Perturbation Analysis Of Heat Transfer in Porous Media with Small Thermal Conductivity

The study of heat transfer in porous media has many applications in industry. In this work, heat transfer between an inert gas and a semi infinite porous media based on Singular Perturbation method and with using of Laplace Transform, has been studied. To solve this problem with this approach, the thermal conductivity is assumed to be small. Also, the solution is expressed in both inner and outer layer. For matching these two layers a matching method is suggested. This approach shows a good accuracy for small values of parameter, small thermal conductivity. One time the problem is solved by using the third kind boundary condition on the wall and one time this boundary condition is changed into first kind and then has been considered in problem. With comparing between this solution and the solution of using boundary condition of third kind shows the good accuracy of this approach, except near the wall that there occurred small differences between these two solutions. This idea can be used as a useful method in simplifying the analysis of the issues. But in cases that the good accuracy of solution or slop changes with high precision is important, this procedure may be caused approximate results.