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.

Heat Transfer Analysis of Viscous Incompressible Fluid by Combined Natural Convection and Radiation in an Open Cavity

“…The time dependent vorticity transport equation (14) and thermal conduction-convection equation (15) are solved using the Alternate Direct Implicit method. The details of the proposed method are also given in [21][22][23]27]. A simple discretization procedure given by Bello-Ochende [17] is adopted for the solution of radiation equation (16) and heat function equation given by (21).…”

“…The details of the proposed method are also given in [21][22][23]27]. A simple discretization procedure given by Bello-Ochende [17] is adopted for the solution of radiation equation (16) and heat function equation given by (21). As a simple case, all computations are performed for square cavity.…”

“…The study of heat function profile becomes more important when the natural convection flow is combined with radiation, as the inclusion of radiation raises the energy level of the fluid in domain considerably (see Larson and Viskanta [3]). A very recent study of heatlines formulation for surface radiation case in enclosures has been made by Hossain et al [21]. Further, the problem of natural convection in open ended cavity is recently addressed by Saleem et al [22,23].…”

“…When energy transfer takes place in combined mode, the net heat transfer rate is also defined as the combined mechanism of these modes (Lauriat [4]). Thus for combined mechanism of convection and radiation the net heat transfer for solid wall boundaries can be defined by the following relations (see [4][5][6]21]):…”

“…Equations (13) to (16) are solved with the boundary conditions given by (17) and (19) to solve the system. The heat lines are given by (21) whereas the average heat transfer is calculated from (24).…”