Variable conductivity in forced convection for a tube filled with porous media: A perturbation solution

Abstract

In this study, the forced convective in a tube filled with porous media is investigated analytically based on the perturbation methods. Thermal conductivity of the medium is assumed to be a linear function of radius. The Brinkman–Forchheimer-extended Darcy and local thermal equilibrium models are applied for momentum and energy equations. Analytical expressions for the temperature profile and Nusselt number as functions of porous medium shape parameter and thermal conductivity variation parameter are introduced. An analytical expression of the Nusselt number based on a variable conductivity with radius for the extended model of Darcy–Brinkman–Forchheimer has not been previously proposed, and the present study aims at filling this gap. The effects of porous media shape parameter (s), Forchheimer number (F) and linear parameter of conductivity (ɛ) on the Nusselt number and temperature profile are discussed. Results show that the Nusselt number increases with a linear increase in the thermal conductivity of the medium. Keywords: Porous media, Variable conductivity, Brinkman–Forchheimer–Darcy model, Perturbation analysis