Mixed Convection in a Two-Sided and Four-Sided Lid-Driven Square Porous Cavity

Abstract

The present paper investigates the mixed convection in a two-sided and four-sided lid-driven square cavity in porous media. In the two-sided porous cavity, the left and right walls of the enclosure are maintained at constant but different temperatures, while the top and bottom walls are adiabatic. The top and the bottom walls of the enclosure move with a constant speed from left to right. In the four-sided porous cavity, the top and the bottom walls of the enclosure move from left to right and right to left, respectively, while the left and the right walls move from top to bottom and bottom to top, respectively, with a constant speed. The left and right walls of the enclosure are maintained at different heat fluxes, while the top and bottom walls are maintained at hot and cold temperatures, respectively. The governing equations are discretized by the fully implicit finite difference method, namely, Alternating-Direction-Implicit (ADI) method. The numerical results are analyzed for the effect of Darcy number (Da = 0.001, 0.01), Prandtl number (Pr = 7), Grashof number (Gr = 50,000), porosity (ε = 0.2) and viscosity ratio (Λ = 1, 3). The stability and convergence of the considered problem have been proved using the Matrix method.

Heat and mass transfer under MHD mixed convection in a four‐sided lid‐driven square cavity

“…, we look at two different scenarios based on heat generation or absorption coefficient. If ϕ is the heat absorption coefficient, that is, ϕ ϕ = − 0 for some ϕ > 0 0 , then this situation can be treated in the same manner as Bagai et al 13,14…”

“…To establish $$\parallel {A}_{2}{A}_{1}\parallel \le 1$$, one can accomplish $$\rho ({A}_{1})\le 1$$, and $$\rho ({A}_{2})\le 1$$ in the same way as given by Ambethkar and Kumar 1 and Patel et al 21 To prove $$\parallel {B}_{4}{B}_{3}\parallel \le 1$$, we look at two different scenarios based on heat generation or absorption coefficient. If $$\phi $$ is the heat absorption coefficient, that is, $$\phi =-{\phi }_{0}$$ for some $${\phi }_{0}\gt 0$$, then this situation can be treated in the same manner as Bagai et al 13,14 case of $$\parallel {G}_{1}{E}_{1}\parallel \le 1$$. The energy equation (17) may be interpreted as follows if $$\phi $$ is the heat‐generating coefficient, that is, $$\phi \gt 0$$.…”

“…Azwadi et al 11 present the Adams–Bashforth approach for simulating a four‐sided lid‐driven square cavity (4S‐LDSC) flow exhibiting stable velocity on all sides under the threshold Reynolds level. Bagai et al 12,13 used the stream function‐vorticity $$(\psi -\xi )$$ formulation to study the mixed or natural convection flow with/without porous materials in square cavities driven by two‐ and four‐sided lids with sinusoidal heat distributions. Bagai et al 14 have studied mixed convection in a four‐sided lid‐driven sinusoidally heated porous cavity under two different cases of the direction of moving lid, namely, antiparallel diagonal and antiparallel antidiagonal.…”

Mixed Convection Flow and Heat Transfer of Two Rotating Cylinders in a Trapezoidal Enclosure Filled with Porous Medium

“…Due to its importance in various applications such as nuclear reactors, chemical catalytic reactors, petroleum reservoirs, solar power, microelectronics, and ground hydrology, mixed convection flow and heat transfer in porous medium have sparked a lot of attention in the literature [1][2][3][4][5][6][7]. Free convection in cavities with single and multiple cylinders has been widely investigated both computationally and experimentally [8][9][10][11][12][13][14].…”