Physics of bifurcation of the flow and heat transfer through a curved duct with natural and forced convection

In the ongoing exploration, a mathematical model is analyzed to study the combined effects of centrifugal and buoyancy forces on fluid flow and heat transfer through a curved square duct of fixed curvature, δ = 0.1 . The outer and bottom walls of the duct are heated while the inner and ceiling walls are in room temperature. Firstly, grid efficiency for different Grashof numbers is checked with evaluating percent relative errors and then the accuracy of the numerical investigation with numerous articles is also compared. After numerical calculation, the steady solution branches with their linear stability have been performed by adopting spectral method. As a result, two branches of asymmetric steady solutions are obtained comprising with two- to four-vortex solutions. Linear stability analysis shows that only the first branch is linearly stable while the other branch is linearly unstable. It is found that the flow is stable at small values of Dean (Dn) whatever the Grashof (Gr) number is, and the stability is delayed as the Grashof number is increased. A substantial interaction is observed between the steady solution branches and the secondary flow structure. A diagram has also been presented which describes the creation of vortex structure of secondary flows for various Dn and Gr. Time history analysis shows that for G r = 200 periodic flow turns into steady-state flow before turning into periodic or multi-periodic oscillation once. For Gr > 200, however, the flow undergoes "multi-periodic/periodic → steady-state'', if Dn is increased. Phase space and power spectrum are obtained to confirm the non-linear characteristics of the flow. Nusselt numbers are computed as an exponent of heat transfer and it is detected that convective heat transfers to periodic and multi-periodic flows have boosted significantly more than steady-state flows. Finally, A comparison among the numerical data and experimental results has been conferred which has shown that there is good consent between them.