The Conditions for the Existence of the Optimal Thickness of a Cooled Anisotropic Wall Subjected to Local Heat Exposure

Abstract

The problem of the determination of sufficient conditions for the existence of the optimal thickness of an anisotropic wall, one of whose surfaces of is exposed to axisymmetric stationary heat flux with the intensity of the Gaussian type, while the other is cooled by the external medium with a constant temperature, was formulated and solved using the two-dimensional exponential integral Fourier transform. The requirement for minimization of the temperature of the most heated point of object of study was used as an optimality criterion. The sufficient condition that was obtained is an inequality that establishes the link between the thermophysical characteristics of the anisotropic material of a wall, the intensity of heat transfer on its cooled surface, and the factor of the concentration of the outer heat flux. These results confirm the well-known effect of the “drift” of the temperature field in an anisotropic material with the common type of anisotropy of its properties.