Exact solution of Guyer-Krumhansl type heat equation by operational method

摘要

We construct particular solutions for some heat transport differential equations, in particular, for extended forms of hyperbolic heat equation and of Guyer-Krumhansl (GK) equation. The operational approach, integral transforms, generalized orthogonal polynomials and special functions are used. Examples of heat propagation in non-Fourier models are studied and compared with each other. Analytical solutions for some three-dimensional heat transport equations are obtained. The exact analytical solutions for GK type heat equation with linear term are derived. The description of an instant heat surge propagation and of power-exponential pulse is given in heat transport models of Fourier, Cattaneo and Guyer-Krumhansl. Space-time propagation of a periodic function, obeying telegraph and GK equations with linear terms is studied by the operational technique. The exact bounded analytical solutions are obtained. The role of various terms in the equations is illustrated and their influence on the solutions is elucidated. The application for ballistic heat flow study with account for Knudsen number is provided.