LAUSR

Abstract Inspired by the various applications of non-Newtonian fluids, we carried out a numerical study for multiple solutions in MHD flow of Carreau viscosity model over a shrinking cylinder. This article is presumably the first contribution to the analysis of multiple solutions for the Carreau fluid flow over a shrinking cylinder. The effects due to heat transfer mechanism along with the diffusion of chemically reactive species are further taken into account in order to govern the flow characteristic. Rather than no-slip condition at the stretching surface, velocity-slip condition has been employed. The governing conservation equations are transformed to non-linear ordinary differential equations, in a single independent variable by adopting non-dimensional variables. These emerging foremost non-linear equations have been tackled numerically by means of a collocation technique. The interference impacts and the flow characteristics are presented in the form of fluid velocity, temperature and concentration distributions. The critical values have additionally been acquired by using the graphs of reduce skin friction and Nusselt number. The review demonstrates that the multiple branches of the solution exists for the certain range of important physical parameters, for instance, shrinking parameter λ, curvature parameter γ, Hartmann number Ha , velocity-slip parameter δ, suction parameter f w , Schmidt number Sc and rate parameter β. The outcomes reported herein manifest that presence of velocity slip phenomenon widens the range of shrinking parameter for which the multiple solution exists. Another interesting observation is that the non-dimensional fluid velocity is significantly raised by the curvature parameter and Hartmann number for the first branch solution and an opposite is seen for the second branch solution. For verification of the current model, the obtained results are distinguished with earlier works in particular cases and admirable agreement has been noted.