Local Entropy Rate of Production at Boundary Conditions of the Third Kind

• Published in: Measurement techniques 2023-08, Vol.66 (5), p.336-342
• Main Authors: Kostanovskiy, A. V., Kostanovskaya, M. E.
• Format: Article
• Language: English
• Subjects: Analytical Chemistry; Boundary conditions; Characterization and Evaluation of Materials; Criteria; Cylinders; Entropy; Exact solutions; Infinity; Mathematical analysis; Measurement Science and Instrumentation; Physical Chemistry; Physics; Physics and Astronomy; Principles; Thermodynamics
• ISSN: 0543-1972; 1573-8906
• DOI: 10.1007/s11018-023-02232-7

This research confirms the basic theoretical assumptions of the linear regime of thermodynamics, which, as a rule, uses a thermodynamic function, especially the change in entropy production per unit volume. This thermodynamic function fulfills the extremum principle, Bilinear dependency on force and flux for thermal, electrical, diffusion, and simplest chemical issues, and linear dependence of the flow on the force corresponding to the flow. Due to the identity of the linear laws of Fourier, Ohm, and Fick, it is possible to extrapolate the obtained results to a larger range of physical phenomena using the regularities of changes in the local entropy rate of production (LERP) in time and space, which are determined from the solution of thermal issues. The change in the LERP of simple-shaped bodies in a nonstationary thermal regime under boundary conditions of the third kind is determined. The well-known analytical solutions of one-dimensional problems of heating the bodies of simple shape (unbounded plate, sphere, and unbounded cylinder), obtained under boundary conditions of the third kind in the approximation of constant properties, were used. We considered solutions corresponding to the LERP of the Fourier number greater than 0.55 (excluding the initial section) and two areas of variations of the Biot criterion, especially the Biot criterion less than 0.1 and that approaching infinity. It is demonstrated that for the case of the Biot criterion less than 0.1 (no temperature gradient), the nonstationary component of the LERP corresponds to the extremum principle when approaching a stationary state. It was confirmed that one of the main assumptions of the linear regime of thermodynamics, namely, the linear dependence of the flow on the force in the plate in an unbounded cylinder and sphere, is fulfilled for the Biot criterion of 10 and that approaching infinity when the contribution of the temperature gradient prevails over the nonstationary component of the entropy rate of production. Depending on the coordinate, the gradient component of the LERP is determined for these three bodies. The obtained results apply to the physics of processes that can be attributed to the linear regime of thermodynamics and are extended to diffusion and electrical problems.