New analytical and numerical solutions for mixed convection boundary-layer nanofluid flow along an inclined plate embedded in a porous medium

Two different analytical and numerical methods have been applied to solve the system describing the mixed convection boundary-layer nanofluids flow along an inclined plate embedded in a porous medium,namely,homotopy perturbation method (hpm) and chebyshev pseudospectral differentiation matrix (chpdm),respectively. further,chpdm is used as a control method to check the accuracy of the results obtained by hpm. the analytical method is applied using a new way for the deformed equations,and the resulted solution was expressed in terms of a well-known entire error function. in addition,using only two terms of the homotopy series,the approximate analytical solution is compared with the numerical solution obtained by the accurate chpdm approach. the results reveal that good agreements have been achieved between the two approaches for various values of the investigated physical parameters. © 2013 emad h. aly and abdelhalim ebaid.