The flow of alumina–water nanofluid across heated circular tubes arranged in inline and staggered arrays in a heat exchanger has been studied numerically using the finite volume method (FVM). For calculating the nanofluid’s thermophysical properties such as effective thermal conductivity and effective viscosity, Corcione’s correlations are utilized. Corcione’s correlations consider nanoparticles size, their Brownian motion, and operating temperature while calculating these effective properties of nanofluids. The impact of three parameters on heat transfer characteristics across inline and staggered arrays of heated circular cylinders has been examined. These parameters are nanoparticle diameter d p , which is varied between 10 nm and 50 nm, nanoparticle volume fraction ɸ varying from 0.01 to 0.05, and Reynolds number Re ranging from 10 to 200. It is observed that heat transfer augmentation across both inline and staggered arrays occurs when nanoparticle concentration is increased and smaller diameter nanoparticles are used. Mean Nusselt number Nu M is increased by 31% when ɸ is increased from 0.01 to 0.05 at Re = 200 and d p = 10 nm in an inline array and by 25% in a staggered array. Nu M is enhanced by 20% for the inline array and 16% for the staggering array when d p decreases from 50 nm to 10 nm at Re = 200 and ɸ = 0.05. At any given value of d p , ɸ, and Re, the mean Nusselt number is always higher for staggered array in comparison with the inline array. The results reported in the present study can be utilized for the optimal design of various heat exchange systems under the given operating conditions. The present results are extensively validated with the available experimental/numerical studies.

In the present work, large eddy simulation (LES) was performed to access the film cooling performance in the supersonic flow over a flat plate with a perpendicular slot injection configuration. The study was carried out for three mainstream Mach No.; M α = 1.2, 2.67, and 3.3 and three coolant stream Mach No.: 0.05, 0.1, and 0.15. In supersonic flow, temperature rise inside the boundary layer is a major issue considering it causes high rates of heat transfer to the coolant film. To select a suitable LES sub-grid scale (SGS) model, LES results obtained from the present study using the LES SGS models such as Smagorinky-Lilly, wall adapted local eddy viscosity (WALE), and wall-modeled LES (WMLES) models were compared with DNS results of Keller and Kloker. The parametric study showed that the higher mainstream Mach No. caused increased wall temperature and reduced effectiveness. The film cooling effectiveness appeared to reduce almost by 10% when the mainstream Mach No. is increased from 1.2 to 2.67; however, no apparent difference was observed in effectiveness between the mainstream Mach No. 2.67 and 3.3. It was found that doubling and tripling the coolant stream Mach No. from 0.05 to 0.1 and 0.15, the length of potential core region also doubled and tripled, respectively, from 4 X/S to 8 X/S and 13 X/S and hence significant improvement in the film cooling effectiveness was observed.

This study used numerical analysis to investigate the effects of nonlinear radiation and variable viscosity on free convection of a power-law nanofluid over a vertical truncated cone in porous media with Rosseland diffusion approximation considering zero nanoparticles flux and internal heat generation. The internal heat generation is of an exponential decaying form and the viscosity of the fluid is assumed to follow Reynolds viscosity model. The surface boundary conditions of vertical truncated cone is maintained at the uniform wall temperature (UWT) and the zero nanoparticle flux (ZNF) to cause the results to be more realistic and useful. The nanofluid model considered the effects of Brownian motion and thermophoresis. The nonsimilar governing equations are obtained by using a suitable coordinate transformation and then solved by Keller box method (KBM). Comparisons with previously published work obtained good agreement. Graphical and tabular presentations of numerical data for the dimensionless temperature profile and the local Nusselt number were presented for main parameters: dimensionless streamwise coordinate, thermophoresis parameter, Lewis number, radiation parameter, surface temperature parameter, viscosity parameter, power-law index of the non-Newtonian fluid, and internal heat generation coefficient. The local Nusselt number increased when the following parameters were increased: radiation parameter, surface temperature parameter, viscosity parameter, power-law index of the non-Newtonian fluid, and dimensionless streamwise coordinate. In contrast, the local Nusselt number decreased when the following parameters were increased: internal heat generation coefficient, thermophoresis parameter, and Lewis number. Besides, the physical aspects of the problem are discussed in details.

Boussineśq and non-Boussineśq fluid with thermo-physical property variation have been investigated for a vertical fin array. Computations are executed for the range of parameter such as Grashof number 1.86 × 10 5 and 4.42 × 10 5 , non-dimensional S* = 0.2, 0.3, and 0.5, and non-dimensional clearance C * = 0.10, 0.15, and 0.40. The axial development of various fluid flow quantities, such as the pressure defect (P*), local Nusselt number (Nu l ), and the bulk temperature of the fluid (θ b ) has been presented for each of the property combinations. Nu l is observed to have reduced by 70% near the exit from the Boussineśq fluid with fixed viscosity and thermal conductivity to the non-Boussineśq fluid with the variable property. Furthermore, the overall Nusselt number (Nu) at S* = 0.2 in an isothermal vertical fin array for an increase in Gr from 1.86 × 10 5 to 4.42 × 10 5 with different combination of properties such as Boussineśq fluid with fixed viscosity and thermal conductivity (ρb μc kc), Boussineśq fluid with variable viscosity and thermal conductivity (ρb μv kv), non-Boussineśq fluid with fixed viscosity and thermal conductivity (ρv μc kc), and non-Boussineśq fluid with variable viscosity and thermal conductivity (ρv μv kv) are observed to have an increase of 138%, 148%, 150%, and 160%, respectively.

Fourier law of heat conduction, its analog Fick's first law, and Newton's law of viscosity are classical laws that are not capable of exhibiting memory effects. Conservation laws based on these classical laws do not give predictions about memory effects on the transport phenomena. Recently, proposed novel laws are called Cattaneo–Christov heat flux. Models are based on the generalization of classical laws of heat conduction, mass diffusion, and Newton's law of viscosity. This investigation considers this generalized theory to model the impact of relaxation phenomenon on the transport of momentum, heat, and mass in Maxwell fluid (viscoelastic fluid) of temperature-dependent viscosity and thermal conductivity in the presence of temperature-dependent mass diffusion coefficients. It is observed from the simulations that memory effects play a key role in controlling momentum, thermal and concentration boundary layer thicknesses. It is also noted that the rate of diffusion of heat and mass has shown an increasing trend when thermal conductivity and mass diffusion coefficients are increased via rise in temperature of the fluid. The generative chemical reaction on the transport of specie relative to the impact on the transport of specie when it is compared with the impact of destructive chemical reaction on the transport of specie.

Phase change materials (PCMs) generally suffer from low thermal conductivity which limits their application in thermal systems. The effective thermal conductivity may be improved by including fins, metallic powders, fine wires, and nanoparticles. The objective of this study is to investigate the thermal performance of graphene nanoplatelets (GNPs) dispersed in small quantities in 1-tetradecanol (C 14 H 30 O) PCM. This nano-enhanced PCM (NPCM) is placed in the annular space of a shell and tube in a solar thermal storage unit. The numerical simulations have been carried out using a numerical model based on the enthalpy-porosity and the control volume methods. The numerical model has been successfully validated by comparison with experimental data available in the literature. The numerical results showed that the higher the GNPs concentration, the lower the stored energy. The higher the GNPs concentration the shorter the discharging time. But, during the charging process, though the reduction in the melting time by 9.5% for GNPs concentration increase from 0 to 1 wt%, the melting time increased in contrast by 10.5% for GNPs content increasing from 1 to 3 wt%. For the GNPs concentration of 3 wt%, the heat transfer rate enhancement was limited by an undesirable increase in viscosity which led to weak natural convection and hence a longer charging time. Thus, the GNPs concentration of 1 wt% showed better thermal performance than that of 3 wt% concentration. These results may guide the improvement of solar thermal storage by dispersing GNPs in PCM.

In this investigation, the performance of the shell and tube heat exchanger operated with tin nanoparticles-water (SnO 2 -W) and silver nanoparticles-water (Ag-W) nanofluids was experimentally analyzed. SnO 2 -W and Ag-W nanofluids were prepared without any surface medication of nanoparticles. The effects of volume concentrations of nanoparticles on thermal conductivity, viscosity, heat transfer coefficient, fiction factor, Nusselt number, and pressure drop were analyzed. The results showed that thermal conductivity of nanofluids increased by 29% and 39% while adding 0.1 wt% of SnO 2 and Ag nanoparticles, respectively, due to the unique intrinsic property of the nanoparticles. Further, the convective heat transfer coefficient was enhanced because of improvement of thermal conductivity of the two phase mixture and friction factor increased due to the increases of viscosity and density of nanofluids. Moreover, Ag nanofluid showed superior pressure drop compared to SnO 2 nanofluid owing to the improvement of thermophysical properties of nanofluid.

In this paper, two-dimensional unsteady simulations of yield-stress fluids in the Poiseuille–Rayleigh–Bénard flow between two horizontal plates were performed. The laminar flow of these fluids is characterized by the existence of high- and low-viscous zones. The thermal and hydrodynamic behaviors were studied in the case where the convective instability was developed, and the high-viscous zones were minimized. The commercial computational fluid dynamics (CFD) package fluent was adopted to perform the different simulations. The average Nusselt number over time of the two plates was chosen to characterize the thermal transport, while the average of the maximum vertical velocity component over time in the horizontal mid-plane described the hydrodynamics of the flow. It was found that the fluid behaved according to a range of viscosities with the same order of magnitude as the plastic viscosity. The effect of the dimensionless numbers on the flow showed that the yield-stress fluid could mimic a Newtonian behavior in the pre-described conditions. Although, the fluid still held the non-Newtonian character distinguished by the dependency on the Bingham number Bn. This returned to the increase of the apparent viscosity with Bn which contributed to the weakening of the convective streams, and consequently, reduced convective thermal transport.

Results of an experimental investigation on heat transfer characteristics of kerosene flowing in vertical upward high-flux tubes at supercritical pressures are presented. Three metal powder-coated tubes (high-flux tubes) and one smooth tube have been tested and compared. The three high-flux tubes all perform much better than the smooth tube at the same parameters of the tube and same working conditions. The observed enhancement in heat transfer is mainly due to the disturbance introduced in the low field by the metal powder coatings and the differences in the thermophysical properties. The heat transfer coefficient in the metal-coated tube (200 mesh) has been found to be 2.5 times that in the smooth tube. Yet, it has been found that both too large and too small of a particle diameter of the metal powder coating on the tube surface could cause the heat transfer to deteriorate. The high-flux tube with a particle diameter of 200 mesh was found to exhibit the best cooling performance. The pressure drop was observed to increase with the increase of the particle diameter. However, the pressure drop was found to be three orders of magnitude smaller than the working pressure in the test section, thus the pressure drop for all practical purposes may be neglected. The density, viscosity, and thermal conductivity of kerosene at different temperatures and supercritical pressures were evaluated using the extended corresponding state principle, which has been proven to show good consistency with the experimental results.

The mixed convective heat transfer of a micropolar nanofluid in a square lid-driven cavity has been numerically studied. The lid is thermally insulated, the side walls are kept cold, and the bottom wall is kept hot with sinusoidally thermal boundary condition. The governing equations were solved by finite volume method using the SIMPLE algorithm. The effect of Grashof number (10 2 –10 5 ), the volume fraction of nanoparticles (0.0–0.1), and micropolarity (0.0–2.0) has been investigated on the heat transfer of Al 2 O 3 –water nanofluid. Also, the variable model was used to calculate fluid viscosity and thermal conductivity coefficient of the nanofluid. The results showed that an increase in Grashof amplifies the buoyancy force and enhances the Nusselt number. Also, an increase in vortex viscosity at low Grashof numbers strengthens the forced convection and increases the Nusselt number over the bottom wall. However, at Gr = 10 5 , the increase in vortex viscosity up to K = 1.0 leads to a decrease in the amount of heat transfer, but its further increase entails the increase in heat transfer. Although the addition of nanoparticles to the fluid improves heat transfer rate, the extent of improvement at nonzero K values is lower than that in the Newtonian fluid. The comparison of the average Nusselt number computed on the hot wall under two different states of temperature-depended thermo-physical properties and constant thermo-physical properties reveals that their difference is more significant for the Newtonian fluid especially at higher volume fraction.

Stability analysis for the Walters-B model saturated with permeable nanofluid is taken under study including cross diffusion effects. The porous medium is defined using modified Darcy model, and the nanofluid is considered to have the impact of thermophoresis and Brownian motion. The thermal energy equation includes the effects of diffusion and also cross diffusion. For the study of linear theory, normal mode procedure is applied and to understand the nonlinear theory, the method of minimal representation of double Fourier series is utilized. The effects of nondimensional parameters such as concentration Rayleigh number, Lewis number, Soret and Dufour parameters, Solutal Rayleigh number, elastic parameter, Prandtl number, viscosity ratio, and conductivity ratio on the stationary and oscillatory convections are represented graphically. The effect of time on transient Nusselt numbers is also taken under investigation. It is concluded that when time is small, the three Nusselt numbers oscillate for all the governing parameters and approach to steady-state as time increases.

Turbulent characteristics of Czochralski melt flow are presented using the unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence modeling approach. Three-dimensional, transient computations were performed using the Launder and Sharma low-Re k-ε model and Menter shear stress transport (SST) k-ω model on an idealized Czochralski setup with counterrotating crystal and crucible. A comparative assessment is performed between these two Reynolds-averaged Navier–Stokes (RANS) models in capturing turbulent thermal and flow behaviors. It was observed that the SST k-ω model predicted a better resolution of the Czochralski melt flow capturing the near wall thermal gradients, resolving stronger convective flow at the melt free surface, deciphering more number of characteristics Czochralski recirculating cells along with predicting large number of coherent eddy structures and vortex cores distributed in the melt and hence a larger level of turbulent intensity in the Czochralski melt compared with that by Launder and Sharma low-Re k-ε model.

This paper presents an investigation of a three-phase oscillating heat pipe (3P OHP). The working fluid in the OHP consists of phase change material (PCM) and water. During the operation, the PCM changes the phase between solid and liquid, and water changes phase between liquid and vapor. The OHP investigated herein contains three phases: solid, liquid, and vapor. Erythritol was selected as the PCM with an instant cooling effect when dissolved in water due to the high fusion heat of 340 J/g. When the working fluid flows into the evaporator section, the PCM solid phase of the working fluid can become liquid phase in the evaporator, and the PCM liquid phase of the working fluid become solid phase in the condenser. The effects of heat input ranging from 100 to 420 W, and the erythritol concentration ranging from 1 to 50 wt % on the slug oscillations, and the OHP thermal performance was investigated. Experimental results show that while the erythritol can help to increase the heat transfer performance of an OHP, the heat transfer performance depends on the erythritol concentration. With a range of 1–5 wt % concentration of erythritol/water mixtures, a maximum 10% increase in the thermal performance was observed. When the erythritol concentration of erythritol/water mixtures was increased to a range of 10–50 wt %, the thermal performance of OHPs was lower than pure water-filled OHP, and the thermal performance decreased as the erythritol concentration was further increased. In addition, visualization results showed that slug oscillation amplitudes and velocities were reduced in the OHPs with erythritol solution compared with water-filled OHP.

This article presents a numerical study of particle deposition in two fluids, i.e., liquid and droplet flow in a single row tube bundle heat exchanger. The tubes in the heat exchanger are modeled as heating sources. Two level-set functions are used to capture the liquid-droplet interface and the liquid-deposit front. The effects of different parameters, including Damköhler number, thermal conductivity of the deposit, viscosity of the liquid, and the heating power of the tube on the flow and heat transfer, are investigated. The deposit profiles on the tube surface are analyzed. Comparison is made for the averaged Nusselt number for the case without and with deposition. It is found that the tube surface has a thicker deposit at the upstream facing side compared with that of the downstream facing side. Generally, the heat transfer rate reduces with the growth of the deposit. Under certain conditions, heat transfer can be increased because of the increase in fluid velocity due to blockage of the flow area by the deposit. The averaged Nusselt number oscillated temporally in response to the droplet movement across the tube. Generally, the temperature at the liquid-deposit front decreases with thicker deposit formed. The averaged Nusselt number along the liquid-deposit front increases to a critical value initially, and it starts to decrease with the growth of the deposit.

In this study, the influence of the applied magnetic field is investigated for magneto-micropolar fluid flow through an inclined channel of parallel porous plates with constant pressure gradient. The lower plate is maintained at constant temperature and the upper plate at a constant heat flux. The governing motion and energy equations are coupled while the effect of the applied magnetic field is taken into account, adding complexity to the already highly correlated set of differential equations. The governing equations are solved numerically by explicit Runge–Kutta. The velocity, microrotation, and temperature results are used to evaluate second law analysis. The effects of characteristic and dominate parameters such as Brinkman number, Hartmann Number, Reynolds number, and micropolar viscosity parameter are discussed on velocity, temperature, microrotation, entropy generation, and Bejan number in different diagrams. The results depicted that the entropy generation number rises with the increase in Brinkman number and decays with the increase in Hartmann Number, Reynolds number, and micropolar viscosity parameter. The application of the magnetic field induces resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the presence of magnetic field tends to increase the contribution of fluid friction entropy generation to the overall entropy generation; in other words, the irreversibilities caused by heat transfer reduced. Therefore, to minimize entropy, Brinkman number and Hartmann Number need to be controlled.

Steam-assisted gravity drainage (SAGD) process has been an optimized method to explore heavy oil reservoirs in the world. The oil viscosity reduction and gravity force near the interface of steam–chamber are the main development mechanisms. In classical models, conductive heat transfer plays the only or dominant role in the heat transmission from high-temperature steam to low-temperature oil sands. Although some mathematical studies have paid attention to the convective heat transfer, the role of heat transfer by flowable oil normal to the steam–chamber interface has been given little attention. In SAGD, the viscosity of bitumen can be reduced by several orders of magnitude by the release of latent heat from injected steam. In this study, an analytical model is developed for the heat transfer process induced by flowable oil. Also, in order to accurately simulate the oil viscosity characteristics in steam–chamber, a correlation between oil viscosity and pressure is proposed. Results indicate that the oil mobility plays an important role on the flow normal to interface when the distance is smaller than 6 m. Even under the most extreme circumstances ( μ w = 0.1127 cp), the flowing of oil normal to steam–chamber interface also cannot be ignored. Comparing to Irani and Ghannadi model, it can be easy to draw the conclusion that the new model consists with the underground test facility (UTF) field data much better. This new analytical model will benefit to understanding the convective heat transfer mechanism in SAGD process.

In this paper, the effect of magnetic field on natural convection of Al 2 O 3 /water nanofluid in an enclosure containing twin protruding heat sources placed on top and bottom walls arranged in-line and staggered manner is presented. For this purpose, coupled equations governing fluid flow and heat transfer are solved in Cartesian framework using streamline upwind/Petrov–Galerkin (SUPG) finite element method. Numerical computations are performed to predict the fluid flow, heat transfer, and entropy generation for a wide range of Hartmann number (0.0 ≤ Ha ≤ 100.0), Rayleigh number ( 10 3 ≤ Ra ≤ 10 6 ), and nanoparticle volume fraction ( 0.0 ≤ ϕ ≤ 0.1 ). The simulated results indicate that, for both in-line and staggered arrangement, the entropy generation due to heat transfer is significant along isothermal surfaces, whereas entropy generation due to fluid friction is higher at no-slip walls and along the regions of contact between adjacent recirculation cells. For both in-line and staggered arrangement, increase in global total entropy generation and average Nusselt number along top and bottom heat sources is obtained with decreasing Ha and increasing Ra. Furthermore, for both in-line and staggered arrangement, variation in global total entropy generation and average Nusselt number along top and bottom heat sources with increasing nanoparticle volume fraction, depend on both Ha and Ra.

A mathematical model has been constructed for determining the effects of variable viscosity and thermal conductivity on unsteady Jeffery flow over a stretching sheet in the presence of magnetic field and heat generation. The governing partial differential equations are transformed into a set of nonlinear coupled ordinary differential equations and then solved numerically by using the Runge–Kutta–Fehlberg method with shooting technique. A critical analysis with earlier published papers is done and the results are found to be in accordance with each other. Numerical solutions are then obtained and investigated in detail for different physical parameters such as skin-friction coefficient and reduced Nusselt number as well as other parametric values such as the velocity and temperature.

In this study, the influences of the applied magnetic field and fluid elasticity were investigated for a nonlinear viscoelastic fluid obeying the Carreau equation between concentric annulus where the inner cylinder rotates at a constant angular velocity and the outer cylinder is stationary. The governing motion and energy balance equations are coupled while viscous dissipation is taken into account, adding complexity to the already highly correlated set of differential equations. The numerical solution is obtained for the narrow gap limit and steady-state base flow. Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow was investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effects of the Hartmann number, the Brinkman number, the Deborah number, and the fluid elasticity on the stability of the flow were investigated. The application of the magnetic field induces a resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the study shows that the presence of magnetic field tends to slowdown the fluid motion and thus increases the fluid temperature. However, the total entropy generation number decreases as the Hartmann number and fluid elasticity increase and it increases with increasing Brinkman number.

The thermal characteristics of Bingham plastic fluid flows are analyzed in circular microchannels under uniform wall heat flux condition. The analytic approach presented here reveals that the governing parameters are Bingham number, dimensionless radius of the plug flow region, and Brinkman number. The results demonstrate that there is a strong influence of viscous dissipation on heat transfer and entropy generation for Brinkman numbers greater than a specific value. With increasing the Brinkman number and dimensionless radius of the plug flow region, entropy generation is increased, while the Nusselt number is decreased. The influence of these parameters on the entropy generation from heat transfer is strongly higher than the entropy generation from fluid friction. The average dimensionless total entropy shows that the Bingham plastic fluids generate entropy more than Newtonian fluids; also, an increase in the dimensionless radius of the plug flow region results in increasing the average dimensionless total entropy generation. By letting the dimensionless radius of the plug flow region equal to zero, the generalized expressions and results will be simplified to Newtonian fluids.