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.
Abstract: Double-diffusive natural convection in an open top
square cavity and heated from the side is studied numerically.
Constant temperatures and concentration are imposed along the right
and left walls while the heat balance at the surface is assumed to obey
Newton-s law of cooling. The finite difference method is used to
solve the dimensionless governing equations. The numerical results
are reported for the effect of Marangoni number, Biot number and
Prandtl number on the contours of streamlines, temperature and
concentration. The predicted results for the average Nusselt number
and Sherwood number are presented for various parametric
conditions. The parameters involved are as follows; the thermal
Marangoni number, 0 ≤ MaT ≤1000 , the solutal Marangoni number,
0 1000 c ≤ Ma ≤ , the Biot number, 0 ≤ Bi ≤ 6 , Grashof number,
5 Gr = 10 and aspect ratio 1. The study focused on both flows; thermal
dominated, N = 0.8 , and compositional dominated, N = 1.3 .