Non-Fourier heat conduction in a finite medium with insulated boundaries and arbitrary initial conditions

The non-Fourier transient heat conduction in a finite medium with insulated boundaries under the influence of arbitrary initial conditions is investigated analytically. The solution is expressed in the form of Fourier cosine series. The obtained analytical closed-form solution can be used for validation of numerical solutions. The resulting solution is valid for any choice of integrable initial conditions. The significant feature of proposed solution is its generality. In order to show the applicability of the presented solution, two numerical examples are solved.