Thermodynamical potentials and mathematical modeling of the process of viscous medium flow (Q1278062)

The author considers the thermodynamics of irreversible multiparametric processes. The key point is the representation of the increments of internal energy density and heat density by using linear differential forms. Here the coefficients depend on the process parameters, that are determined through the current values of temperature field, the viscous part of deformation tensor, and the deformation tensor expressed through the dispacement vector (translated here by translation vector). The basic hypotheses are: the increment of heat density corresponds to the densities of influx heat energy density, \(q_{e},\) and to the mechanical energy transformed into heat, \(q_{i},\) while the increment of internal energy density is produced by the work of the stress tensor on the increment of deformation tensor and by the increment of \(q_{e}.\) In the thermodynamic approach to irreversible processes the author assumes that the increments of internal energy density and of the heat density can be expressed through a system of independent functions of the process parameters. These thermodynamic potentials generalize the traditional ones if the increment of the internal energy density is a completely integrable form, and if the heat density admits an integrating factor. Under some simplified conditions (on the constitutive functions, character of the flow, the meaning of the viscous part of deformation tensor, and so on), the author shows the existence of such potentials.