Stability analysis of flow and heat transfer over a permeable stretching/shrinking sheet with internal heat generation and viscous dissipation

In this study, a steady two-dimensional boundary layer flow and heat transfer in an incompressible viscous fluid over a stretching/shrinking sheet with suction, internal heat generation and viscous dissipation is studied. The governing equations are first reduced to the nonlinear ordinary differential equations using a set of similarity variables. The obtained equations are then solved numerically using the bvp4c function in MATLAB. It is found that the nonlinear ordinary differential equations have dual (first and second) solutions in a certain range of the suction parameter. Stability analysis is employed to test the stability of the dual solutions. The results indicate that the first solution is stable while the second solution is unstable.