Maximum Density Effects on Natural Convection over an Isothermal Vertical Plate Embedded in an Anisotropic Porous Medium

Abstract

Keywords: Natural convection, anisotropic porous medium, inversion of density.Abstract. The natural convection in the porous medium has attracted considerable attention with its applications in various industrial sectors, such as the agro-alimentary, the pharmaceutical and oil processing industries. The present work is about the study of the phenomenon of natural convection at 4°C on the vertical plate lining in an anisotropic porous medium in permeability. The wall of the vertical surface is subjected to a constant temperature with defined hydrodynamic conditions and thermal limits. Generalized Darcy’s law was used to establish the governing equations of the system. The control parameters governing the system are respectively the permeability ratio K*, the angle ϴ of the major axis and the inversion parameter R. The general basic equations were solved numerically using Runge-Kutta and shooting method. There was validated against previous work. The effect of these parameters on the heat transfer was highlighted. From the analysis result, it comes out the following conclusions: The convective flow is significantly affected by the anisotropic parameter; heat transfer along the vertical surface is maximum (minimum) when the main shaft having the high permeability is oriented parallel (perpendicular) to the gravitational field; the rate of heat transfer is depending on the inversion parameter R. The convective transfer rate illustrated by the local Nusselt number is symmetric with respect to R=0.45, where it reaches its smallest value. It is inversely proportional to the distribution of the thickness of boundary layer. A high convective transfer rate corresponds to a low boundary layer thickness and this inversely.