Non-isothermal flow of a Johnson–Segalman liquid in a lubricated pipe with wall slip

Abstract

This work focuses on the unsteady, axi-symmetric, non-isothermal flow of a viscoelastic Johnson–Segalman liquid in a lubricated pipe which allows for wall slip. In simple flows, the Johnson–Segalman constitutive model under certain conditions allows for a non-monotonic relationship between the shear stress and the rate of shear, hence, leading to shear banded flow phenomena. Wall slip has been conjectured to play a role or at least occur simultaneously with shear banding in certain cases. We investigate the relationships between wall slip and shear banding in non-isothermal pipe flow of a Johnson–Segalman fluid under axi-symmetric conditions and Arrhenius chemical kinetics. The wall slip in our investigation is postulated to arise, say, from wall lubrication; both constant and variable wall slip effects are here considered. The set of coupled non-linear time dependent partial differential equations for the fluid velocity, temperature and viscoelastic stresses are solved via semi-implicit finite difference techniques. We discuss the effect of wall slip on the flow profiles while varying certain flow and fluid material parameters.