Multiple Regression and Numerical Analysis of Dual Solutions in Mixed Convection Non-newtonian Fluid Flow

This work considers mixed convection flow of a non-Newtonian Prandtl-Eyring fluid over a stretching/shrinking vertical surface with suction and thermal radiation. The non-Newtonian property of the fluids makes the partial differential equations governing them highly nonlinear, which has established significant difficulties in both numerical and analytical solutions. Lie symmetry analysis is employed to transform these equations into a system of ordinary differential equations, which are solved numerically using MATLAB’s ‘bvp4c’ solver. Dual solutions are noticed from the numerical simulation in the opposing flow region for the stretching and shrinking cases. These solution branches exist for values of the critical buoyancy parameter ($$\beta> \beta _c$$), where the absolute stretching/shrinking parameter ($$\lambda$$) enhances the value of the critical point along with the range for co-existing solutions. The stability analyses show that the upper solution is stable while the lower solution remains unstable. The multiple regression analysis correlates flow variables with relevant parameters. The lower branch has better predictive ability for the skin friction coefficient; on the other hand, the upper branch gives extraordinarily well defined accuracy for Nusselt number calculations compared with the lower branch for thermal conduction analysis. The results indicate that fluid velocity and temperature decrease with increasing non-Newtonian parameter (K) along the upper branch. The results indicate more complicated flow behavior and heat transfer phenomena in the mixed convection regime. The results are presented in the form of detailed graphical aids and tables, which help in penetrating the depth of the phenomena concerning the dynamics of the non-Newtonian fluids in the process involving stretching/shrinkage.