Non-Fourier heat conduction in a slab with non- homogeneous boundary conditions

This study presents an analytical method which combines the superposition technique along with the solution structure theorem such that a closed-form solution of the hyperbolic heat conduction equation can be obtained using fundamental mathematics. In this solution, a complicated problem is split into multiple simpler problems which in turn can be combined to obtain a solution to the original problem. The original problem is divided into five subproblems by setting the heat generation term, the initial conditions and the boundary conditions to different values in each subproblem. All solutions given in this paper can be easily proven by substituting them into the governing equation.

Keywords:

structure theorem , subproblems , heat conduction equation , Non-Fourier