Free Convection in a Darcy Thermally Stratified Porous Medium That Embeds a Vertical Wall of Constant Heat Flux and Concentration
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:71857", author = "Maria Neagu", title = "Free Convection in a Darcy Thermally Stratified Porous Medium That Embeds a Vertical Wall of Constant Heat Flux and Concentration", 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.", volume = "10", number = "1", pages = "65-10", }
