Heat transfer for a Giesekus fluid in a rotating concentric annulus

Annular flow of a viscoelastic fluid described by the Giesekus model has received some attention over the years, both concerning the fluid mechanical and thermal aspects, yet no investigation has been carried out using the analytical solution for the velocity profile in the energy equation to determine temperature distribution and heat transfer characteristics. Moreover, viscous dissipation, when accounted for, is usually defined by a formulation of the Brinkman number which proves inconsistent when applied to non-Newtonian fluids. In this work the purely tangential flow of a Giesekus fluid in an annulus with rotating inner wall subject to thermal boundary conditions of the first kind (imposed temperature) at the walls is investigated employing the analytical solution for the velocity profile. Viscous dissipation is accounted for by first deriving a consistent Brinkman number which is easily related to the one usually employed in previous studies and the temperature profiles are obtained for different values of the Deborah number and the non-dimensional mobility factor. Results for the Nusselt numbers at the inner and outer wall are also discussed.