Numerical and Computer Simulations of Cross-Flow in the Streamwise Direction through a Moving Surface Comprising the Significant Impacts of Viscous Dissipation and Magnetic Fields: Stability Analysis and Dual Solutions

The inspiration for this study is to explore the crucial impact of viscous dissipation (VISD) on magneto flow through a cross or secondary flow (CRF) in the way of streamwise. Utilizing the pertinent similarity method, the primary partial differential equations (PDEs) are changed into a highly nonlinear dimensional form of ordinary differential equations (ODEs). These dimensionless forms of ODEs are executed numerically by the aid of bvp4c solver. The impact of pertinent parameters such as the suction parameter, magnetic parameter, moving parameter, and viscous dissipation parameter is discussed with the help of plots. Dual solutions are obtained for certain values of a moving parameter. The velocities in the direction of streamwise, as well as cross-flow, decline in the upper branch solution, while the contrary impact is seen in the lower branch solution. However, the influence of suction on the velocities in both directions uplifts in the upper branch solution and shrinks in the lower branch solution. The analysis is also performed in terms of stability to inspect which solution is stable or unstable, and it is observed that the lower branch solution is unstable, whereas the upper branch one is stable.