Surface-radiation effect on natural convection flow in a fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls

Abstract

Purpose – The purpose of this work is to study the effect of surface-radiation on the phenomenon of natural convection flow of a Newtonian fluid in a non-Darcian porous media cavity. The study is mainly focused on the interaction between the inertial resistance of the fluid layers and the surface radiation. Design/methodology/approach – For numerical simulation of transient vorticity transport and energy equations, the paper uses the alternate direct implicit method. Forward Time Central Space descretization is used for the transient and diffusion terms in the alternate direct implicit method, whereas for the convective terms, the method is modified using second upwind differencing technique. ADI method is adopted here, since this technique is unconditionally stable as a complete sweep and is second-order accurate in time for low velocity changes. The stream function equation is solved using the successive over relaxation technique with residual tolerance of order 10-5. Findings – It was found that despite the reduction of flow, the heat transfer increases as the Forschheimer resistance is increased. Further, with the increase in the Planck number, the heat transfer from the bottom radiating wall increases. Darcy drag parameter did not have a significant impact on flow properties except a slight reduction in the flow. Nevertheless, the increase in temperature ratio has a significant impact on flow properties. Research limitations/implications – The analysis is valid for unsteady, two-dimensional natural convection flow in a fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls. As a first case, the study is conducted for square cavity. An extension to three-dimensional flow case and the study of Darcy-Forschheimer medium with effect of viscous dissipation is left as a part of future work. Practical implications – The approach is applicable to the modeling of geothermal systems where the inertial resistance to flow also comes into act with the non-uniform temperature distribution. The method is very useful to analyze solar receiver systems, fire research, electronic cooling, brake housing of an aircraft and many environmental geothermal processes. Originality/value – The study may be of some interest to engineers interested in heat transfer in ventilated rooms or enclosures, the industrial waste, water and atmospheric pollution.