Abstract
This numerical study documents the phenomena of heat transfer by natural convection in thermally non-equilibrium porous cavity for Darcy flow model. The cavity is heated from below at constant temperature with keeping the upper plate isothermal . The side walls were assumed to be thermally insulated. Finite difference method has been employed for discretization of governing equations which include a Darcian momentum equation and energy equations for solid and fluid phases. An iterative Guass-Seidle method was applied for determination of final solution of governing equations. This investigation was performed under the effect of the following non-dimensional groups: modified Rayleigh number , scaled heat transfer coefficient and thermal conductivity ratio . The non-equilibrium is found to be affected by scaled heat transfer coefficient more than being affected by the thermal conductivity ratio. So It had been noticed that all Nusselt numbers are affected by the thermal conductivity ratio, while the effect of scaled heat transfer coefficient was confined to a solid phase Nusselt number. Keywords: Porous Layer, Heated from Below, Thermal Non-equilibrium Model
Highlights
The local thermal equilibrium in porous media may be failed for the conditions that subjected to graduated changes between solid and fluid temperatures, which occur during the early stages of transportation processes
This occur during the latest stages of transportation processes, such that occur at high speed flow and through a porous medium of high porosity where the time of thermal communication and the area of communication are insufficient to bring both phases to be in thermal equilibrium[1]
Many researchers studied the problem of local thermal non-equilibrium in porous medium, i.e. Minkowycs et al [3] studied the effect of Sparrows number on local thermal non-equilibrium in porous layer heated from below by sinusoidal heat flux, their results showed that the increase of Sparrows number over than 100 makes the system reaches to local thermal equilibrium rapidly
Summary
The local thermal equilibrium in porous media may be failed for the conditions that subjected to graduated changes between solid and fluid temperatures, which occur during the early stages of transportation processes. Nanna et al [5] did a practical investigation to study the thermal non-equilibrium in porous medium saturated with a fluid subjected to phase change effect. Their model was insulated box made from insulated material called (Plexiglas) and filled with glass balls of (3mm) diameter immersed in (Tetracosane). The present work focus on the local thermal non-equilibrium in a porous cavity heated from below as shown in (fig.1), the lower and upper walls at temperatures Th and Tc respectively, the other two walls are thermally insulated, and the flow is steady and according to Darcy model. The non-dimensional continuity, momentum, fluid phase and solid phase energy equations expressed respectively as the following:
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