^{1}

^{2}

^{1}

^{2}

This investigation presents a mathematical model describing the momentum, heat and mass transfer characteristics of magnetohydrodynamic (MHD) flow and heat generating/absorbing fluid near a stagnation point of an isothermal two-dimensional body of an axisymmetric body. The fluid is electrically conducting in the presence of a uniform magnetic field. The series solution is obtained for the resulting coupled nonlinear differential equation. Homotopy analysis method (HAM) is utilized in obtaining the solution. Numerical values of the skin friction coefficient and the wall heat transfer coefficient are also computed.

Stagnation point flows are classic problems in the theory of fluid dynamics. Pioneering works of Hiemenz [

In the present paper, we developed the homotopy analysis solution for the problem considered in [

Here we consider the steady and MHD stagnation point flow impinging on a horizontal surface. The considered viscous fluid generates or absorbs heat at uniform rate. The

The boundary conditions for the problem under consideration are

Writing

Invoking (

The boundary conditions (

The expression of skin friction coefficient (

According to equations (

From (

According to the rule of solution expression denoted by (

For simplicity, here we take

At the

We use the widely applied symbolic computation software MATHEMATICA to solve (

The

The

Also, by computing the error of norm 2 for two successive approximation of

The norm 2 error of

Figure

Effect of

Effect of

Effect of

The so-called homotopy-Padé technique (see [

Results for [

[ | [ | [ | HAM | [ | [ | [ | HAM | |

0.7 | 0.7060 | 0.7080 | 0.7054 | 0.70812 | 0.9438 | 0.9507 | 0.95421 | 0.95036 |

1.0 | 0.5700 | 0.5705 | 0.57235 | 0.56963 | 0.7620 | 0.7624 | 0.76421 | 0.76154 |

10.0 | 0.1432 | 0.1339 | 0.1446 | 0.13377 | 0.1914 | 0.1752 | 0.1925 | 0.13868 |

100.0 | 0.0360 | 0.0299 | 0.0381 | 0.02477 | 0.0481 | 0.0387 | 0.04923 | 0.02767 |

Homotopy analysis method is employed to analyze the MHD flow near a stagnation point. The resulting nonlinear differential system is solved analytically. The effects of Hartman number, the Prandtl number and the heat generation/absorption coefficient are seen on the normal component of velocity and temperatures respectively in both plane and axisymmetric stagnation point cases. It is noticed that temperature profiles increase by increasing the heat generation/absorption coefficient. The behavior of Prandtl number on the temperature profile is similar to that of heat generation/absorption coefficient in a qualitative sense.

The authors acknowledge the financial support provided by the Higher Education Commission (HEC) of Pakistan.