Dual solutions in a thermal diffusive flow over a stretching sheet with variable thickness

The development of thermal diffusive flow over a stretching sheet with variable thickness has been investigated. The non-linear coupled partial differential equations governing the flow and thermal fields are first transformed into a set of non-linear coupled ordinary differential equations by a set of suitable similarity transformations. The resulting system of coupled non-linear differential equations is solved using the 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. It is interesting to note that multiple solutions are observed for certain wall thickness parameter (β) and velocity power index (m). Velocity overshoot near the wall is observed for certain solution branches. The significant impacts on the boundary layer development along the wall on the velocity profiles and on the shear stress distribution in the fluid have been found by the non-flatness of the stretching surface. The mass suction effect is introduced by the non-flatness, when the velocity power index is less than one. The mass injection effect is lead to non-flatness when the velocity power index is greater than one. It is found that dual solution exists only for negative value of velocity power index (m). The presence of dual solutions in velocity and temperature fields for certain values of wall thickness parameter (β) and velocity power index (m) are revealed by this study.