An analytical solution for convective heat transfer of viscoelastic flows in rotating curved pipes

Abstract

This research reports an analytical solution for flow and convective heat transfer of an Oldroyd-B viscoelastic fluid in rotating curved pipes with viscous dissipation effects. In order to solve the momentum and energy conservation equations, a perturbation method is employed. Fully-developed hydrodynamic and thermal boundary conditions are considered with a constant heat flux imposed at the pipe wall. A physical solution based on the H2 boundary condition is presented and it is shown that the results of the present study are more physically realistic than those reported in previous studies utilizing only the H1 assumption. The computations have shown that due to the large gradient of velocity field and rheological properties of viscoelastic fluids, the internal heat generated by viscous dissipation exerts a significant role on both flow and heat transfer characteristics in the present regime. Furthermore, the interesting phenomenon of dissipation of mechanical energy is also investigated. Therefore, the current study emphasizes the substantial effects of viscous dissipation on the heat transfer in non-symmetric temperature distributions. The present analysis evaluates in detail the collective effects of Coriolis force, inertia forces, elastic force and dissipation effects, via the Rossby, Reynolds, Weissenberg and Brinkman numbers, respectively. An increase in Rossby number for the co-rotation case is observed to displace the minimum temperature location toward the outer side of the pipe and additionally enhances the sensitivity of the flow to Reynolds, Weissenberg, Prandtl numbers, viscosity ratios and curvature ratios. Visualization of the main and secondary flows is also presented. The study is relevant to thermal polymeric flow processing.