Fourier-homotopy perturbation method for heat and mass transfer with 2D unsteady squeezing viscous flow problem

In this article, the homotopy perturbation method (HPM) and Fourier transform (FT) were combined to construct a hybrid method that can be represented by the symbol (FT-HPM), the new technique succeeded to find an approximate solution for the model of heat and mass transfer in the unsteady squeezing flow between parallel plates analytically. The similarity transformation methodology was relied upon to convert a system of partial differential equations into a system of ordinary differential equations. The influence of physical parameters (squeeze number, Prandtl number, Schmidt number and the Eckert number) on velocity, temperature and concentration with different values is discussed. In addition, the physical quantities represented by the Nusselt number, Sherwood number, and the skin friction coefficient were studied, and the new numerical results of these quantities were compared with the results of previously published works. Finally, the convergence of the new method was studied theoretically by formulating the basic convergence theorem. In addition, this theorem was applied to the results of the solutions obtained using FT-HPM. The tables and graphs of the new analytical solutions showed the possibility and usefulness of using the new algorithm to deal with many non-linear problems, especially natural convection problems.