Mixed convection nonaxisymmetric Homann stagnation-point flow under the influence of magnetic field

Abstract

In the present study, we have investigated the steady mixed convection nonaxisymmetric Homann stagnation-point flow in the presence of a magnetic field over a vertical flat wall immersed in a viscous and incompressible fluid. The magnetic field is applied in the normal direction to the plate. The governing equations are reduced to a system of nonlinear ordinary differential equations with suitable boundary conditions by applying similarity transformations to the equations and the boundary conditions. Using an efficient shooting method, the transformed equations are numerically solved. The solution involves the dimensionless governing parameters: γ representing the shear-to-strain-rate ratio, a mixed convection parameter λ, a magnetic field parameter M, and Prandtl number Pr. An important observation is that dual solutions exist for a certain range of mixed convection parameter λ. It is noticed that critical values λ_c of λ are found in opposing flow, which produce two solution branches by making saddle-node bifurcation at λ = λ_c. Numerical results are obtained for representative values of γ, λ, and M and are explored in depth. Through the use of graphs, the properties of the flow and temperature profiles for various values of the governing parameters γ, λ, and M are examined. Also, we examined how the solution varied with λ for representative values of M (magnetic field parameter). A parametric analysis is conducted to investigate how different governing parameters affect the characteristics of fluid flow and temperature. Also, we derive asymptotic results for large λ.