On Comparison of Homotopy Analysis Method and Finite Difference Method for Two Dimensional Steady Compressible Flow with Pressure Gradients

Abstract

In this paper we analyse the effect of suction/injection on steady compressible fluid flow in boundary layer region. Falkner–Skan transformations will reduce the governing partial differential equations (pde’s) into two nonlinear pde’s. Finite difference method is applied to the system of equations to compare with the semi analytical results obtained by homotopy analysis method, which shows good agreement for the velocity and temperature profiles with suction, injection and no suction effects. The effect of injection, suction are studied for velocity and temperature distribution which are depicted in a graph. It is observed that the flow separation exists for large values of suction and injection in boundary layer region. The error estimates of $$l_1$$ , $$l_2$$ and $$l_{\infty }$$ for all the three cases are listed for velocity and temperature which are the indications of the obtained numerical solutions is close to HAM solution.