Transient Heat and Fluid Flow through a Rotating Curved Rectangular Duct: The Case of Positive and Negative Rotation

Abstract

Abstract A comprehensive numerical study is presented for the fully developed two-dimensional thermal flow of viscous incompressible fluid through a rotating curved rectangular duct of constant curvature δ=0.1 Numerical calculations are carried out by using a spectral method, and covering a wide range of the Taylor number -1000 ≤ Tr ≤ 3000 and the Dean number 100≤ Dn ≤1000 for the Grashof number Gr 100. The outer wall of the duct is heated while the inner wall cooled. Flow characteristics are investigated for two cases of the duct rotation, Case I : Positive rotation and Case II : Negative rotation. For positive rotation, we investigate the unsteady flow characteristics for the Taylor number 0≤ Tr ≤3000 and it is found that the unsteady flow undergoes in the scenario ‘ Chaotic→multi-periodic → periodic → steady-state’ , if Tr is increased in the positive direction. For negative rotation, however, we investigate the unsteady flow behavior for 1000≤ Tr ≤100, and it is found that the unsteady flow undergoes through various flow instabilities, if Tr is increased in the negative direction. Contours of secondary flow patterns and temperature profiles are also obtained at several values of Tr , and it is found that there exist two- and multi-vortex solutions if the duct rotation is involved in both the directions.