Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium

Abstract

Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.

Exact solution to a multidimensional wave equation with delay

“…As is well known, the MSV is implemented for bounded spatial domains. The approach followed in this paper could be applied to other delay problems on infinite mediums too, by relying on Fourier transforms instead of the MSV [28]. Several contributions on retarded heat and wave equations, based on Fourier transforms, are programmed for the future.…”

Numerical Simulation of Thermal Processes in a Domain of Thin Metal Film Subjected to an Ultrashort Laser Pulse

“…The solution is obtained using the Green function method and finite integral transform technique. The solution concerning the heating of the plate in which the thermal processes are described by the higher order DPLE supplemented by the Dirichlet or Neumann boundary conditions and initial ones is reported by Castro et al [13]. The interesting (from the practical point of view) analytical solution is discussed by Ciesielski [14].…”