Two-Dimensional Flow Analysis of Nanofluid through a Porous Channel with Suction/Injection at Slowly Expanding/Contracting Walls using Variation of Parameter Method

In this work, variation of parameter method is applied to study two-dimensional flow of nanofluid in a porous channel through slowly deforming walls with suction or injection. the results of the developed approximate analytical solution using the variation of parameter method is verified with the results of numerical solution using fourth-order runge-kutta method coupled with shooing techniques. thereafter, parametric studies are carried. the graphical illustrations of simulated results of the approximate analytical solutions show that during the expansion, the axial velocity at the center of the channel decreases as the reynolds number increases while the axial velocity increases slightly near the surface of the channel when the wall contracts at the same rate. also, the axial velocity decreases at the center of the channel but increases near the wall as the wall expansion ratio increases. due to the high accuracy of the variation of parameter method, the results given in the work may be used for benchmark analysis of the subsequent studies on laminar flow behaviour of nanofluid in a porous channel through slowly deforming with injection or suction.