Steady Flow About A Sphere In A Porous Medium Subject To An Oscillating Temperature

Abstract

The study of free convection about a sphere in a porous medium, when the temperature of the sphere is oscillating harmonically is considered for Rayleigh number, Ra=100. By using the matched asymptotic expansion, the flow field is divided into an inner region and an outer region, where the inner region is adjacent to the sphere and the outer region is far from the sphere. In the inner region, the separation technique is used to divide the second-order temperature and stream function into steady and unsteady parts. The analytical solution is obtained up to second-order steady term. For outer region, the numerical result up to first order is obtained by using a finite difference scheme. It is found that, a steady flow is induced at the outer edge of the inner region. The temperature and flow patterns are discussed and compared for some frequencies of oscillation, ω and dimensionless parameter ε. It is found that both the magnitudes of temperature and stream functions decreases as ω increases or decreases but the effect of ε is not significant in the outer region. In the inner region, the magnitude of steady flow is also determined by frequency.