Dual Solutions of MHD Stagnation-point Flow and Heat Transfer past a Stretching/Shrinking Sheet in a Porous Medium

In this paper, the magnetohydrodynamics (MHD) stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in a porous medium is studied numerically. Similarity transformation has been used to transform the governing boundary layer equations to a system of ordinary differential equations from the system of partial differential equations and further solved by the numerical Matlab solver "bvp4c" function. The numerical solutions are illustrated graphically and discussed in the relevance of the governing parameters. It is found that the dual solutions occur when the sheet is stretched and shrunk. Stability analysis is done to determine which solution is stable and valid physically. The results of the stability analysis show that the first solution (upper branch) is stable while the second solution (lower branch) is unstable and may not be physically feasible in practice.