The role of Brinkmann ratio on non-Newtonian fluid flow due to a porous shrinking/stretching sheet with heat transfer

Abstract

A Magnetohydrodynamic (MHD) non-Newtonian liquid flow caused by porous stretching/shrinking sheet with mass transpiration and MHD in a Darcy–Brinkmann model is investigated. This type of flow problem is significant in industrial processes involving polymer extrusion, metal spinning, metal thinning, polymer fiber, glass blowing, manufacturing of petrochemical products, and the allied areas of hydro-physics. Ultimately, the flow problem is modeled into a system of nonlinear partial differential equations (PDE) later converted into an ordinary differential equation (ODE) taking advantage of similarity transformations. The heat transfer requires investigating two types of conditions, namely the sheet with a specified surface temperature(PST) and another with wall heat flux (PHF). This eventually culminates into a nonlinear ODE which is solved analytically. We eventually map the linear ODE with a variable coefficient into a confluent hypergeometric differential equation using a new variable accompanied by a Rosseland approximation for radiation. The analysis is carried out by using the viscosity ratio or the Brinkmann model. Further, effects on the velocity and temperature distribution by the Brinkmann number or viscosity ratio as well as the other physical parameters involved in the model are discussed graphically. Such flow problems are encountered in industrial processes such as composite fabrication, metal spinning, hot air coils, glass blowing.