Application of solution structure theorems to Cattaneo–Vernotte heat conduction equation with non-homogeneous boundary conditions

Abstract

In this study, a non-Fourier heat conduction problem formulated using the Cattaneo–Vernotte (C–V) model with non-homogeneous boundary conditions is solved with the superposition principle in conjunction with solution structure theorems. It is well known that the aforementioned analytical method is not suitable for such a class of thermal problems. However, by performing a functional transformation, the original non-homogeneous partial differential equation governing the physical problem can be cast into a new form such that it consists of a homogeneous part and an additional auxiliary function. As a result, the modified homogeneous governing equation can then be solved with solution structure theorems for temperatures inside a finite planar medium. The methodology provides a convenient, accurate, and efficient solution to the C–V heat conduction equation with non-homogeneous boundary conditions.