Application of homotopy perturbation method to find an analytical solution for magnetohydrodynamic flows of viscoelastic fluids in converging/diverging channels

In this article, an analytical solution for magnetohydrodynamic flows of viscoelastic fluids in converging/diverging channels is presented. A similarity transform reduces the Navier—Stokes and energy equations to a set of non-linear ordinary differential equations that are solved analytically by means of the homotopy perturbation method (HPM). The results obtained in this study are compared with numerical results and previous studies. Close agreement of the two sets of results indicates the accuracy of HPM. An expression that is acceptable for all values of effective parameters is obtained by HPM. The numerical solution of the similarity equations is developed and the results are in good agreement with the analytical results based on HPM.