Stability analysis of unsteady MHD stagnation point flow and heat transfer over a shrinking sheet in the presence of viscous dissipation

Highlights

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The unsteady flow is possible only when the mass suction parameter increases.

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Dual solutions exist for certain value of shrinking sheet parameter.

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Skin friction and Nusselt number increases along with the increasing of suction.

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The increasing value of Eckert number causes the Nusselt number to decrease.

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The first solution is linearly stable while the second solution is not.

Abstract

The unsteady MHD stagnation-point flow and heat transfer over a shrinking sheet was carried out. This study also was conducted in the existence of suction and viscous dissipation. In order to convert the governing partial differential equations to an ordinary differential equation, an appropriate similarity transformation was applied in this study. Then, the resulting equations are worked out by Bvp4c solver in Matlab. The impacts of the parameters involved in this study towards skin friction, Nusselt number, velocity and temperature profile are showed graphically and thoroughly discussed. Remarkably, there were dual solutions present in this study which made us continue deeper in performing the stability analysis. As expected, our study proves that the solution is stable only in the first one while not in the second solution.