Free Convection in a Darcy Thermally Stratified Porous Medium That Embeds a Vertical Wall of Constant Heat Flux and Concentration

Authors: Maria Neagu

Abstract:

This paper presents the heat and mass driven natural convection succession in a Darcy thermally stratified porous medium that embeds a vertical semi-infinite impermeable wall of constant heat flux and concentration. The scale analysis of the system determines the two possible maps of the heat and mass driven natural convection sequence along the wall as a function of the process parameters. These results are verified using the finite differences method applied to the conservation equations.

Keywords: Finite difference method, natural convection, porous medium, scale analysis, thermal stratification.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1110974

References:

[1] G. Degan, C. Akowanou, N. C. Awanou, “Transient natural convection of non-Newtonian fluids about a vertical surface embedded in an anisotropic porous medium,” International Journal of Heat and Mass Transfer, vol. 50, no. 23−24, pp. 4629−4639, 2007.
[2] C. ‘O.-K. Chen, C.-R. Lin, “Natural convection from an isothermal vertical surface embedded in a thermally stratified high-porosity medium,” International Journal of Engineering Science, vol. 33, no. 1, pp. 131−138, 1995.
[3] K. Tewari. P. Singh, “Natural convection in a thermally stratified fluid saturated porous medium,” International Journal of Engineering Science, vol. 30, no. 8, pp. 1003−1007, 1992.
[4] C.-I. Hung, C.-H. Chen, C.-B. Chen, “Non-Darcy free convection along a nonisothermal vertical surface in a thermally stratified porous medium,” International Journal of Engineering Science, vol. 37, no. 4, pp. 477−495, 1999.
[5] F. C. Lai, “Non-Darcy natural convection from a line source of heat in saturated porous medium,” International Communications in Heat and Mass Transfer, vol. 18, no. 4, pp. 445−457, 1991.
[6] Z. H. Kodah, A. M. Al-Gasem, “Non-Darcy mixed convection from a vertical plate in saturated porous media-variable surface heat flux,” Heat and Mass Transfer , vol. 33, no. 5−6, pp. 377−382, 1998.
[7] R. S. Telles, O. V. Trevisan, “Dispersion in heat and mass transfer natural convection along vertical boundaries in porous media,” International Journal of Heat and Mass Transfer, vol. 36, no. 5, pp. 1357−1365, 1993.
[8] D. Angirasa, G. P. Peterson, “Natural convection heat transfer from an isothermal vertical surface to a fluid saturated thermally stratified porous medium,” International Journal of Heat and Mass Transfer, vol. 40, no. 18, pp. 4329−4335, 1997.
[9] J.-Y. Jang, J.-R. Ni, “Transient free convection with mass transfer from an isothermal vertical flat plate embedded in a porous medium,” International Journal of Heat and Fluid Flow, vol. 10, no. 1, pp. 59−65, 1989.
[10] A. Bejan, K. R. Khair, “Heat and mass transfer by natural convection in a porous medium,” International Journal of Heat and Mass Transfer, vol. 28, no. 5, pp. 909−918, 1985.
[11] D. Angirasa, G. P. Peterson, I. Pop, “Combined heat and mass transfer by natural convection with opposing buoyancy effects in a fluid saturated porous medium,” International Journal of Heat and Mass Transfer, vol. 40, no. 12, pp. 2755−2773, 1997.
[12] I. Pop, H. Herwig, “Transfer mass transfer from an isothermal vertical flat plate embedded in a porous medium,” International Communications in Heat and Mass Transfer, vol. 17, no. 6, pp. 813−821, 1990.
[13] C. Allain, M. Cloitre, A. Mongruel, “Scaling in flows driven by heat and mass convection in a porous medium,” Europhysics Letters, vol. 20, no. 4, pp. 313−318, 1992.
[14] M. A. El-Hakiem, M. F. El-Amin, “Mass transfer effects on the non- Newtonian fluids past a vertical plate embedded in a porous medium with non-uniform surface heat flux,” Heat and Mass Transfer, vol. 37, no. 2−3, pp. 293−297, 2001.
[15] R. Tsai, J. S. Huang, “Numerical study of Soret and Dufour effects on heat and mass transfer from natural convection flow over a vertical porous medium with variable wall heat fluxes,” Computational Materials Science, vol. 47, no. 1, pp. 23−30, 2009.
[16] C.-Y. Cheng, “Natural convection heat and mass transfer of non- Newtonian power law fluids with yield stress in porous media from a vertical plate with variable wall heat and mass fluxes,” International Communications in Heat and Mass Transfer, vol. 33, no. 9, pp. 1156−1164, 2006.
[17] M. K. Partha, P. V. S. N. Murthy, G. P. Raja Sekhar, “Soret and Dufour effects in a non-Darcy porous medium,” ASME Journal of Heat Transfer, vol. 128, no. 6, pp. 605−610, 2006.
[18] R. R. Kairi, P. A. L. Narayana, P. V. S. N. Murthy, “The effect of double dispersion on natural convection heat and mass transfer in a non- Newtonian fluid saturated non-Darcy porous medium,” Transport in Porous Media, vol. 76, no. 3, pp. 377−390, 2009.
[19] P. Singh, K. Tewari, “Non-Darcy free convection from vertical surfaces in thermally stratified porous media,” International Journal of Engineering Science, vol. 31, no. 9, pp. 1233−1242, 1993.
[20] I. Y. Hussain, B. K. Raheem, “Natural convection heat transfer from a plane wall to thermally stratified porous media,” International Journal of Computer Applications, vol. 65, no. 1, pp. 42−49, 2013.
[21] P. Singh, K. Sharma, “Integral method to free convection in thermally stratified porous medium,” Acta Mechanica, vol. 83, no. 3−4, pp. 157−163, 1990.
[22] P. A. Lakshmi Narayana, P. V. S. N. Murthy, “Free convective heat and mass transfer in a doubly stratified non-Darcy porous medium,” ASME Journal of Heat Transfer , vol. 128, no. 11, pp. 1204−1212, 2006.
[23] S. W. Armfield, J. C. Patterson, W. Lin, “Scaling investigation of the natural convection boundary layer on an evenly heated plate,” International Journal of Heat and Mass Transfer, vol. 50, no. 7-8, pp. 1592-1602, 2007.
[24] A. Bejan, Convection Heat Transfer. New York: Wiley, 1995, pp. 18−21, pp. 535-539.
[25] C. A. J. Fletcher, Computational Techniques for Fluid Dynamics 1. Fundamental and General Techniques. New York: Springer-Verlag, 1991, pp. 296-299.
[26] J. C. Tannehill, D. A. Anderson, R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer. Washington: Taylor&Francis, 1997, ch 3.
[27] O. V. Trevisan, A. Bejan, “Natural convection with combined heat and mass transfer buoyancy effects in a porous medium,” International Journal of Heat and Mass Transfer, vol. 28, no. 8, pp. 1597-1611, 1985.
[28] D. Getachew, D. Poulikakos, W. J. Minkowycz, “Double diffusion in a porous cavity saturated with non-Newtonian fluid,” Journal of Thermophysics and Heat Transfer, vol. 12, no. 3, pp. 437−446, 1998.
[29] R. Bennacer, A. Tobbal, H. Beji, P. Vasseur, “Double diffusive convection in a vertical enclosure filled with anisotropic porous media,” International Journal of Thermal Sciences, vol. 40, no. 1, pp. 30-41, 2001.