Analytical solutions for non-isothermal viscoelastic torsional flow in a bounded domain

Abstract

The effects of viscous heating on torsional flow of viscoelastic fluids in the parallel-plate viscometer are considered. The fluid is modelled by the Oldroyd-B constitutive equation with temperature-dependent viscosities and relaxation time which obey a Nahme type law. Analytic solutions are obtained in the limit of small Nahme–Griffith number which are uniformly valid up to the fluid–air interface. If the aspect ratio, α is small then there is a thermal boundary layer of width α at the free surface.