Dual solutions in a double-diffusive convection near stagnation point region over a stretching vertical surface

The development of double-diffusive convection near stagnation point region over a stretching vertical surface with constant wall temperature has been investigated. The external flow and the stretching velocities are assumed to vary with image where x is the distance from the slot where the stretching surface is issued. Using the local similarity method, it has been shown that a set of suitable similarity transformations reduces the non-linear coupled partial differential equations governing the flow, thermal and concentration fields into a set of non-linear coupled ordinary differential equations. The non-linear self-similar equations along with the boundary conditions form a two point boundary value problem and are solved using Shooting method, by converting into an initial value problem. In this method, the system of equations is converted into the set of first order system which is solved by fourth-order Runge–Kutta method. Flows with both assisting and opposing buoyancy forces are considered in the present investigation. The study reveals that the dual solutions of velocity, temperature and concentration exist for certain values of suction/injection and buoyancy parameters. Prandtl and Schmidt numbers strongly affect the thermal and concentration boundary layer thicknesses, respectively. The effects of various parameters on the velocity, temperature and concentration profiles are also presented here.