A Non-Field Analytical Method for Solving Some Nonlinear Problems in Heat Transfer

This paper presents an extension of the non-field analytical method – known as the method of Kulish – to some nonlinear problems in heat transfer. In view of the fact that solving nonlinear problems is very complicated in general, the extension of the method is presented in the form of several important illustrative examples. Two classes of problems are considered: first are the problems, in which the heat equation contains nonlinear terms, while the second type of the problems includes some problems with nonlinear boundary conditions. From the practical viewpoint, the case considered in Section 4 is of the greatest interest. In that section, it is shown that, for complex heat transfer problems, where applications of the non-field method are practically impossible due to a large volume of necessary computations, it is still possible to analyse the solution behaviour and automatically determine similarity criteria for the limiting values of the parameters. Wherever possible the obtained solutions are compared with known solutions obtained by other methods. The practical advantages of the non-field method over other analytical methods are emphasised in each case.