Singular perturbation and differential transform methods to two-dimensional flow of nanofluid in a porous channel with expanding/contracting walls subjected to a uniform transverse magnetic field

Abstract

This paper presents a comparative study of two approximate analytical methods for the analysis of two-dimensional unsteady flow of nanofluid in a porous channel through expanding/contracting walls with large injection or suction under the influence of a uniform transverse magnetic field. Similarity transformations are used to reduce the systems of the governing partial differential equations to a nonlinear fourth-order ordinary differential equation which is solved using method of matched asymptotic expansion and differential transform method. From the verification of the approximate analytical solutions, it is established that the results obtained using differential transformation method demonstrate remarkable accuracy and better agreements with the results of numerical method than the results obtained using method of matched asymptotic expansion. Therefore, the differential transform method gives more accurate results than method of matched asymptotic expansion. Also, due to the higher accuracy of the differential transformation method than the method of matched asymptotic expansion, the approximate analytical solutions through the differential transformation method are used to investigate the effects of permeation Reynolds number, wall expansion ratio and magnetic parameter on the flow behavior of the fluid. From the results, it is established that increase in the Reynolds number decreases the axial velocity at the center of the channel during the expansion while the axial velocity increases slightly near the surface of the channel when the wall contracts at the same rate. Also, as the wall expansion ratio increases, the velocity at the center decreases and increases near the wall. For every level of injection or suction, in the case of expanding wall, increasing the wall dilation rate leads to increase in axial velocity near the center and decrease in the axial velocity near the wall. The results present in this work can serve as references for the other methods of analysis of the problem.