The local entropy rate of production in unsteady-state conditions at presence of a gradient of temperature

Abstract

Problems of a linear mode of thermodynamics with the purpose of studying the change of local entropy rate of production in a non-stationary thermal mode at presence of a gradient of temperature in bodies of the simple form are considered. Article is development of earlier work of authors in which on the basis of experimental thermogram by the electrostatic levitation method received and fixing process of spontaneous cooling of the spherical sample of the molybdenum which is being a solid phase, change of local entropy rate of production from time has been calculated. It has been shown, that in absence of a gradient of temperature on radius of sphere change of local entropy rate of production from time corresponds to a principle of an extremum. In the given work change of local entropy rate of production from time for a case when the non-stationary thermal mode is combined with presence of a gradient of temperature is defined. The task is solved on the basis of known analytical decisions of one-dimensional problems of heating of bodies of the simple form (a unlimited plate, sphere and the unlimited cylinder), under boundary conditions of the second sort which have been received in approach of constant properties. The general meaning of local entropy rate of production is calculated as the sum of the task with gradient of temperature by a making constant in time and the non-stationary task counted in absence of a gradient of temperature. The estimation of the contribution of temperature drop on thickness of a plate in a general meaning of local entropy rate of production is executed, as product of force and a heat flux corresponding force and is widespread to a case of sphere and the cylinder by virtue of equality of temperature drop for all three bodies. The size of a nonstationary component in a general meaning of local entropy rate of production pays off as function of the logarithm, which argument is the relation of two instant temperatures, and the function of the logarithm is divided on a difference the values of time. It is shown, that the non-stationary component in a general meaning of local entropy rate of production also corresponds to a principle of an extremum at increase of Fourier number. For the first time have made comparison a part of non-stationary local entropy rate of production for a plate, sphere and the cylinder which shows, that the principle of an extremum is most brightly shown for sphere.