Unsteady flow with heat transfer over a shrinking surface and linear temporal stability analysis

The present study accentuates an unsteady flow and heat transfer over a shrinking surface in the presence of magnetic field and suction effects. Similarity solutions of the self-similar equations are generated via Matlab solver 'bvp4c'. The solutions corresponding to different values of the velocity ratio parameter (c) reveal some interesting results, which are discussed in detail. It has been observed that adequate suction is required to obtain the similarity solutions. The shear stresses and heat transfer rate are prominently affected by the intensity of suction, velocity ratio parameter, and magnetic field. Unlike an unsteady stretching sheet problem, dual solutions of the self-similar equations are found in a certain range of unsteadiness parameter. An emphasis has been given to performing a temporal stability analysis which reveals that the upper branch is a stable solution branch.