Comparison of the solutions of a phase-lagging heat transport equation and damped wave equation with a heat source

In this article, we study the difference between the solutions of the phase-lagging equation (PLE), a new heat conduction equation, and the damped wave equation (DWE) with a heat source. The exact solution of the PLE is obtained using the Laplace transform method, and is approximated using an approximate analytical method when the time lag is small since the exact solution is practically not computable for the small time lag case. Results show that the DWE is a good approximation to the PLE when the time lag is small.