Non-isothermal flow with convective heat transfer through a curved duct for various aspect ratios

Due to ample engineering applications, flow in a curved duct has become one of the most challenging research fields of fluid mechanics. In this paper, a computational numerical study of flow and heat transfer through a curved rectangular duct of various aspect ratios has been analyzed by using a spectral method and covering a wide range of the pressure gradient parameter, the Dean number 0 < Dn ≤ 1000 for the Grashof number Gr=1000. Unsteady solutions are obtained by time evolution calculations for the aspect ratios ranging from 1 to 3 with constant curvature 0.5. The outer wall of the duct is heated while the inner wall is in normal temperature, the top and bottom walls being thermally insulated. The main concern of this paper is to investigate the effects of aspect ratios on time-dependent solutions such as steady-state, periodic, multi-periodic or chaotic solution, if Dn is increased. For square duct flow, it is observed that there appears steady-state solution whether Dn is small or large. For rectangular duct of aspect ratio 2, however, the steady-state solution turns into chaotic solution, if Dn is increased. For aspect ratio 3, on the other hand, the steady-state solution turns into chaotic solution via periodic or multi-periodic flows. To justify the flow transition from one state to another, phase portrait of the time evolution results are obtained. Secondary flow patterns and temperature profiles on the flow characteristics are also obtained. Nusselt numbers are calculated as an index of convective heat transfer, and it is found that convective heat transfer is significantly enhanced by the secondary flow and as the flow becomes chaotic heat transfer occurs substantially. Finally, our numerical results are validated with experimental investigations and it is found that there is a good agreement between the numerical and experimental data.