Numerical Prediction of Non-isothermal Flow with Convective Heat Transfer through a Rotating Curved Square Channel with Bottom Wall Heating and Cooling from the Ceiling

The present paper investigates numerical simulation of fluid flow and heat transfer through a rotating curved square channel of curvature ratios ranging from 0.001 to 0.5. Crank-Nicolson and Adams-Bashforth methods together with the function expansion and the collocation methods are applied to obtain the numerical solution. The bottom wall of the channel is heated while cooling from the ceiling. The channel is rotated in the positive direction for the Taylor number 0 <= Tr <= 2000 and combined effects of the centrifugal, Coriolis and buoyancy forces are investigated. As a result, two branches of asymmetric steady solutions comprising with two- to multi-vortex solutions are obtained. Linear stability analysis shows that the flow is stable only for a small region 164.82 <= Tr <= 601.62 while unstable otherwise. In the unstable region, time-dependent solutions are obtained and flow transitions are well determined by obtaining power spectrum density of the solutions and it is found that the time-dependent flow undergoes through various flow instabilities, if Tr is increased in the positive direction. The results clearly show the existence of multiple Dean vortices along the duct while axial velocity profile is related to the outer Dean vortices, the wall pressure is more influenced by the Dean vortices attached to the outer concave wall. The present study elucidates the role of secondary vortices on convective heat transfer which shows that convective heat transfer is significantly enhanced by the secondary flow; and the chaotic flow, which takes place at large Tr's, enhances heat transfer more efficiently than the steady-state or periodic solutions. This study also reveals that there is a sharp influence between the ardor-induced buoyancy force and centrifugal-Coriolis instability in the rotating curved channel that inspires fluids mixing and consequently enhances heat transfer in the fluid. Finally, our numerical results are compared with the experimental investigations, and it is found that there is a good agreement between the numerical and experimental data.