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

Based on the principles of locally-nonequilibrium thermodynamics, the mathematical models of heat, mass, momentum transfer processes were developed taking into account spatial and temporal nonlocality. The derivation of the differential equations is based on the taking into account accelerate in time as the specific fluxes (heat, mass, momentum) and the gradients of the corresponding variables in the Fourier’s, Fick’s, Newton’s, Hooke’s, Ohm’s, etc. diffusion laws. Studying of 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.

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