Application of HAM to laminar boundary layer flow over a wedge with an external magnetic field

Abstract

The incompressible laminar along with injection or suction over a wedge for a boundary layer flow is studied. Falkner-Skan transformations reduce the governing partial differential equations (PDEs) to two nonlinear coupled PDEs and are solved by the homotopy analysis method (HAM). The variation of a dimensionless temperature and velocity profiles f η ( )and θ η ( ) for Ec = 0.001, Mp = 0.05, m = 0.0909 and to the nonidentical values of the parameter s for injection/suction has been shown in the graph. The results hence obtained show that the flow field is determined by the existence of the applied magnetic field. The finite difference method is applied to the reduced PDEs and the velocity and temperature profiles are compared with the HAM solutions and depicted graphically. To distinguish singularities in the graph, we have applied Pade for the HAM series solution, which is depicted in graphs for all three cases. We have also estimated the radius of convergence of HAM solutions by Domb-Sykes plot for injection, no suction, and suction respectively. The important observation made by us through HAM and numerical solution is the existence of flow separation for injection, which is not shown by previous authors.

MHD slip flow and heat transfer of UCM fluid with the effect of suction/injection due to stretching sheet: OHAM solution

“…Series solution convergence calculated by using OHAM is much faster than that in the case of HAM. In HAM, we plot curves that give the region of convergence 58–60 . But, by means of these curves one cannot recognize the proper value for which convergence of the obtained solution is quicker.…”

“…In HAM, we plot curves that give the region of convergence. [58][59][60] But, by means of these curves one cannot recognize the proper c 0 value for which convergence of the obtained solution is quicker. For solving the two coupled nonlinear ODEs, HAM has been used by Yabushita et al 61 in 2007 and they recommended the "optimization method" through the minimum of the squared residual of governing equation to obtain the two convergence-control parameters.…”