Unsteady Heat and Mass Transfer Near the Stagnation-point on a Vertical Permeable Surface: a Comprehensive Report of Dual Solutions

In this paper, the problem of unsteady mixed convection boundary layer flow of a viscous incompressible fluid near the stagnation-point on a vertical permeable plate with both cases of prescribed wall temperature and prescribed wall heat flux is investigated numerically. Here, both assisting and opposing buoyancy forces are considered and studied. The nonlinear coupled partial differential equations governing the flow, thermal and concentration fields are first transformed into a set of nonlinear coupled ordinary differential equations by a set of suitable similarity transformations. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the Runge-Kutta scheme coupled with a conventional shooting procedure. Numerical results are obtained for the skin-friction coefficient, Nusselt number and Sherwood number as well as for the velocity, temperature and concentration profiles for some values of the governing parameters, namely, the unsteadiness parameter A, permeability parameter f(0) and mixed convection parameter lambda. It is found that dual solutions exist for both assisting and opposing flows, and the range of the mixed convection parameter for which the solution exists, increases with suction and unsteadiness parameters.