dual solutions in boundary layer stagnation-point flow and mass transfer with chemical reaction past a stretching/shrinking sheet

in this paper, an analysis is presented to study dual nature of solution of mass transfer with first order chemical reaction in boundary layer stagnation-point flow over a stretching/shrinking sheet. the governing equations are transformed into a set of self-similar ordinary differential equations by similarity transformations. the transformed equations are solved numerically using very efficient shooting method. the study reveals that the dual solutions of velocity and concentration exist for certain values of velocity ratio parameter (the ratio of stretching/shrinking rate and straining rate). the concentration boundary layer thickness decreases with increasing values of schmidt number and reaction-rate parameter for both solutions.