Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

doi:10.1007/s10483-014-1836-9

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (7): 813-820.doi: https://doi.org/10.1007/s10483-014-1836-9

Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

N. S. AKBAR¹, Z. H. KHAN^2,3, R. U. HAQ⁴, S. NADEEM⁴

1. Department of Basic Science & Humanities, College of Electrical & Mechanical Engineering CEME, National University of Sciences and Technology, Islamabad 46000, Pakistan;
2. School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China;
3. Department of Mathematics, University of Malakand, Khyber Pakhtunktwo 18800, Pakistan;
4. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan

收稿日期:2013-07-23 修回日期:2013-12-27 出版日期:2014-07-01 发布日期:2014-07-01
通讯作者: Z. H. KHAN, Ph.D., E-mail:zafarhayyatkhan@gmail.com E-mail:zafarhayyatkhan@gmail.com

Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

N. S. AKBAR¹, Z. H. KHAN^2,3, R. U. HAQ⁴, S. NADEEM⁴

1. Department of Basic Science & Humanities, College of Electrical & Mechanical Engineering CEME, National University of Sciences and Technology, Islamabad 46000, Pakistan;
2. School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China;
3. Department of Mathematics, University of Malakand, Khyber Pakhtunktwo 18800, Pakistan;
4. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan

Received:2013-07-23 Revised:2013-12-27 Online:2014-07-01 Published:2014-07-01

摘要/Abstract

摘要：

The present article investigates the dual nature of the solution of the magnetohydrodynamic (MHD) stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting method. It is found that the dual solutions of the flow exist for certain values of the velocity ratio parameter. The special case of the first branch solutions (the classical Newtonian fluid model) is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.

关键词: dual solution, stagnation-point flow, magnetohydrodynamic (MHD), shrinking sheet, Prandtl fluid, shooting method

Abstract:

Key words: Prandtl fluid, magnetohydrodynamic (MHD), shooting method, stagnation-point flow, dual solution, shrinking sheet

中图分类号:

O361.3

N. S. AKBAR;Z. H. KHAN;R. U. HAQ;S. NADEEM. Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(7): 813-820.

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Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet

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