Unsteady heat transfer enhancement and suppression around a heated circular cylinder in Bingham plastic fluids

This numerical study investigates unsteady flow and heat transfer characteristics of Bingham plastic fluids past a heated cylinder. Simulations span plastic Reynolds numbers (10 ≤ Re ≤ 180), Prandtl numbers (1 ≤ Pr ≤ 100), and Bingham numbers (0 ≤ Bn ≤ 104), employing the Papanastasiou regularization method to model the yield-stress behavior. Re and Pr are defined explicitly in terms of the plastic viscosity and Bn as the ratio of the fluid's yield stress to a characteristic viscous stress scale. The results reveal a subcritical Hopf bifurcation in vortex shedding, characterized by a hysteresis loop for Re ≥ 60 between two critical Bingham numbers above which vortex shedding disappears, BncI (for the increasing Bn process) and BncD (for the decreasing Bn process), indicating a strong dependence on initial conditions. Bn plays a dual role in heat transfer. In steady flow, the Nusselt number (Nu) increases monotonically with Bn at low Pr, while at high Pr (10, 100), it exhibits a non-monotonic behavior with a minimum at a critical Bingham number Bnc2 that scales linearly with Re. In unsteady flow, vortex shedding enhances heat transfer by up to 20%. Abrupt jumps in the time-averaged Nusselt number (Nu¯) occur near BncI and BncD due to flow transitions. Yield stress redistributes the shear strain rate, thins the boundary layers, and alters the morphology of yielded and unyielded regions. These effects govern the competition between suppressed wake recirculation and enhanced near-wall convection, which ultimately dictates global heat transfer performance. Furthermore, the mean drag coefficient follows Cd¯ = 24.84/Re* for Re* < 0.5, where Re* = Re/(1 + Bn), with discontinuous jumps observed during flow transitions. These findings provide practical insights for optimizing heat transfer in yield-stress fluid applications, such as food processing and cosmetics.