geometry and physical properties into account, as well as the subcooling effect, while the other correlations focus mainly on the liquid properties. The main difference between Kutateladze and Zuber's correlation is the modified K constant. Kutateladze has a higher range of K values depending on the liquid properties making it more suitable. Even though TME correlation has a better prediction range, it is more complicated and harder to use, especially with the development of nanofluids, which requires a new term to be added. One limitation present in all these mentioned correlations is the exclusion of the orientation effect. Even though the correlation still predicts the CHF with high accuracy, the innovation in thermal management has proposed a lot of complex geometrical structures for the heating surfaces that cannot be encountered using TME correlation. Furthermore, researchers have been using different kinds of nanofluids and mixtures with some unknown thermophysical properties such as thermal conductivity, latent heat of evaporation, and specific heat. Thus, CHF cannot be accurately predicted in many cases. In conclusion, TME correlation is so good for predicting the CHF for plain surfaces with liquids of known properties, and for future works, a new term can be developed that would contribute to more accurate CHF prediction.

Fig. 21
Fig. 21
Close modal

## 5 Summary and Future Research Perspectives

An extensive review of studies was carried on CHF and selected pool boiling parameters for electronics' thermal management in this paper. Several aspects, which are pressure, liquid subcooling, working fluids, surface topography, and its orientation, have been pointed out in terms of their influence on the overall phase-change mechanism. The distribution of research has been illustrated to show vulnerable study ranges. The maximum CHF values of the studies reached under several operating conditions were ordered chronologically. At least, the most proposed prediction methods have been compared by using data from recent studies. The resulting insights can be summarized as follows:

1. Pressure, as one of the major influencing parameters, has a significant impact on CHF, HTC, bubble departure diameter, bubble detachment, bubble frequency, and surface activation with different rates. An increase in pressure means larger CHF and HTC due to small-sized bubbles and intensified activation of surface cavities. On the other hand, subatmospheric pressure causes a lower bubble growth rate and frequency and is suitable for observing the bubble nucleation. These properties increase the surface temperature while decreasing CHF, but subatmospheric conditions can be an appropriate solution for the heat transfer of more than 100 W/cm2 with several surface modifications.

2. Experimental results show good agreement with the correlations developed based on the original Kutateladze–Zuber and Rohsenow correlations. However, those correlations are valid for conditions only with intermediate pressures and cannot predict the heat transfer parameters for large and subatmospheric pressure levels. Additionally, the mathematical predictions are not appropriate when boiling is present with mixtures such as nanofluids. This means, predictive expressions for a broader spectrum of operating conditions, fluid chemical composition, or even surface topography can still be developed in order to forecast heat transfer parameters such as CHF and HTC.

3. The bubble generation and the bubble diameter that develop in a subcooling liquid are slower and smaller, respectively, than saturated bulk liquid. This condition obstructs the traceability of vapor bubbles. Subcooling contributes to heat transfer with elevated CHF values as it decreases surface temperature. The studies mostly focus on saturation temperature because, at the end of long-term operations, the bulk liquid in closed systems reaches its saturation point. Therefore, this parameter can be an optional operating condition to maintain the surface temperature in confidence by exceeding the limits of surface heat fluxes.

4. The heater size does not have an apparent influence on the nucleate boiling regime unless the heater size is considerably larger than the capillary length to be buoyancy dominated. Particularly, as the surface is inclined, the surface size becomes a great contributor to CHF. Some studies demonstrate that bubble departure frequency is modified by placing limitations on the growing bubbles on the surface. Therefore, regulating wettability, thermocapillarity, and instability of the surface size influence the nucleation site density and capillary suction positively, which contribute to boiling heat transfer. Concerning this aspect, a limited number of studies have been done until now. Therefore, detailed investigations can be carried out into the boiling of nonflat geometries, since most scientists use planar substrates for their experiments due to better manufacturability, observability of bubbles, and surface treatment issues.

5. Surface topography is one of the most powerful parameters effecting overall heat transfer due to the interaction between the surface wall and the working liquid. The surface modification leads to effective surface area, nucleation site density, bubble growth and departure, rewetting, capillary suction, etc., which are the key parameters for pool boiling. Some fundamental surface modifications, micro/nanoscale and hybrid surface treatments, were introduced and discussed for several conditions, in addition to innovative surface structures.

6. Surface orientation has a considerable effect on CHF. While the orientation angle increases from 0 deg to 90 deg, CHF decreases slightly. The CHF for downward-facing surfaces decreases exponentially as the orientation angle approaches 180 deg. This point is essential and represents a limiting factor for cooling systems used in most aerospace, aircraft and computer applications where the direction of the vehicle changes the orientation of the heated surface. Most of the studies incorporating parametric experiments on varying tilting angles of the heater surface have been performed for water. However, the phase change phenomenon in low boiling liquids at large tilt angles is not well understood and can be targeted as a research topic, since surface tension and viscous forces are developing thermophysical parameters affecting the bubble formation.

7. It is well known that HTC, CHF, active surface area, bubble frequency, bubble size, and bubble growth rate are strongly dependent on the fluid properties. Therefore, novel developed liquids and eventually binary mixtures have an indispensable, and remarkable impact on boiling heat transfer.

8. The suspension of nanoparticles with high thermal conductivity gives liquids better thermal performance than conventional liquids in certain concentrations. Therefore, many studies have been reported that nanofluids have positive effects on both CHF and HTC. In particular, working liquids involving graphene materials are promising for HTC enhancement with low surface tension by bringing more activation sites. Moreover, particle deposition/agglomeration behavior and compatibility issues have to be sufficiently solved before such advanced fluids are used in sophisticated thermal cooling systems.

9. TME correlation proposed by Prof. Bar-Cohen and his team can predict CHF for a wide range of conditions, including recently added data points within ±12.5%. It yields satisfying predictions for CHF values lower than 50 W/Cm2, especially under dielectric liquids. In Addition, the enhanced TME demonstrated a grateful performance for the CHFS under water within an error of ±7.5%, where CHF spectrum is 90–250 W/Cm2 while other prediction methods show acceptable results, but with larger deviations.

The knowledge in understanding the mechanisms of nucleate pool boiling, which can be named as a centennial research topic, showed significant progress in the last decade. Research activities on this phenomenon have considered improvements in manufacturing and material technology, as well as chemical application, and taken a large number of different operating conditions and combinations into account. Each work is unique and contributes essentially to further understanding the overall phase change phenomenon. However, current industrial systems' rate of waste heat production steadily increases while at the same time the miniaturization of the system is an inalienable aspect of their design. These intricate requirements highlight the necessity for complex geometries used for the heater surfaces, while at the same time a more capable working fluid with extraordinary thermophysical properties is needed.

Recent studies have revealed that microscale surface implements and greatly enhances the nucleate pool boiling performance up to 420 W/cm2 [123,124,139,153]. Therefore, it has been constituted that microchannel and microporous surfaces are extremely promising methods for the increase of heat transfer [238]. By using microtexturing, additional surface cavities are obtained by enhanced selectively manufactured geometries leading to the intensification of a larger number of active nucleation sites. This in turn can lead to improved rewetting ability resulting in an elevation of the heat transfer limit. In addition to the contribution of high thermal performance by using microchannel and microporous surfaces, using the additive manufacturing process, which is a very auspicious technique, well-defined microstructuring on a bare surface [138,170] can be achieved. This technology also saves a lot of time, eases surface manufacturing at high precision, and gives a large range of flexibility in terms of geometry selection and miniaturization. A very controversial example can be seen in the development of the atlas robot by Boston Dynamics. The first few prototypes were built by using partially selective laser sintering and mostly normal cutting machines to achieve lightweight and complex geometries for parts. At that time, the power block was externally mounted on the robot's body. The latest prototype, though, has a power block inside the torso embedded fully in the base material utilizing an in-house developed additive manufacturing laser machine operating with three synchronized lasers. This means that additive manufacturing technology can be adapted in order to provide flexibility in the manufacturing of complex surfaces/parts for boiling purposes.

In terms of liquid selection, refrigerants [175,176], dielectric liquids [134,143], and nanofluids [104,213] are preferable owing to the enhancement on bubble generation and heat transfer coefficients, whereas water continuously shows adequate performance. Moreover, graphene [230,232] is proposed as an innovative and suitable material for liquid mixtures creating ultimate heat fluxes. The best performance of graphene nanofluids is achieved on horizontal surfaces while the surface orientation benefit heat transfer rate at low heat fluxes [32].

To put it in a nutshell, current technologies comprise several different operating principles, varying materials, the apparent change in an operating state, and system complexity. To overcome the resulting technical boundaries for thermal management systems, one has to join multiple techniques and should take into account to ensure maximum efficiency, long-term reliability, and a wide range of flexibility by tracking several novel future perspectives such as mechanical surface enhancement/design at microscale together with a combination of cost-effective highly capable working fluids consisting of nanosized particles acting as a thermal booster.

## Acknowledgment

The authors are grateful to EVATEG Research Center at Ozyegin University for the given spiritual and financial support. Also, they thank to the Deutsche Forschungsgemeinschaft (DFG)—German Research Foundation, Grant No. 441193154 for providing support for Dr. Mete Budakli.

## Funding Data

• Deutsche Forschungsgemeinschaft (DFG)—German Research Foundation (Grant No. 441193154; Funder ID: 10.13039/501100001659).

## Nomenclature

• A =

area (m2)

•
• C =

constant

•
• cpl =

specific heat of the liquid (J/kg K)

•
• Cf ,w,sat =

fluid constant

•
• Cw =

compensating factor

•
• Dh =

equivalent heated surface diameter (m)

•
• Dp =

particle diameter (m)

•
• Ds =

surface diameter (m)

•
• fls =

solid fraction of the liquid–solid interface

•
• fs =

friction factor

•
• g =

acceleration of gravity (m/s2)

•
• hiv =

latent heat of vaporization (J/kg)

•
• Ja =

volumetric Jacob number

•
• keff =

effective thermal conductivity (W/m K)

•
• kl =

thermal conductivity of liquid (W/m K)

•
• l =

channel length (m)

•
• L =

heater length (m)

•
• $L′$(P) =

nondimensional characteristic length

•
• Pe =

effective Peclet number

•
• qCHF =

critical heat flux (W/m2)

•
• Ra =

average roughness (pm)

•
• s =

channel gap size (m)

•
• S =

thermal activity parameter

•
• Sa =

accommodation factor

•
• Sm =

mean spacing (m)

•
• Tl =

liquid temperature (K)

•
• Tsat =

saturation temperature (K)

•
• W =

wicking coefficient

•
• z =

stability factor of nucleate boiling

•
• αl =

thermal diffusivity of liquid (m2/s)

•
• ΔTsub =

liquid subcooling; Tsat (Psys) – Tbulk (K)

•
• η =

•
• θ =

liquid–surface contact angle (deg)

•
• λd =

Rayleigh–Taylor interfacial wavelength (m)

•
• λm =

vapor escape length (m)

•
• ρl =

density of liquid (kg/m3)

•
• ρv =

density of vapor (kg/m3)

•
• σ =

surface tension (N/m)

•
• τ =

bubble residence time (s)

•
• ϕ =

orientation angle (deg)

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