Application of Homotopy methods in heat transfer Problems

Most scientific phenomena, such as heat transfer, are nonlinear phenomena and are described by nonlinear equations.In general, we have three general, numerical and analytical methods for solving equations and engineering problems. The analytical method itself is divided into two parts: exact analytical solution and approximate analytical solution.Since we deal with complex and nonlinear problems in many industrial and engineering applications and there is no exact solution to these problems, we have to rely on numerical or approximate solution methods.Recently, hematopoietic methods have been considered by many researchers in the science of heat transfer.One of these approximation methods, called the porturbation method, is one of the older methods and has limitations for solving nonlinear equations.To overcome the problems and limitations of this method, newer methods for solving problems have recently been proposed, such as the hemotopic method of portorbation (HPM) and the method of c alculating repetitive changes (VIM), which have the ability to solve nonlinear equations of the extreme type.They can be used for various problems in the field of engineering, including heat transfer.In this paper, we solve the equation of heat transfer of cooling of a compact system under the mechanisms of convection and radiation by two methods (HPM and VIM) and compare the results.