Analytical Solution of the Problem of Conjugate Heat Transfer between a Gasdynamic Boundary Layer and Anisotropic Strip

Abstract

The paper focuses on the problem of conjugate heat transfer between the thermal-gas-dynamic boundary layer and the anisotropic strip in conditions of aerodynamic heating of aircraft. Under the assumption of an incompressible flow which takes place in the shock layer behind the direct part of the shock wave, we found a new analytical solution for the components of the velocity vector, temperature distribution, and heat fluxes in the boundary layer. The obtained heat fluxes at the interface between the gas and the body are included as boundary conditions in the problem of anisotropic heat conduction in the body. The study introduces an analytical solution to the second initial-boundary value problem of heat conduction in an anisotropic strip with arbitrary boundary conditions at the interfaces, with heat fluxes which are obtained by solving the problem of a thermal boundary layer used at the interface. An analytical solution to the conjugate problem of heat transfer between a boundary layer and an anisotropic body can be effectively used to control, e.g. to reduce, heat fluxes from the gas to the body if the strip material chosen is such that the longitudinal component of the thermal conductivity tensor is many times larger than the transverse component of the thermal conductivity tensor. Such adjustment is possible due to an increase in body temperature in the longitudinal direction, and, consequently, a decrease in the heat flow from the gas to the body, as well as due to a favorable change in the physical characteristics of the gas. Results of numerical experiments are obtained and analyzed