A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model

Abstract

This work uses a thermal non-equilibrium model to study the free convection boundary layer flow driven by temperature gradients near a permeable horizontal cylinder of elliptic cross-section with constant wall temperature in a fluid-saturated porous medium. A coordinate transformation is used to obtain the nonsimilar boundary layer equations. The transformed boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt numbers are presented as functions of the porosity scaled thermal conductivity ratio, the heat transfer coefficient between solid and fluid phases, the transpiration parameter, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). An increase in the porosity scaled thermal conductivity ratio or the heat transfer coefficient between the solid and fluid phases increases the heat transfer rates. Moreover, the use of suction (positive transpiration parameter) tends to increase the heat transfer rates between the porous medium and the surface.