Multiple solutions of steady two-dimensional magnetohydrodynamic boundary layer flow of non-newtonian fluids with stability analysis - Lund, Liaquat Ali (2021)
Over the last few years, non-Newtonian fluids have gained more attention due to their vast real-life applications, particularly in engineering and industries. Previous studies reveal that multiple solutions to these fluids problems occur due to the existence of nonlinearity nature in viscous shear stress. However, these solutions are hard to detect experimentally as they are close to each other. Although from a mathematical point of view, all solutions should be considered since they satisfy all the conditions stipulated, only the stable one is meaningful and applicable. The main objective of this study is to find all possible solutions to six new problems and determine the solutions’ stability. Three of these problems use the Buongiorno nanofluid model while the remaining use viscous non-Newtonian fluids models proposed by Eringen and Casson. By using suitable similarity variables, the governing equations of each problem in partial differential equations have been transformed into boundary value problems (BVPs) of nonlinear ordinary differential equations (ODEs). The shooting method with the help of shootlib function in Maple software was employed to convert the resultant BVPs into initial value problems (IVPs) of first-order ODEs which were then solved using Runge- Kutta method of fourth-order. The numerical results for specific cases obtained in this study have been compared with the solutions in literature for validation purposes and found in excellent agreement. The effects of various involved physical parameters on the skin friction coefficient, heat and mass transfer rates, and profiles of velocity, angular velocity, temperature, and concentration have been investigated. Numerical results indicate that there are four and three solutions in nanofluid and Casson fluid problems, respectively, on the vertically exponential surface, while the dual solutions exist in the remaining problems. It is observed that there are different regions for multiple, unique, and no solutions for each considered problem. The stability analysis has been performed to determine the stability of multiple solutions and the results suggest that only the first solution is stable. This study has successfully discovered multiple solutions to the considered problems and contributed to the body of knowledge in fluid dynamics. The findings of this study can also be used as a reference to reduce the experimental cost in the applications of related areas.