This work presents a study of double-diffusive free convection in a porous square cavity under turbulent flow regime and with aiding drive. The thermal nonequilibrium model was employed to analyze the energy and mass transport across the enclosure. Governing equations were time- and volume-averaged according to the double-decomposition concept. Analysis of a modified Lewis number, Lem, showed that for porous media, this parameter presents opposite behavior when varying the thermal conductivity ratio or the Schmidt number, while maintaining the same value for Lem. Differently form free flow, the existence of the porous matrix contributes to the overall thermal diffusivity of the medium, whereas mass diffusivity is only effective within the fluid phase for an inert medium. Results indicated that increasing Lem through an increase in Sc reduces flow circulation inside porous cavities, reducing Nuw and increasing Shw. Results further indicate that increasing the buoyancy ratio N promotes circulation within the porous cavity, leading to an increase in turbulence levels within the boundary layers. Partial contributions of each phase of the porous cavity (solid and fluid) to the overall average Nusselt number become independent of n for higher values of the thermal conductivity ratio, ks/kf. Further, for high values of ks/kf, the average Nusselt number drops as N increases.
Issue Section:
Natural and Mixed Convection
References
1.
Condorelli
, P.
, and George
, S. C.
, 1999
, “Theoretical Gas Phase Mass Transfer Coefficients for Endogenous Gases in the Lungs
,” Ann. Biomed. Eng.
, 27
(3
), pp. 326
–339
.2.
Chilton
, T. H.
, and Colburn
, A. P.
, 1935
, “Distillation and Absorption in Packed Columns—A Convenient Design and Correlation Method
,” Industrial and Eng. Chem.
, 27
(3
), pp. 255
–260
.3.
Nield
, D. A.
, and Bejan
, A.
, 2017
, Convection in Porous Media
, 5th ed., Springer
, New York
.4.
Ingham
, D. B.
, and Pop
, I.
, 1998
, Transport Phenomena in Porous Media
, Elsevier
, Amsterdam, The Netherlands
.5.
Hsu
, C. T.
, and Cheng
, P.
, 1990
, “Thermal Dispersion in a Porous Medium
,” Int. Heat Mass Transfer
, 33
(8
), pp. 1587
–1597
.6.
Bear
, J.
, 1972
, Dynamics of Fluids in Porous Media
, American Elsevier Pub. Co
, New York
.7.
Whitaker
, S.
, 1966
, “Equations of Motion in Porous Media
,” Chem. Eng. Sci.
, 21
(3
), pp. 291
–300
.8.
Whitaker
, S.
, 1967
, “Diffusion and Dispersion in Porous Media
,” J. Am. Inst. Chem. Eng.
, 13
(3
), pp. 420
–427
.9.
Gray
, W. G.
, and Lee
, P. C. Y.
, 1977
, “On the Theorems for Local Volume Averaging of Multiphase System
,” Int. J. Multiphase Flow
, 3
(4), pp. 333
–340
.10.
Trevisan
, O. V.
, and Bejan
, A.
, 1985
, “Natural Convection With Combined Heat Mass Transfer Buoyancy Effects in a Porous Medium
,” Int. J. Heat Mass Transfer
, 28
(8
), pp. 1597
–1611
.11.
Trevisan
, O. V.
, and Bejan
, A.
, 1986
, “Mass and Heat Transfer by Natural Convection in a Vertical Slot Filled With Porous Medium
,” Int. J. Heat Mass Transfer
, 29
(3
), pp. 403
–415
.12.
Goyeau
, B.
, Songbe
, J. P.
, and Gobin
, D.
, 1996
, “Numerical Study of Double-Diffusive Natural Convection in a Porous Cavity Using the Darcy-Brinkman Formulation
,” Int. J. Heat Mass Transfer
, 39
(7
), pp. 1363
–1378
.13.
Mamou
, M.
, Vasseur
, P.
, and Bilgen
, E.
, 1995
, “Multiple Solutions for Double-Diffusive Convection in a Vertical Porous Enclosure
,” Int. J. Heat Mass Transfer
, 38
(10
), pp. 1787
–1798
.14.
Mamou
, M.
, Hasnaoui
, M.
, Amahmid
, A.
, and Vasseur
, P.
, 1998
, “Stability Analysis of Double-Diffusive Convection in a Ertical Brinkman Porous Enclosure
,” Int. Commun. Heat Mass Transfer
, 25
(4
), pp. 491
–500
.15.
Bennacer
, R.
, Tobbal
, A.
, Beji
, H.
, and Vasseur
, P.
, 2001
, “Double Diffusive Convection in a Vertical Enclosure Filled With Anisotropic Porous Media
,” Int. J. Therm. Sci.
, 40
(1
), pp. 30
–41
.16.
Chen
, S.
, Tölke
, J.
, and Krafczyk
, M.
, 2010
, “Numerical Investigation of Double-Diffusive (Natural) Convection in Vertical Annuluses With Opposing Temperature and Concentration Gradients
,” Int. J. Heat Fluid Flow
, 31
(2
), pp. 217
–226
.17.
Chen
, S.
, Liu
, H.
, and Zheng
, C.
, 2012
, “Numerical Study of Turbulent Double-Diffusive Natural Convection in a Square Cavity by LES-Based Lattice Boltzmann Model
,” Int. J. Heat Mass Transfer
, 55
(17–18
), pp. 4862
–4870
.18.
Bhadauria
, B.
, 2012
, “Double-Diffusive Convection in a Saturated Anisotropic Porous Layer With Internal Heat Source
,” Transp. Porous Media
, 92
(2
), pp. 299
–320
.19.
Malashetty
, M. S.
, Pop
, I.
, Kollu
, P.
, and Sidram
, W.
, 2012
, “Soret Effect on Double-Diffusive Convection in a Darcy Porous Medium Saturated With a Couple Stress Fluid
,” Int. J. Therm. Sci.
, 53
, pp. 130
–140
.20.
de Lemos
, M. J. S.
, 2012
, Turbulence in Porous Media: Modeling and Applications
, 2nd ed., Elsevier
, Amsterdam, The Netherlands
.21.
Braga
, E. J.
, and de Lemos
, M. J. S.
, 2004
, “Turbulent Natural Convection in a Porous Square Cavity Computed With a Macroscopic k-ε Model
,” Int. J. Heat Mass Transfer
, 47
(26
), pp. 5639
–5650
.22.
Braga
, E. J.
, and de Lemos
, M. J. S.
, 2006
, “Simulation of Turbulent Natural Convection in a Porous Cylindrical Annulus Using a Macroscopic Two-Equation Model
,” Int. J. Heat Mass Transfer
, 49
(23–24
), pp. 4340
–4351
.23.
Braga
, E. J.
, and de Lemos
, M. J. S.
, 2008
, “Computation of Turbulent Free Convection in Left and Right Tilted Porous Enclosures Using a Macroscopic k-Eps Model
,” Int. J. Heat Mass Transfer
, 51
(21–22
), pp. 5279
–5287
.24.
Braga
, E. J.
, and de Lemos
, M. J. S.
, 2006
, “Turbulent Heat Transfer in an Enclosure With a Horizontal Porous Plate in the Middle
,” ASME J. Heat Transfer
, 128
(11
), pp. 1122
–1129
.25.
Braga
, E. J.
, and de Lemos
, M. J. S.
, 2009
, “Larninar and Turbulent Free Convection in a Composite Enclosure
,” Int. J. Heat Mass Transfer
, 52
(3–4
), pp. 588
–596
.26.
Graminho
, D. R.
, and de Lemos
, M. J. S.
, 2008
, “Laminar Confined Impinging Let Into a Porous Layer
,” Numer. Heat Transfer—Part A Appl.
, 54
(2
), pp. 151
–177
.27.
Saito
, M. B.
, and de Lemos
, M. J. S.
, 2005
, “Interfacial Heat Transfer Coefficient for Non-Equilibrium Convective Transport in Porous Media
,” Int. Commun. Heat Mass Transfer
, 32
(5
), pp. 667
–677
.28.
Saito
, M. B.
, and de Lemos
, M. J. S.
, 2006
, “A Correlation for Interfacial Heat Transfer Coefficient for Turbulent Flow Over an Array of Square Rods
,” ASME J. Heat Transfer
, 128
(5
), pp. 444
–452
.29.
Saito
, M. B.
, and de Lemos
, M. J. S.
, 2010
, “A Macroscopic Two-Energy Equation Model for Turbulent Flow and Heat Transfer in Highly Porous Media
,” Int. J. Heat Mass Transfer
, 53
(11–12
), pp. 2424
–2433
.30.
Carvalho
, P. H. S.
, and de Lemos
, M. J. S.
, 2013
, “Turbulent Free Convection in a Porous Square Cavity Using the Thermal Equilibrium Model
,” Int. Commun. Heat Mass Transfer
, 49
, pp. 10
–16
.31.
Carvalho
, P. H. S.
, and De Lemos
, M. J. S.
, 2014
, “Passive Laminar Heat Transfer Across Porous Cavities Using the Thermal Non-Equilibrium Model
,” Numer. Heat Transfer. Part A, Appl.
, 66
(11
), pp. 1173
–1194
.32.
Carvalho
, P. H. S.
, and de Lemos
, M. J. S.
, 2014
, “Turbulent Free Convection in a Porous Square Cavity Using the Two-Temperature Model and the High Reynolds Closure
,” Int. J. Heat Mass Transfer
, 79
, pp. 105
–115
.33.
de Lemos
, M. J. S.
, and Tofaneli
, L. A.
, 2004
, “Modeling of Double-Diffusive Turbulent Natural Convection in Porous Media
,” Int. J. Heat Mass Transfer
, 47
(19–20
), pp. 4221
–4231
.34.
Tofaneli
, L. A.
, and de Lemos
, M. J. S.
, 2009
, “Double-Diffusive Turbulent Natural Convection in a Porous Square Cavity With Opposing Temperature and Concentration Gradients
,” Int. Commun. Heat Mass Transfer
, 36
(10
), pp. 991
–995
.35.
Carvalho
, P. H. S.
, and de Lemos
, M. J. S.
, 2017
, “Effect of Thermal Conductivity Ratio on Laminar Double-Diffusive Free Convection in a Porous Cavity
,” ASME J. Heat Transfer
, 139
(10
), p. 104506
.36.
de Lemos
, M. J. S.
, 2014
, “Analysis of Turbulent Double-Diffusive Free Convection in Porous Media Using the Two-Energy Equation Model
,” Int. Commun. Heat Mass Transfer
, 52
, pp. 132
–139
.37.
Carvalho
, P. H. S.
, and de Lemos
, M. J. S.
, 2017
, “Double-Diffusive Laminar Free Convection in a Porous Cavity Simulated With the Two-Energy Equation Model
,” Int. Commun. Heat Mass Transfer
, 82
, pp. 89
–96
.38.
Krishnan
, S.
, Murthy
, J. Y.
, and Garimella
, S. V.
, 2004
, “A Two-Temperature Model for the Analysis of Passive Thermal Control Systems
,” ASME J. Heat Transfer
, 126
(4
), pp. 628
–637
.39.
AlazmiVafai
, K.
, 2000
, “Analysis of Variants Within the Porous Media Transport Models
,” ASME J. Heat Transfer
, 122
(2
), pp. 303
–326
.40.
Ergun, S.,
1952
, “Fluid Flow Through Packed Columns
,” Chem. Eng. Prog.
, 48
(2
), pp. 89
–94
.41.
Wakao
, N.
, Kaguei
, S.
, and Funazkri
, T.
, 1979
, “Effect of Fluid Dispersion Coefficients on Particle-to-Fluid Heat Transfer Coefficients in Packed Bed
,” Chem. Eng. Sci.
, 34
(3
), pp. 325
–336
.42.
Kuwahara
, F.
, Shirota
, M.
, and Nakayama
, A.
, 2001
, “A Numerical Study of Interfacial Convective Heat Transfer Coeficiente in Two-Energy Equation Model for Convection in Porous Media
,” Int. J. Heat Mass Transfer
, 44
(6
), pp. 1153
–1159
.43.
Kader
, B. A.
, and Yaglom
, A. M.
, 1972
, “Heat and Mass Transfer Laws for Fully Turbulent Wall Flows
,” Int. J. Heat Mass Transfer
, 15
(12
), pp. 2329
–2351
.44.
Suga
, 2016
, “Understanding and Modelling Turbulence Over and Inside Porous Media
,” Flow, Turbul. Combust.
, 96
(3
), pp. 717
–756
.45.
Silva
, R. A.
, and de Lemos
, M. J. S.
, 2011
, “Turbulent Flow in a Composite Channel
,” Int. Commun. Heat Mass Transfer
, 38
(8
), pp. 1019
–1023
.46.
Silva
, R. A.
, and de Lemos
, M. J. S.
, 2003
, “Turbulent Flow in a Channel Occupied by a Porous Layer Considering the Stress Jump at the Interface
,” Int. J. Heat Mass Transfer
, 46
(26
), pp. 5113
–5121
.47.
de Lemos
, M. J. S.
, 2009
, “Turbulent Flow around Fluid-Porous Interfaces Computed With a Diffusion-Jump Model for k and ε Transport Equations
,” Transp. Porous Media
, 78
(3
), pp. 331
–346
.48.
Beavers
, G. S.
, and Joseph
, D. D.
, 1967
, “Boundary Conditions at a Naturally Permeable Wall
,” J. Fluid Mech.
, 30
(1
), pp. 197
–207
.49.
Lai
, F. C.
, and Kulacki
, F. A.
, 1991
, “Coupled Heat and Mass Transfer by Natural Convection From Vertical Surfaces in Porous Media
,” Int. J. Heat Mass Transfer
, 34
(4–5
), pp. 1189
–1194
.50.
Javaheri
, M.
, and Abedi
, J.
, 2010
, “Linear Stability Analysis of Double-Diffusive Convection in Porous Media, With Application to Geological Storage of CO2
,” Transp. Porous Media
, 84
(2
), pp. 441
–456
.51.
Trevisan
, O. V.
, and Bejan
, A.
, 1987
, “Mass and Heat Transfer by High Rayleigh Number Convection in a Porous Medium Heated From below
,” Int. J. Heat Mass Transfer
, 30
(11
), pp. 2341
–2356
.52.
Rosenberg
, N. D.
, 1992
, “Thermohaline Convection in a Porous Medium Heated From below
,” Int. J. Heat Mass Transfer
, 35
(5
), pp. 1261
–1273
.53.
Patankar
, S. V.
, 1980
, Numerical Heat Transfer and Fluid Flow
, Hemisphere
, New York
.54.
Stone
, H. L.
, 1968
, “Iterative Solution of Implicit Approximations of Multi-Dimensional Partial Differential Equations
,” SIAM J. Numer. Anal.
, 5
(3
), pp. 530
–558
.55.
Yu
, W.
, France
, D. M.
, Routbort
, J. L.
, and Choi
, S. U. S.
, 2008
, “Review and Comparison of Nanofluid Thermal Conductivity and Heat Transfer Enhancements
,” Heat Transfer Eng.
, 29
(5
), pp. 432
–460
.56.
Ampofo
, F.
, and Karayiannis
, T. G.
, 2003
, “Experimental Benchmark Data for Turbulent Natural Convection in an Air Filled Square Cavity
,” Int. J. Heat Mass Transfer
, 46
(19
), pp. 3551
–3572
.57.
Wilcox
, D. C.
, 1998
, Turbulence Modeling for CFD
, 2nd ed., DCW Industries
, La Cañada Flintridge, CA
.58.
de Lemos
, M. J. S.
, and Braga
, E. J.
, 2018
, “Use of Porous-Continuum and Continuum Models for Determining the Permeability of Porous Cavities Under Turbulent Free Convection
,” Numer. Heat Transfer, Part B: Fundam.
, 73
(2
), pp. 78
–93
.59.
de Lemos
, M. J. S.
, and Coutinho
, J. E. A.
, 2017
, “Turbulent Flow in Porous Combustor Using the Thermal Non-Equilibrium Hypothesis and Radiation Boundary Condition
,” Int. J. Heat Mass Transfer
, 115
, pp. 1043
–1054
.60.
de Lemos
, M. J. S.
, and Pivem
, A. C.
, 2014
, “Turbulent Heat Transfer in a Counterflow Moving Porous Bed Using a Two-Energy Equation Model
,” Int. J. Heat Mass Transfer
, 72
, pp. 98
–113
.61.
Pivem
, A. C.
, and de Lemos
, M. J. S.
, 2013
, “Turbulence Modeling in a Parallel Flow Moving Porous Bed
,” Int. Commun. Heat Mass Transfer
, 48
, pp. 1
–7
.62.
Pivem
, A. C.
, and de Lemos
, M. J. S.
, 2013
, “Numerical Simulation of a Crossflow Moving Porous Bed Using a Thermal Non-Equilibrium Model
,” Int. J. Heat Mass Transfer
, 67
, pp. 311
–325
.63.
de Lemos
, M. J. S.
, and Dorea
, F. T.
, 2011
, “Simulation of Turbulent Impinging Jet Into a Layer of Porous Material Using a Two-Energy Equation Model
,” Numer. Heat Transfer
, 59
(10
), pp. 769
–798
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