Development of mathematical models and research strongly nonequilibrium developments taking into account space-time nonlocality

I. V. Kudinov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 1, pp. 116-152

Résumé

Based on the principles of locally-nonequilibrium thermodynamics were developed mathematical processes models of heat, mass, momentum, taking into account spatial and temporal nonlocality. The output of the differential equations is based on the account in the diffusion laws Fourier's, Fick's, Newton's, Hooke's, Ohm's, etc. accelerate in time as the specific fluxes (heat, mass, momentum) and the gradients of the corresponding variables. Study exact analytical solutions of the obtained models allowed us to discover new regularities of the changes of the desired parameters at low and ultra low values of temporal and spatial variables, and for all fast processes, time change which is comparable with the relaxation time. And, in particular, from the analysis of the exact analytical decision the fact of a time lag of acceptance of a boundary condition of the first kind demonstrating that in view of resistance of the body shown to warmth penetration process, its instantaneous warming up on boundary is impossible under no circumstances heat exchange with the environment is found. Therefore, the heat emission coefficient on a wall depends not only on heat exchange conditions (environment speed, viscosity and so forth), but also on physical properties of a body and it, in the first, is variable value in time and, in the second, it can not exceed some value, limit for each case.

Détail

Keywords: local nonequilibrium heat transfer processes, spatial and temporal nonlocality, vibrations of elastic bodies, fluids and gases, abnormal conduction, dynamic thermal stresses, thermal ignition.
Mots-clés : relaxation coefficients