Free convection flow of Newtonian fluid along a vertical plate embedded in a double layer porous medium

Porous medium has got a great interest especially in the recent years, for its wide application in geophysics, petroleum, and air conditioning. Many studies related to porous medium were performed, and most of them are dealing with constant porosity. For the act: that porosity is non-uniform, a great concern has been directed toward the variable porosity studies. In this study, the effects of a double layer porous medium on the free convection along vertical plate embedded in this porous medium were investigated. The governing partial nonlinear differential equations were transformed into a set of ordinary differential equations, which have been solved by the fourth-order Runge-Kutta method. The results are obtained for different layer permeability K, and layer length, L. One case is compared with the previous study, and the result is found to be in good agreement with the result of previous study. Results show that permeability ratios greater than one tend to increase in Nusselt number, and it is valuable to use a high permeability ratio layer in the range of 0.2 eta to get higher heat transfer rate instead of using constant permeability medium.