Heat transfer analysis in unsteady boundary layer stagnation-point flow towards a shrinking/stretching sheet

The heat transfer in unsteady boundary layer stagnation-point flow over a shrinking/stretching sheet is investigated. The surface temperature of the sheet is taken time dependent. The governing equations are transformed into self-similar ordinary differential equations by adopting similarity transformations and then the converted equations are solved numerically by shooting method. The study reveals that in addition to the velocity field, for the temperature distribution the dual solutions exist for some values of velocity ratio parameter. The heat transfer rate enhances due to the unsteadiness of the flow. The temperature for first solution decreases with unsteadiness parameter, and for second solution the temperature initially decreases, but it increases at large distance from the sheet. Moreover, for dual solutions as well as unique solution cases, the heat transfer rate increases with the Prandtl number in presence of unsteadiness.