Mixed Convection in a Two-Sided and Four-Sided Lid-Driven Square Porous Cavity Shobha Bagai 1* , Manoj Kumar 2 , Arvind Patel 2 1 Cluster Innovation Centre, 3rd Floor University Stadium, G C Narang Road, University of Delhi, Delhi 110007, India 2 Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110007, India Corresponding Author Email: mkumar@maths.du.ac.in https://doi.org/10.18280/ijht.390305 ABSTRACT Received: 20 August 2019 Accepted: 19 March 2021 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. Keywords: alternating-direction-implicit (ADI) method, finite difference method, mixed convection, two-sided and four-sided lid-driven flow, porous media 1. INTRODUCTION During the past few decades, the problem of natural or mixed convection in lid-driven square or rectangular cavity with porous media has been widely studied due to its simple geometrical settings and its practical applications [1] such as nuclear waste disposal, coal and grain storage, textile materials, geothermal systems, biological processes, and many others. Mixed convection in lid-driven square or rectangular cavity has various applications in engineering science [2], such as lubricant technology, chemical processing, cooling of microprocessors and electronic components, float glass production, etc. The lid-driven cavity in porous media whose all four walls are kept at different heat flux or temperatures has been studied by many researchers. Mixed or natural convection in a square cavity with three different cases, i.e. (a) all walls of the cavity are kept stationary, (b) one side of the wall is in motion (c) two sides of the cavity are in motion, has been studied in the following literature. Mixed convection in a square cavity with all walls at rest has been studied by Venkatachalappa et al. [1], Saeid and Mohamad [3], Mansour et al. [4], Basak et al. [5], and Badruddin et al. [6]. Venkatachalappa et al. [1] investigated natural convection inside a square porous cavity using the finite-difference ADI method. Saeid and Mohamad [3] studied the natural convection within the square cavity by keeping its right wall at hot temperature and sinusoidal condition on its left wall. In contrast, the top and bottom walls are adiabatic. Mansour et al. [4] investigated the numerical study of natural convection with thermal radiation inside a wavy porous cavity. Basak et al. [5] examined the natural convection flow inside a square cavity keeping its top wall adiabatic. In contrast, the bottom wall is maintained at hot temperature or a sinusoidal boundary condition. The left and right wall of the cavity is maintained at a cold temperature. They have obtained numerical results for various parameters; Rayleigh number (10 3 ≤ Ra ≤ 10 6 ), Darcy number (10 -5 ≤ Da ≤ 10 -3 ), and Prandtl number (0.71 ≤ Pr ≤ 10). Badruddin et al. [6] examined the heat transfer by convection, conduction, and radiation using a non-equilibrium thermal model inside a square porous cavity. The numerical results are discussed for various parameters like Rayleigh number, inter-phase heat transfer coefficient radiation, and modified conductivity ratio in terms of Nusselt number for solid and fluid. Natural or mixed convection in the one-sided lid-driven square porous cavity has been studied by Chattopadhyay and Pandit [7], Kandaswamy et al. [8], Mohan and Satheesh [9], Md. Hidayathulla Khan et al. [10]. Chattopadhyay and Pandit [7] have used the higher-order compact (HOC) scheme to analyze the mixed convection in a lid-driven trapezoidal porous enclosure whose top wall is kept at a motion from left to right. The effect of convection in a trapezoidal porous enclosure is examined for different Peclet numbers. Kandaswamy et al. [8] have numerically investigated the effect of Prandtl number on mixed convection in a one-sided lid-driven square cavity filled with porous media. They have found that conduction is dominated at low Prandtl numbers, while mixed and forced convection dominates the temperature field as the Prandtl number increases. Mohan and Satheesh [9] investigated the double-diffusive mixed convection with magnetohydrodynamic effect in a one-sided lid-driven porous cavity. They have examined the fluid flow in the top-sided lid- driven square cavity in both directions with a constant velocity. They analyzed streamline contours, concentration, temperature gradients, and velocity components for a wide range of non-dimensional parameters like Hartmann (1 ≤ Ha International Journal of Heat and Technology Vol. 39, No. 3, June, 2021, pp. 711-726 Journal homepage: http://iieta.org/journals/ijht 711