Stability analysis of dual solutions magnetohydrodynamics stagnation-point flow of Carreau fluid towards a stretching/shrinking surface with induced magnetic field and convective boundary conditions

The problem of the steady two-dimensional magnetohydrodynamics (MHD) stagnation-point flow of Carreau fluid towards a permeable stretching/shrinking sheet is studied. The effect of the induced magnetic field and convective boundary conditions are taken into account. The nonlinear partial differential equations are transformed into nonlinear ordinary differential equations by using similarity transformations. The transformed governing equations are solved numerically via the boundary value problem solver (bvp4c) in MATLAB software. Numerical solutions for the physical quantities as well as the velocity and temperature profiles are obtained. It is found that dual solutions exist for a certain range of the controlling parameter. Therefore, a stability analysis is performed to determine which solution is linearly stable and valid physically.

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