Arcangelo Labianca†, Lidia Palese‡, Liliana Restuccia§
In some previous papers, within the framework of the thermodynamics of irreversible processes with internal variables, a linear theory for magnetic relaxation phenomena in anisotropic mixtures, consisting of n reacting fluid components, was developed. In particular, assuming that the macroscopic magnetization m can be split in two irreversible parts m = m(0) + m(1) a generalized Snoek equation was derived. In this paper we derive for these reacting anisotropic mixtures the heat conduction equation. We show that the heat dissipation function is due to the chemical reactions, the magnetic relaxation, the electric conduction, the viscous, magnetic, temperature fields and the diffusion and the concentrations of the n fluid components. Also, the Snoek and De Groot special cases are studied. The obtained results find applications in nuclear resonance, in biology, in medicine and other fields, where different species of molecules have different magnetic susceptibilities and relaxation times and contribute to the total magnetization.
Keywords: continuum thermodynamics, classical irreversible thermodynamics, reacting fluid mixtures with magnetic relaxation, internal variables.
MSC: 74A15, 74A20, 74E10, 74F05.
DOI https://doi.org/10.56082/annalsarscimath.2024.2.227
†arcangelo.labianca@uniba.it University of Bari, Department of Mathematics, Via E. Orabona, 4, 70125 Bari, Italy; paper written with financial support of I.N.D.A.M.
‡University of Bari, Department of Mathematics, Via E. Orabona, 4, 70125 Bari, Italy
§University of Messina, Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, Viale F. Stagno d’Alcontres, Salita Sperone 31, 98166 Messina, Italy
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 16 no 2, 2024
