A Nonfield Analytical Method for Solving Some Nonlinear Problems in Heat Transfer

Abstract

Abstract This paper presents an extension of the nonfield 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 problems includes some problems with nonlinear boundary conditions. From the practical viewpoint, the case considering asymptotic solutions is of the greatest interest: it is shown that, for complex heat transfer problems, where applications of the nonfield method are practically impossible due to a large volume of necessary computations, it is still possible to analyze the solution behavior 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 nonfield method over other analytical methods are emphasized in each case.