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Technical Brief

# Effect of Thermal Conductivity Ratio on Laminar Double-Diffusive Free Convection in a Porous Cavity

[+] Author and Article Information
Paulo H. S. Carvalho

Departamento de Energia—IEME,
Instituto Tecnológico de Aeronáutica—ITA,
São José dos Campos, SP 12228-900, Brazil

Marcelo J. S. de Lemos

Fellow ASME
Departamento de Energia—IEME,
Instituto Tecnológico de Aeronáutica—ITA,
São José dos Campos, SP 12228-900, Brazil
e-mail: delemos@ita.br

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 28, 2016; final manuscript received April 20, 2017; published online June 1, 2017. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 139(10), 104506 (Jun 01, 2017) (4 pages) Paper No: HT-16-1696; doi: 10.1115/1.4036617 History: Received October 28, 2016; Revised April 20, 2017

## Abstract

This work presents a study on double-diffusive free convection in a porous square cavity using the thermal equilibrium model. Transport equations are discretized using the control-volume method, and the system of algebraic equations is relaxed via the SIMPLE algorithm. The effect of ks/kf on average Nusselt and Sherwood values was investigated. Results show that increasing ks/kf affects Nuw and Shw boosting mass transfer at the expense of reducing overall heat transport across the enclosure.

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## References

Nield, D. A. , and Bejan, A. , 2017, Convection in Porous Media, 5th ed., Springer, New York.
Ingham, D. B. , and Pop, I. , 1998, Transport Phenomena in Porous Media, Elsevier, Amsterdam, The Netherlands.
Bejan, A. , 1979, “ On the Boundary Layer Regime in a Vertical Enclosure Filled With a Porous Medium,” Lett. Heat Mass Transfer, 6(2), pp. 93–102.
Manole, D. M. , and Lage, J. L. , 1992, “ Numerical Benchmark Results for Natural Convection in a Porous Medium Cavity,” Heat and Mass Transfer in Porous Media, Vol. HTD-216, ASME, New York, pp. 55–60.
Trevisan, O. V. , and Bejan, A. , 1985, “ Natural Convection With Combined Heat and Mass Transfer Buoyancy Effects in a Porous Medium,” Int. J. Heat Mass Transfer, 28(8), pp. 1597–1611.
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.
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.
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.
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.
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.
Bhadauria, B. , 2012, “ Double-Diffusive Convection in a Saturated Anisotropic Porous Layer With Internal Heat Source,” Transp. Porous Media, 92(2), pp. 299–320.
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.
Yadav, D. , Agrawal, G. S. , and Bhargava, R. , 2013, “ Onset of Double-Diffusive Nanofluid Convection in a Layer of Saturated Porous Medium With Thermal Conductivity Ratio and Viscosity Variation,” J. Porous Media, 16(2), pp. 105–121.
de Lemos, M. J. S. , 2012, Turbulence in Porous Media: Modeling and Applications, 2nd ed., Elsevier, Amsterdam, Netherlands.
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.
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. 666–676.
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.
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.
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.
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, 66(11), pp. 1173–1194.
Carvalho, P. H. S. , and de Lemos, M. J. S. , 2014, “ Turbulent Free Convection in a Porous Cavity Using the Two-Temperature Model and the High Reynolds Closure,” Int. J. Heat Mass Transfer, 79, pp. 105–115.
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.
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.
Alazmi, B. , and Vafai, K. , 2000, “ Analysis of Variants Within the Porous Media Transport Models,” ASME J. Heat Transfer, 122(2), pp. 303–326.
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, New York.
Stone, H. L. , 1968, “ Iterative Solution of Implicit Approximations of Multi-Dimensional Partial Differential Equations,” SIAM J. Numer. Anal., 5(3), pp. 530–558.

## Figures

Fig. 1

Effects of ks/kf for aiding drive, ϕ = 0.8, Da = 10−7, Le = 1, and N = 10 on (a) Nuw, (b) Shw, and (c) v/V0 at X* = 0.003

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