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

Appl. Math. Mech. -Engl. Ed., 35(7), 813–820 (2014) Applied Mathematics DOI 10.1007/s10483-014-1836-9 and Mechanics c Shanghai University and Springer-Verlag Berlin Heidelberg 2014 (English Edition) Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet∗ 1 2,3 4 4 N. S. AKBAR , Z. H. KHAN , R. U. HAQ , S. NADEEM (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) Abstract The present article investigates the dual nature of the solution of the magneto- hydrodynamic (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 cer- tain 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. Key