Unsteady boundary layer flow and heat transfer over a permeable shrinking sheet with non-uniform heat source

In this paper we investigate theoretically the unsteady boundary layer flow and heat transfer over a permeable shrinking sheet with non-uniform heat source. The nondimensional governing equations have been solved numerically using the bvp4c function from Matlab for different values of the pertinent parameters; shrinking parameter λ, suction parameter S, unsteadiness parameter β, space dependent heat source parameter A, and temperature dependent heat source parameter B, keeping Prandtl number Pr fixed. Numerical results are obtained for the reduced skin-friction and heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for a shrinking (λ < 0) sheet for certain values of the parameter space. The results show that unsteadiness significantly control the flow and heat transfer characteristics.