Laminar Mixed Convection in a Parallel Two-Sided Lid-Driven Differentially Heated Square Cavity Filled with a Fluid-Saturated Porous Medium

Abstract

Two-dimensional, steady, mixed convection flow in an enclosure filled with a Darcian fluid-saturated uniform porous medium is considered. Both the left wall and the right wall are moving upwards with same velocity. They are maintained at cold and hot constant temperatures respectively. The top and the bottom walls are fixed and are thermally insulated. The governing equations are normalized and solved numerically with boundary conditions by finite volume approach using third order accurate upwinding scheme (deferred QUICK). To validate the code, comparisons are made with previously published work and are found to be in excellent agreement. The study is conducted by varying the key parameters i.e., Richardson number (Ri = Gr/Re ²), Darcy number (Da = κ/H ²) and Grashof number (Gr = g β H ³ΔT/ν ²) and fixing Prandtl number (Pr = 0.71). A parametric study is conducted and a set of streamline and isotherm plots are presented. The average Nusselt number reaches a value of 1 asymptotically when the Ri is gradually increased for Gr up to 10³. For Gr = 10⁴, the asymptotic value is 1.5. An empirical heat transfer correlation is also presented.