Numerical study of steady and periodic mixed convection of Bingham fluid in a narrow annulus with the exact Bingham model

This article numerically investigates the mixed convection of Bingham fluid in a narrow annulus. The temperature of the inner fixed cylinder (?i) is higher than that of the outer one (?(o)), which rotates at a constant angular velocity. An OpenFOAM solver, icoFoam, which works based on the finite volume method and the PISO algorithm, is modified to perform the simulations. The modified solver can solve unsteady heat transfer problems for Bingham fluids without using regularization methods. After validating the solver, it solves the problem in different conditions to show the effect of relevant parameters, such as Reynolds number, Bingham number, and aspect ratio, on the flow field and thermal performance of the enclosure for constant amounts of Grashof and Prandtl numbers. The results are presented as streamlines and isotherms, the size and shape of the unyielded regions, the local and mean Nusselt number, and the torque coefficient. The results demonstrate that the flow is steady at Re=10 for all Bingham numbers, and a decrease in the Reynolds number may result in an unsteady flow depending on the value of the Bingham number. The flow's time history reveals that at a fixed Reynolds number, the flow shifts from periodic to steady-state by enhancing the Bingham number so that the flow becomes entirely steady for a given Bingham number. An interesting phenomenon is observed, the formation, movement, and disappearance of the plug zones (unyielded regions) for the periodic flow at Re=1 and Bn=5.

Automated summary

This article numerically investigates the mixed convection of Bingham fluid in a narrow annulus. An OpenFOAM solver, icoFoam, is modified to solve unsteady heat transfer problems for Bingham fluids. The simulation results show the effect of Reynolds number, Bingham number, and aspect ratio on the flow field and thermal performance. An interesting phenomenon of the formation, movement, and disappearance of unyielded regions is observed.