Thermal Non-equilibrium in Porous Annulus: A New Finite Element Solution Technique

Thermal non-equilibrium between solid and fluid phases of porous medium is an important condition that exists in many applications when the thermal conductivity ratio and interphase heat transfer coefficient between the solid and fluid phases have low values. The condition of thermal non-equilibrium requires that the mathematical model be comprised of two energy equations to simulate the temperature variations of solid and fluid phases. This necessitates the two energy equations related to solid and fluid phases to be solved. However, this brings an additional difficulty to simulate thermal non-equilibrium in porous annulus. The difficulty of simulating thermal non-equilibrium condition arises due to involvement of multiple partial differential equations that should be solved simultaneously. The aim of the present work is to propose a novel method that combines the two energy equations into a single equation at the solution stage. The adopted methodology depends on converting the partial differential equations into simpler form by utilising the finite element method. The current work comprehensively demonstrates the feasibility of proposed method along with its validation with respect to heat transfer prediction in porous annulus. The proposed method is found to have good accuracy to simulate the heat transfer in porous annulus.