EQUATIONS OF TRANSFER IN NONLOCAL MEDIA

The transfer equations and Fourier law analogues have been obtained fo r three types of non-local media: media with heat memory, spatially no n-local media and media with a discrete structure. The conditions are specified under which these equations reduce into each other or to fam iliar transfer equations, such as the classical parabolic-type transpo rt equation and 'telegraph' equation. It is shown that the type of par tial differential equations derived from discrete transfer equations i s governed by the limiting transition law, i.e. by the relationship be tween the time, tau, and space, h, scales of the medium internal struc ture. In the case of the 'diffusional' law of limiting transition, whe n the thermal diffusivity coefficient a = h2/4tau = const for r, h --> 0, the discrete equations yield parabolic-type partial differential e quations, whereas with the 'wave' law of limiting transition, when the heat wave speed c = h/2tau = const < infinity for tau, h --> 0, they yield partial differential equations of hyperbolic type.