In this study, dynamic and heat transfer equations of two-dimensional laminar plane and axisymmetric stagnation flow are solved by Optimal Homotopy Analysis Method, Boundary Knot-Homotopy analysis method and compared by numerical solution. The optimal convergence-control parameter value is calculated using Chebyshev points. These points are corresponding to the range of solutions to get the best answer for both flows. Boundary Knot Method gives the best initial guess that applies in terms of primary answer of homotopy analysis method. Results are reported by the 50th order approximation. Also, it is considered that the total numbers of knots on the domain and the boundary is 40. It is shown that results have a good agreement with the numerical solution. The stream function, the velocity function, the shear stress function and the temperature distribution for small Prandtl values is shown for plane and axisymmetric stagnation flows using BK-HAM compared with the numerical solution. It can be found that, with increasing vertical distance, because of decreasing the effects of wall, the fluid shear stress will be reduced. Also the temperature distribution in the boundary layer changes linearly with distance from the wall. Also, increasing the Prandtl number and decreasing the thermal boundary layer thickness is leading to increase temperature distribution.

Keywords: viscous fluid, stagnation point flow, Temperature distribution, boundary knot-homotopy analysis method

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