Numerical prediction of unsteady fluid flow and heat transfer through a stationary curved square duct

Abstract

Time-dependent flow behavior through a curved duct is widely encountered in engineering and cell sorting sections. In this article, we have numerically investigated time-dependent fluid flow and dynamic heat transfer related to the stationary curved square duct, paying particular attention to the dependence of velocity and temperature fields on Dean number (Dn), Grashof number (Gr), curvature (δ) and aspect ratio. Here, the outer and bottom walls of the duct are maintained at high temperature whereas the inner and upper walls adiabatically segregated. In the first instance, time evolution calculation of the unsteady solutions has been performed for an extensive range of the Dean number (100 ≤ Dn ≤ 1000) and the Grashof number ( 100 ≤ Gr ≤ 1000) while other parameters have been considered to be fixed. Time-dependent solutions show that the flow undergoes through various flow instabilities regarding the range of parameters. It has been seen that three types of flow characters, steady-state, periodic, multi-periodic oscillations have been constructed in the time vs. Nusselt number for cooling wall plane. To point out the periodic and multi-periodic flow more clearly, power spectrum has been accomplished. Typical contours of two types of flow velocity such as axial and secondary flow and isotherm (temperature profiles) have been obtained for various values of Dn and Gr. It is found that only two-vortex asymmetric solutions appear for the steady-state solution whereas two- to four-vortex for the periodic and multi-periodic flows. Heat transfer has been demonstrated and it is found that heat transfer is enhanced by the secondary flow particularly when the Dean vortices emerge at outer concave wall. The present investigation reveals that there is a sharp influence amidst the ardor-induced buoyancy compulsion and the centrifugal instability in the curved duct that stimulates fluid composition and consequently enhances heat transfer in the fluid.