Behavior of entropy in non-classical heat conduction of incompressible media

Abstract

Abstract The behavior of entropy of a model isolated system in which there is non-classical heat conduction is considered. Within the thermodynamic formal-ism developed, expressions are obtained for the entropy flux and sourceand also for the total entropy of the isolated system. The approach pro-posed leads to a strictly monotonic dependence of the total entropy on timefor the model system considered. 1 Introduction Non-classical heat transfer is well known for metals, porous media, andcomposite materials [1, 2]. When moving media is considered (e.g., thesurface of a rotating cylinder subject to laser irradiation, which is used inthe fabrication of microstructures and synthesis of new materials), the heattransfer equation is given by [3]:ddtdTdtCdTdtD 2r T; (1)where d=dt(D @=@t C v r ) is the material time derivative, v is the mediumvelocity, T is the temperature, is the relaxation time, D =.c/ is thethermal diffusivity, is the thermal conductivity, c is the heat capacity perunit mass, is the mass density. It is assumed that density and all thecoefficients are constant values.