A unified solution of several heat conduction models

Energy transport within a finite thin film subjected to either symmetric or asymmetric heating at the boundaries is investigated. Non-Gaussian heat sources are modeled as time-varying and spatially-decaying laser incidences. Comparison of heat transfer mechanisms based on the classical diffusion, Cattaneo-Vernotte, simplified thermomass, and dual-phase-lag models is undertaken. This study presents a single generalized analytical temperature profile in a finite thin film in terms of an infinite series, utilizing the superposition technique in conjunction with the solution structure theorems, which is found to be applicable to solutions of all the aforementioned models. The temperature solution for a particular model can be obtained directly by applying appropriate coefficients as they appear in the proposed generalized governing heat conduction equation. Through analyses and numerical examples, the time history of heat transfer behaviors due to the collision of energy from both sides of the thin film is compared among these models. It reveals that the method provides a convenient and efficient solution to the classical heat diffusion equation as well as other forms of hyperbolic heat conduction equations.