Alessio Fama†, Liliana Restuccia‡
Abstract: In this paper we derive generalized heat transport laws for an anisotropic rigid heat conductor. We use a model formulated in a previous paper in the framework of non-equilibrium thermodynamics with internal variables. In the thermodynamic state vector beside the internal energy and the heat ux a second order tensor is introduced as internal variable, in uencing the thermal phenomena. In the threedimensional case the phenomenological equations are presented, the entropy production is worked out and anisotropic transport equations for the heat ux are carried out, as Maxwell-Cattaneo and GuyerKrumhansl equations, describing heat waves and the ballistic propagation of the phonons, respectively. The conductivity matrix is given in the Appendix. The obtained results have applications in several technological sectors, as in nanotechnology, where there are situations of high-frequency waves propagation and Knudsen number is comparable or larger than unity.
MSC: 74A15, 74A20, 74E10.
DOI 10.56082/annalsarscimath.2022.1-2.37
†afama@unime.it University of Messina, Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, Viale F. Stagno dAlcontres, Salita Sperone, 31, 98166 Messina, Italy
‡lrestuccia@unime.it University of Messina, Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, Viale F. Stagno dAlcontres, Salita Sperone, 31, 98166 Messina, Italy
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 14 no 1-2, 2022
