Solution of thermal conductivity problems with constant and variable heat exchange coefficients

The paper presents a method for approximate analytical solution of heat conduction problems with constant and variable heat transfer coefficients. In engineering of thermal physics, most heat conduction problems are solved under boundary conditions of the third kind. If heating of the body is caused, in addition to convective heat transfer, by a radiant flux, then the boundary conditions become nonlinear and the analytical determination of temperature field inside the body becomes more complicated. The development of approximate methods for solving the heat conduction equation for variable heat transfer coefficients and the representation of temperature field in a simple analytical form, even at cost of reducing their accuracy, is of practical interest. Representation of temperature fields by simple analytical dependences made it possible to carry out effective research on temperature stresses under various internal and external thermal influences. The advantage of proposed method in comparison with well-known classical, even for multidimensional bodies, irregular and non-classical forms is shown. A simple and sufficiently accurate analytical method for approximate solution of non-stationary heat conduction in bodies of classical and non-classical forms is obtained. This method is used to solve problems with variable transfer coefficients depending on coordinates. (author)