THREE-LAYER PROBLEM ON HEAT EXCHANGE IN A MEDIUM WITH COUNTERFLOWS

With the use of the asymptotic method, it is shown that the three-layer problem on the conjugate heat exchange in an anisotropic medium with counterfl ows of liquid, formulated in the zero approximation, is equivalent to the analogous problem formulated using the Newton law. It was established that in the case where the counterfl ows of liquid in such a medium have equal strengths, the summary convective heat transfer in the medium is suppressed, and the medium takes new properties consisting in the appearance of heat fl ow mixed in nature, whose value is determined by the relation similar to the Fourier heat conduction law. By this meant that in the case where a temperature gradient is superimposed on a three-layer system of equivalent counterfl ows of liquid, in it there arises a heat fl ow having a value proportional to the temperature gradient in the medium and propagating in the direction opposite to the direction of this gradient. The eff ective coeffi cient of heat conductivity of medium, generated in it by the counterfl ows of liquid, separated by an immovable layer, is proportional to the square of the velocity of these fl ows. An immovable layer in a medium, separating the counterfl ows of liquid, increases the generation of heat in the medium, and the heat fl ow generated exceeds substantially the molecular one even in the case where it has a low velocity. Such processes provide the mass exchange in living organisms and their heat exchange with the environment.
With the use of the asymptotic method, it is shown that the three-layer problem on the conjugate heat exchange in an anisotropic medium with counterfl ows of liquid, formulated in the zero approximation, is equivalent to the analogous problem formulated using the Newton law. It was established that in the case where the counterfl ows of liquid in such a medium have equal strengths, the summary convective heat transfer in the medium is suppressed, and the medium takes new properties consisting in the appearance of heat fl ow mixed in nature, whose value is determined by the relation similar to the Fourier heat conduction law. By this meant that in the case where a temperature gradient is superimposed on a three-layer system of equivalent counterfl ows of liquid, in it there arises a heat fl ow having a value proportional to the temperature gradient in the medium and propagating in the direction opposite to the direction of this gradient. The eff ective coeffi cient of heat conductivity of medium, generated in it by the counterfl ows of liquid, separated by an immovable layer, is proportional to the square of the velocity of these fl ows. An immovable layer in a medium, separating the counterfl ows of liquid, increases the generation of heat in the medium, and the heat fl ow generated exceeds substantially the molecular one even in the case where it has a low velocity. Such processes provide the mass exchange in living organisms and their heat exchange with the environment. With the use of the asymptotic method, it is shown that the three-layer problem on the conjugate heat exchange in an anisotropic medium with counterfl ows of liquid, formulated in the zero approximation, is equivalent to the analogous problem formulated using the Newton law. It was established that in the case where the counterfl ows of liquid in such a medium have equal strengths, the summary convective heat transfer in the medium is suppressed, and the medium takes new properties consisting in the appearance of heat fl ow mixed in nature, whose value is determined by the relation similar to the Fourier heat conduction law. By this meant that in the case where a temperature gradient is superimposed on a three-layer system of equivalent counterfl ows of liquid, in it there arises a heat fl ow having a value proportional to the temperature gradient in the medium and propagating in the direction opposite to the direction of this gradient. The eff ective coeffi cient of heat conductivity of medium, generated in it by the counterfl ows of liquid, separated by an immovable layer, is proportional to the square of the velocity of these fl ows. An immovable layer in a medium, separating the counterfl ows of liquid, increases the generation of heat in the medium, and the heat fl ow generated exceeds substantially the molecular one even in the case where it has a low velocity. Such processes provide the mass exchange in living organisms and their heat exchange with the environment.
Author:  A. I. Filippov
Keywords:  heat exchange, counterfl ows, eff ective heat conductivity, temperature gradient
Page:  535