Forced-To-Quasi-Free Vortex Inlet Swirl Velocity and Viscous Dissipation on Heat Transfer in Decaying Swirling Flow with Prescribed Wall Heat Flux

Abstract This study presents a comprehensive numerical investigation of laminar swirling flow and forced convection in the thermal entrance region of a circular duct, addressing the coupled effects of viscous dissipation and decaying swirl for high-viscosity fluids. While prior research has largely neglected viscous dissipation in swirling flows, this work bridges the gap by analyzing the interplay between inlet swirl profiles (forced-to-quasi-free vortex), viscous core size (0.5 ≤ 2λ ≤ 1.0), and Brinkman numbers (0 ≤ Br ≤ 5) on heat transfer characteristics under prescribed wall heat flux conditions. A validated finite-volume solver was employed to solve three-dimensional, axisymmetric governing equations, incorporating viscous dissipation effects through a dissipation function. A vortex breakdown occurrence map linking Rossby and core Reynolds numbers was developed, showing that a critical threshold (2λ 0.5) exists to prevent flow instability, a pivotal criterion for phase separator design. The viscous core size has a critical impact on heat transfer performance. High viscous core values lead to diminished velocity gradients, inhibiting the development of the thermal boundary layer. Conversely, a low viscous core size strengthens velocity gradients, thereby improving heat transfer. The results offer novel insights into thermal management for high-viscosity swirling flows, providing practical guidelines for industrial applications, such as inline cyclonic separators and viscous fluid processing systems.