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.