INTEGRAL METHOD FOR ANALYZING NATURAL CONVECTION OF NONNEWTONIAN FLUID ALONG A VERTICAL HEATED PLATE IN ANISOTROPIC POROUS MEDIUM

Abstract

An analytical study of natural convection boundary-layer flow along a vertical plate embedded in an anisotropic porous medium saturated by a non-Newtonian fluid has been conducted. The principal axis of permeability anisotropy was oriented in oblique direction to the gravity vector. A power-law variation of wall temperature was prescribed at the vertical plate, and in the Darcy-Rayleigh number limit (Rax > 100), a boundary-layer solution based on the integral relations approach was assumed. Scale analysis was applied to determine the order of magnitudes involved in the boundary-layer regime. Analytical expressions were obtained for the boundary-layer thickness and the mean Nusselt number in terms of the governing parameters of the problem. When the power-law exponent was made smaller, the convective flow along the plate became stronger. When the porous matrix was oriented such that the principal axis of higher permeability was parallel to the gravity, the convective heat transfer along the plate attained maximum value.