The local entropy rate of production at boundary conditions of the third kind

The relevance of the work is due to the need to confi rm the basic theoretical assumptions of the linear regime
of thermodynamics, in which, as a rule, a thermodynamic function is used – the change in entropy rate of production. For this function, the extremum principle, the bilinear dependence on force and fl ux for thermal, electrical, diffusion and simplest chemical roblems, as well as the linear dependence of the fl ow on the force corresponding to the fl ow are fulfi lled. The regularities of changes in local entropy rate of production in time and space found from the solution of thermal problems allow us to extend the conclusions obtained to a wider range of physical phenomena due to the identity of the linear laws of Fourier, Ohm, and Fick. The change in local entropy rate of production of simple-shaped bodies in a nonstationary thermal regime under boundary conditions of the third kind is determined. The article is a development of an earlier work of the authors, in which similar problems were analyzed under boundary conditions of the second kind. The well-known analytical solutions of one-dimensional heating problems under boundary conditions of the second and third kind of bodies of simple shape (unlimited plate, sphere and unlimited cylinder) obtained in the approximation of constant properties are used. We consider solutions corresponding to the range of variation of the Fourier number greater than 0.55, which exclude the initial section, and two areas of variation of the Biot criterion: Biot criterion less than 0.1 and Biot criterion tends to infi nity. It is shown that the non-stationary component of
local entropy rate of production corresponds to the extremum principle when approaching a stationary state for the case of Biot criterion less than 0.1 (there is no temperature gradient). It is confi rmed that one of the main assumptions of the linear regime of thermodynamics – the linear dependence of the fl ow on the force in the plate, in an unlimited cylinder and sphere is fulfi lled for the case of Biot criterion tends to infi nity when the contribution of the temperature gradient prevails over the non-stationary component of entropy rate of production. The gradient component of local entropy rate of production depending on the coordinate is determined for these three bodies. The results obtained are applicable to the physics of stationary processes, which can be attributed to the linear regime of thermodynamics, that is, extended, for example, to diffusion and electrical problems. 

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