Unsteady Natural Convection in a Square Cavity Partially Filled with Porous Media Using a Thermal Non-Equilibrium Model
Unsteady natural convection and heat transfer in a square cavity partially filled with porous media using a thermal
non-equilibrium model is studied in this paper. The left vertical wall is
maintained at a constant hot temperature Th and the right vertical wall
is maintained at a constant cold temperature Tc, while the horizontal
walls are adiabatic. The governing equations are obtained by applying
the Darcy model and Boussinesq approximation. COMSOL’s finite
element method is used to solve the non-dimensional governing
equations together with specified boundary conditions. The governing
parameters of this study are the Rayleigh number (Ra = 10^5, and Ra = 10^6 ), Darcy namber (Da = 10^−2, and Da = 10^−3),
the modified thermal conductivity ratio (10^−1 ≤ γ ≤ 10^4), the inter-phase heat transfer coefficien (10^−1 ≤ H ≤ 10^3) and the
time dependent (0.001 ≤ τ ≤ 0.2). The results presented for
values of the governing parameters in terms of streamlines in both
fluid/porous-layer, isotherms of fluid in fluid/porous-layer, isotherms
of solid in porous layer, and average Nusselt number.
[1] G. S. Beavers and D. D. Joseph, “Boundary conditions at a naturally
permeable wall,” Journal of fluid mechanics, 30(01):197–207, 1967.
[2] C. Beckermann, S. Ramadhyani, and R. Viskanta, “Natural convection
flow and heat transfer between a fluid layer and a porous layer inside a
rectangular enclosure,” Journal of heat transfer, 109(2):363–370, 1987.
[3] C. Beckermann, R. Viskanta, and S. Ramadhyani, “Natural convection
in vertical enclosures containing simultaneously fluid and porous layers,”
Journal of Fluid Mechanics, 186:257–284, 1988.
[4] F. Chen and C. F. Chen, “Experimental investigation of convective
stability in a superposed fluid and porous layer when heated from below,”
Journal of Fluid Mechanics, 207:311–321, 1989.
[5] P. L. Breton, J. P. Caltagirone, and E. Arquis, “Natural convection in a
square cavity with thin porous layers on its vertical walls,” Journal of
heat transfer, 113(4):892–898, 1991.
[6] I. T. Webster, S. J. Norquay, F. C. Ross, and R. A. Wooding, “Solute
exchange by convection within estuarine sediments,” Estuarine, Coastal
and Shelf Science, 42(2):171–183, 1996.
[7] B. Goyeau, D. Lhuillier, D. Gobin, and M. G. Velarde, “Momentum
transport at a fluid–porous interface,” International Journal of Heat and
Mass Transfer, 46(21):4071–4081, 2003.
[8] D. Gobin, B. Goyeau, and A. Neculae, “Convective heat and solute
transfer in partially porous cavities,” International Journal of Heat and
Mass Transfer, 48(10):1898–1908, 2005.
[9] M. Prat, “Modelling of heat transfer by conduction in a transition region
between a porous medium and an external fluid,” Transport in porous
media, 5(1):71–95, 1990.
[10] J. Alberto O. Tapia and S. Whitaker, “Heat transfer at the boundary
between a porous medium and a homogeneous fluid,” International
Journal of Heat and Mass Transfer, 40(11):2691–2707, 1997.
[11] O. M. Haddad, “Fully developed free convection in open-ended vertical
channels partially filled with porous material,” Journal of Porous Media,
2(2), 1999.
[12] A. dHueppe, M. Chandesris, D. Jamet, and B. Goyeau, “Boundary
conditions at a fluid–porous interface for a convective heat transfer
problem: Analysis of the jump relations,” International Journal of Heat
and Mass Transfer, 54(15):3683–3693, 2011.
[13] S. A. Khashan, A. M. Al-Amiri, and M. A. Al-Nimr, “Assessment of the
local thermal non-equilibrium condition in developing forced convection
flows through fluid-saturated porous tubes,” Applied thermal engineering,
25(10):1429–1445, 2005.
[14] P. Forooghi, M. Abkar, and M. Saffar-Avval, “Steady and unsteady
heat transfer in a channel partially filled with porous media under thermal
non-equilibrium condition,” Transport in porous media, 86(1):177–198,
2011.
[15] A. dHueppe, M. Chandesris, D. Jamet, and B. Goyeau, “Coupling a
two-temperature model and a one-temperature model at a fluid-porous
interface,” International Journal of Heat and Mass Transfer, 55(9):
2510–2523, 2012.
[16] M. Mharzi, M. Daguenet, and S. Daoudi, “Thermosolutal natural
convection in a vertically layered fluid-porous medium heated from the
side,” Energy conversion and management, 41(10):1065–1090, 2000.
[17] S. B. Sathe, W. Q. Lin, and T. W. Tong, “Natural convection
in enclosures containing an insulation with a permeable fluid-porous
interface,” International journal of heat and fluid flow, 9(4):389–395,
1988.
[18] A. Baytas and I. Pop, “Free convection in a square porous cavity
using a thermal nonequilibrium model,” International Journal of Thermal
Sciences, 41(9):861–870, 2002.
[1] G. S. Beavers and D. D. Joseph, “Boundary conditions at a naturally
permeable wall,” Journal of fluid mechanics, 30(01):197–207, 1967.
[2] C. Beckermann, S. Ramadhyani, and R. Viskanta, “Natural convection
flow and heat transfer between a fluid layer and a porous layer inside a
rectangular enclosure,” Journal of heat transfer, 109(2):363–370, 1987.
[3] C. Beckermann, R. Viskanta, and S. Ramadhyani, “Natural convection
in vertical enclosures containing simultaneously fluid and porous layers,”
Journal of Fluid Mechanics, 186:257–284, 1988.
[4] F. Chen and C. F. Chen, “Experimental investigation of convective
stability in a superposed fluid and porous layer when heated from below,”
Journal of Fluid Mechanics, 207:311–321, 1989.
[5] P. L. Breton, J. P. Caltagirone, and E. Arquis, “Natural convection in a
square cavity with thin porous layers on its vertical walls,” Journal of
heat transfer, 113(4):892–898, 1991.
[6] I. T. Webster, S. J. Norquay, F. C. Ross, and R. A. Wooding, “Solute
exchange by convection within estuarine sediments,” Estuarine, Coastal
and Shelf Science, 42(2):171–183, 1996.
[7] B. Goyeau, D. Lhuillier, D. Gobin, and M. G. Velarde, “Momentum
transport at a fluid–porous interface,” International Journal of Heat and
Mass Transfer, 46(21):4071–4081, 2003.
[8] D. Gobin, B. Goyeau, and A. Neculae, “Convective heat and solute
transfer in partially porous cavities,” International Journal of Heat and
Mass Transfer, 48(10):1898–1908, 2005.
[9] M. Prat, “Modelling of heat transfer by conduction in a transition region
between a porous medium and an external fluid,” Transport in porous
media, 5(1):71–95, 1990.
[10] J. Alberto O. Tapia and S. Whitaker, “Heat transfer at the boundary
between a porous medium and a homogeneous fluid,” International
Journal of Heat and Mass Transfer, 40(11):2691–2707, 1997.
[11] O. M. Haddad, “Fully developed free convection in open-ended vertical
channels partially filled with porous material,” Journal of Porous Media,
2(2), 1999.
[12] A. dHueppe, M. Chandesris, D. Jamet, and B. Goyeau, “Boundary
conditions at a fluid–porous interface for a convective heat transfer
problem: Analysis of the jump relations,” International Journal of Heat
and Mass Transfer, 54(15):3683–3693, 2011.
[13] S. A. Khashan, A. M. Al-Amiri, and M. A. Al-Nimr, “Assessment of the
local thermal non-equilibrium condition in developing forced convection
flows through fluid-saturated porous tubes,” Applied thermal engineering,
25(10):1429–1445, 2005.
[14] P. Forooghi, M. Abkar, and M. Saffar-Avval, “Steady and unsteady
heat transfer in a channel partially filled with porous media under thermal
non-equilibrium condition,” Transport in porous media, 86(1):177–198,
2011.
[15] A. dHueppe, M. Chandesris, D. Jamet, and B. Goyeau, “Coupling a
two-temperature model and a one-temperature model at a fluid-porous
interface,” International Journal of Heat and Mass Transfer, 55(9):
2510–2523, 2012.
[16] M. Mharzi, M. Daguenet, and S. Daoudi, “Thermosolutal natural
convection in a vertically layered fluid-porous medium heated from the
side,” Energy conversion and management, 41(10):1065–1090, 2000.
[17] S. B. Sathe, W. Q. Lin, and T. W. Tong, “Natural convection
in enclosures containing an insulation with a permeable fluid-porous
interface,” International journal of heat and fluid flow, 9(4):389–395,
1988.
[18] A. Baytas and I. Pop, “Free convection in a square porous cavity
using a thermal nonequilibrium model,” International Journal of Thermal
Sciences, 41(9):861–870, 2002.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:58607", author = "Ammar Alsabery and Habibis Saleh and Norazam Arbin and Ishak Hashim", title = "Unsteady Natural Convection in a Square Cavity Partially Filled with Porous Media Using a Thermal Non-Equilibrium Model", abstract = "Unsteady natural convection and heat transfer in a square cavity partially filled with porous media using a thermal
non-equilibrium model is studied in this paper. The left vertical wall is
maintained at a constant hot temperature Th and the right vertical wall
is maintained at a constant cold temperature Tc, while the horizontal
walls are adiabatic. The governing equations are obtained by applying
the Darcy model and Boussinesq approximation. COMSOL’s finite
element method is used to solve the non-dimensional governing
equations together with specified boundary conditions. The governing
parameters of this study are the Rayleigh number (Ra = 10^5, and Ra = 10^6 ), Darcy namber (Da = 10^−2, and Da = 10^−3),
the modified thermal conductivity ratio (10^−1 ≤ γ ≤ 10^4), the inter-phase heat transfer coefficien (10^−1 ≤ H ≤ 10^3) and the
time dependent (0.001 ≤ τ ≤ 0.2). The results presented for
values of the governing parameters in terms of streamlines in both
fluid/porous-layer, isotherms of fluid in fluid/porous-layer, isotherms
of solid in porous layer, and average Nusselt number.
", keywords = "Unsteady natural convection, Thermal non-equilibrium model, Darcy model.", volume = "9", number = "1", pages = "1-6", }
