Heat and mass transfer in a two-sided lid-driven square cavity with non-uniform sinusoidal heating on horizontal walls

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

“…1 ≤ , and ρ A ( ) 1 2 ≤ in the same way as given by Ambethkar and Kumar 1 and Patel et al 21 To prove B B…”

“…The boundary conditions for vorticity can be seen in Patel et al 21 The local Nusselt numbers $$(N{u}_{L},N{u}_{R})$$ and local Sherwood numbers $$(S{h}_{L},S{h}_{R})$$ measure the heat and mass transfer, respectively, at a point on the left‐and‐right wall. The average Nusselt $$(\bar{N{u}_{L}},\bar{N{u}_{R}})$$ and Sherwood numbers $$(\bar{S{h}_{L}},\bar{S{h}_{R}})$$ are the physical quantities of interest for average heat transmission and mass transfer on the vertical walls of the cavity.…”

“…The field variables $$(\psi ,\xi ,\theta ,C,u,\,\text{and}\,v)$$ are indicated at various grid nodes in Figure 2 by a five‐point stencil. The first‐ and second‐order partial derivatives of flow variables (except the time derivative) in the governing equations are discretized using second‐order central difference formulas [21, pp. 6 and 7].…”

“…The time derivative terms are discretized using the first‐order forward difference formula. The details of the complete discretization process of the governing equations are similar to the problem discussed by Patel et al 21 The lower–upper (LU) decomposition method is used to solve the resulting implicit tridiagonal equations. At time step $$\tau +1\unicode{x02215}2$$, a single governing equation is solved in the $$y$$‐direction, followed by $$\tau +1$$ in the $$x$$‐direction.…”

“…Khanafer and Chamkha 20 used a Darcian fluid‐saturated homogeneous porous medium to investigate convection flow in a lid‐driven cavity containing internal heat generation with the top wall in motion. Patel et al 21 explored heat and mass transmission characteristics in a square cavity with moving antiparallel vertical walls and nonuniform sinusoidal heating on its horizontal walls. Raghunatha and Vinod 22 have examined the MHD suction–injection model of viscous fluid flow to analyze the temperature and velocity profiles using the differential transformation approach and the Bernoulli wavelet method.…”