Conditions of heat transfer self-similar process realization in anisotropic half-subspace with movable boundary at local thermal impact in conditions of heat exchange with external environment


Аuthors

Attetkov A. V.*, Vlasov P. A., Volkov I. K.

Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia

*e-mail: fn2@bmstu.ru

Abstract

Due to the pertinence of theoretical and applied studies of self-similar processes of heat

transfer in solids, a problem of determining of non-stationary temperature field of anisotropic

half-subspace, which movable boundary is subjected to a heat impact in conditions of heat exchange

with external environment, was formulated. It was found, that unlike the well-known

self-similar heat transfer processes in isotropic solids, to which the temperature field forming

processes in oil stratums while water flooding in conditions of naphtha frontal driving by water

might be referred to in particular, the use of two, instead of one, self-similar variables is required

while studying heat transfer self-similar process for the situation under consideration.

The first self-similar variable defines the analyzed heat transfer process in the plane, parallel to

the moving boundary of an anisotropic half-subspace, and the second one in the direction of its

external normal. Representation of mathematical model of the formulated problem of heat transfer

in anisotropic half-subspace with moving boundary employing two self-similar variables allows

understanding that realizability of self-similar process of heat transfer in the situation under

consideration is associated with fulfillment of the quite certain conditions. These conditions

define completely and unambiguously the law of movement of the boundary of the subject under

study, as well as the structure of the thermal flow affecting it, and a heat transfer mode

being realized in the studied system «anisotropic half-subspace—external environment», i.e.

functional dependence of Bio’s number (which is criterion of convective-conductive similarity)

on spatial and time variables. It was substantiated theoretically, that in the heat transfer process

being analyzed, self-similar structures of both external heat flow and heat transfer mode being

realized are of the same kind, and functionally dependent on thermal homochronoucity criterion,

i.e. Fourier number.

Keywords:

non-isotropic half-subspace, moving boundary, heat exchange with external environment, local thermal impact, auto-modelling problem of heattransfer.

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