Dual solutions in a double-diffusive MHD mixed convection flow adjacent to a vertical plate with prescribed surface temperature

The development of double-diffusive MHD mixed convection flow adjacent to a vertical plate with prescribed surface temperature has been investigated. 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, Magnetic and buoyancy parameters. It is found that the Magnetic parameter (M) significantly affects the flow and the thermal fields, besides increasing the range of buoyancy parameter image for which dual solutions exist. 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.