Lumped system of combined convection-radiation with variable thermal conductivity

In this paper the temperature transfer in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity is obtained. That is an important problem in Mechanics of fluids and in efficiency oil recovery (EOR) of petroleum reservoirs, when it is used of high explosive composites for EOR in petroleum reservoirs. In this paper the applicability and effectiveness of a new method that is used in recent years as a semi-exact analytical method is shown for solution of nonlinear boundary value problem. This method applied to lumped system arising in Heat transfer phenomena in in a slab made of materials with variable thermal conductivity then the results are compared with numerical solution and homotopy perturbation method (HPM), GA method and variational iteration method (VIM). This technique that is used in this work has this capability to find closed-form solutions of nonlinear problems and this method is easier to use and will be save in time.