Analysis of Thermal Nonequilibrium Inverse Heat Transfer in a Porous Channel

Abstract

This article is concerned with the one-dimensional transient inverse heat conduction between two parallel plates filled with a porous medium under a nonthermal equilibrium condition between the solid and the fluid phases. The estimation of transient heat flux using the conjugate gradient method (CGM) along with the differential adjoint equations has been carried out under nonthermal equilibrium conditions between two phases. Derivation of the adjoint differential equations in the case of nonthermal equilibrium and calculation of gradient function from coupled adjoint equations are presented in detail here. The transient wall heat flux imposed on the porous boundary is estimated using the aforementioned method, and results show that sensor locations and existing error in the measured data have important effects on the calculated heat flux. Nonetheless, accurate heat flux estimation is quite achievable.