Stability analysis of dual solutions for boundary layer stagnation point flow over a shrinking sheet with suction

At the surface of the object in the flow field, there exist stagnation points when the fluid is brought to rest effected from the object. This stagnation region experiences the highest pressure. This thesis studies some problems in stagnation point region by considering five problem in different situation. The five problems considered are stagnation point flow over exponentially shrinking sheet, stagnation point flow over shrinking sheet in homogeneoues heterogeneous reactions, MHD stagnation point flow over shrinking sheet, MHD stagnation point flow over shrinking sheet in nanofluid and unsteady MHD stagnation point flow over shrinking sheet. Shrinking sheet and suction parameter is considered in all the problems. The partial differential equations for each problem are first transformed into similarity equations in ordinary differential equations form by similarity transformations. Then, the equation obtained are then solved numerically by using the bvp4c function and shooting method. We used commercially available software which is Maple to generate the shooting technique where Runge-Kutta method together with Newton-Raphson method is involved. Meanwhile bvp4c function is used in MATLAB. Comparisons with existing solutions in literature for specific cases have been made and the present results show an excellent agreement from previous work. It is found that dual solutions exist for a certain range of shrinking and suction parameter for all problems. Therefore, stability analysis is performed to determine the stable solutions by using the bvp4c function. This analysis concludes that, only the first solution is stable and physically significant while the second solution is unstable.

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