Non-Fourier heat conduction in a finite medium subjected to arbitrary non-periodic surface disturbance

The non-Fourier heat conduction equation is solved for a finite medium under arbitrarily chosen surface disturbances by utilizing the principle of superposition along with the Fourier integral representation of arbitrary non-periodic functions. The obtained solution is such that for a given non-periodic disturbance, we just have to introduce the Fourier integral coefficients of that function to the presented general solution and perform some definite integrations, analytically if possible, but in general numerically which is a straightforward computational task.