Approximate Analytical Solution of the Problem of Conjugate Heat Transfer Between the Boundary Layer and the Anisotropic Strip

Abstract

Optimization of technological processes in metallurgy related to transfer and use of heat energy makes more complicated demands for calculation of heat exchange. Therefore, the work, the approximate analytical method for solving the conjugate problems of viscous gas-dynamic boundary layer and thermal conductivity in the anisotropic strip, has been developed. The paper uses modern numerical methods for solving differential equations in partial derivative and analytic methods on the basis of an integral transform of Fourier and Laplace. Boundary equations have been solved analytically with certain simplifications, and the problem of anisotropic heat conduction has been solved analytically. The heat flows are determined analytically by the longitudinal variable at the interface boundary. It has been established that temperature increase of the external surface contributes to that all factors directly impacting on the magnitude of heat flows act towards their reduction. The analytical solution for the problem of thermal conductivity in the anisotropic strip with a general type of anisotropy when the heat flows from the boundary layer are determined at the boundaries is obtained. The conducted research for the temperature of external boundary and heat flow from gas to it demonstrates that with increasing the degree of longitudinal anisotropy the surface temperature of the strip downstream increases from increasing longitudinal heat conduction An original conjugation method using the continuous heat flows, and temperatures at the interface boundary is found. The numerical results for the heat flows and temperatures at the interface boundary have been obtained and analyzed.