Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models

Abstract

This article presents the mathematical formulations of transient heat conduction problems corresponding to the models of classical heat conduction using the Fourier law and generalized heat conduction based on the Cattaneo–Vernotta–Lykov law (Maxwell–Cattaneo model), as well as the generalized Green–Nagdy type II and III models. The Fourier transforms in spatial coordinates and the Laplace transforms in time were used to obtain the fundamental solutions of the equations of the Maxwell–Cattaneo and Green–Nagdy type II and III models of classical and generalized heat conduction. The results were displayed graphically and analyzed. Differences between the considered heat conduction models were shown, and suggestions for their practical application were given.

Keywords

• classical heat conduction
• maxwell–cattaneo theory
• cattaneo–vernott– lykov law
• green–nagdy theory
• generalized heat conduction
• differential equations
• integral transformations