Fluid Flow and Heat Transfer Due to Differentially Heated Walls of Horizontal Channel Filled with Porous Medium

Abstract This paper reports the fully developed flow and heat transfer in the horizontal channel filled with fluid saturated porous medium. The flow is derived from the combined impact of external pressure gradient and thermal diffusion buoyancy force. The Brinkmann-extended Darcy model describes the behavior of the two-dimensional flow governing equations. The coupled governing equations are solved numerically using the alternate direction implicit (ADI) method. The influence of physical parameters, Reynolds number (Re), Darcy number (Da), and Grashof number (Gr), on the dynamics of flow and heat transfer mechanism is investigated. From our numerical investigation, it is found that the flow structure is either uniform or recirculation and depends on Da, Gr, as well as Re. For Re = 10, the flow structure is multicellular and flow oscillation, whereas for Re = 100 the flow structure is unicellular. The size and position of flow circulation are changed significantly for relatively large media permeability. For Ri≥10, the linear contours in the profile of temperature distribution are found via convection as well as conduction mode, whereas curvature contours in the same are found via convection mode only which is the consequence of natural convection dominant. For Ri = 1, the curvature contour in the profile of temperature distribution is found by mixed convection only.