ON THE MODELING OF THE HYPERBOLIC HEAT TRANSFER PROBLEMS IN PERIODIC LATTICE-TYPE CONDUCTORS

摘要

The aim of this contribution is to propose, compare, and apply two kinds of simplified mathematical models for the analysis of hyperbolic problems describing heat transfer in dense periodic lattice-type conductors of an arbitrary form. The considerations are based on the Cattaneo-type constitutive heat transfer law. We begin with the formulation of a discrete model represented by a system of ordinary differential equations that have a finite difference form with respect to the spatial coordinates. By using some smoothness operations we derive continuum models from the aforementioned finite difference formulation. The general results are illustrated and compared in the example of a temperature wave propagating in a certain special lattice-type periodic conductor.