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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Investigation of unsteady flow characteristics through a curved duct is widely used in many engineering applications such as in fluid transportation, rotating machinery and metallic industry. Fluid behavior depends not only on the rotation of the duct but also on physical properties such as fluid pressure, curvature and aspect ratio of the duct. The present paper focuses on the time-dependent flow behavior through a rotating curved square duct. The bottom wall of the duct is heated while cooling from the ceiling, the inner and outer sidewalls being thermally insulated. Numerical calculations are carried out by using a spectral technique, where function expansion and collocation methods are applied for constant Dean number, Dn = 1000, the Grashof number, Gr = 100 and curvature, δ = 0.01 over a wide range of the Taylor number, −1500≤Tr≤1500. In this paper, we investigated flow characteristics for both positive and negative rotation of the duct. Due to combined action of the centrifugal, Coriolis and buoyancy forces various types of physically realizable transient solutions such as steady-state, periodic, multi-periodic and chaotic solutions have been obtained. Flow transitions are well determined by obtaining the power spectrum of the solutions. Typical contours of axial flow, secondary flow and temperature profiles have also been obtained and it is found that time-dependent solutions are comprised of two-to six-vortex solutions. The present study shows that convective heat transfer is significantly enhanced by the secondary flow and there is a strong interaction between the heating-induced buoyancy force and the centrifugal-Coriolis instability in the rotating curved duct that stimulates fluid mixing and consequently enhances heat transfer in the fluid. Finally, our numerical results have been compared with the experimental investigations and it is found that there is a good agreement between the numerical and experimental investigations. [ABSTRACT FROM AUTHOR]

In this paper, a viscous incompressible fluid flow through a tightly coiled rectangular duct of large aspect ratio has been studied numerically by using a spectral method and covering a wide range of the pressure gradient parameter, the Dean number, Dn (0 < Dn ≤ 1000) for both isothermal and non-isothermal flow. For non-isothermal flow, a temperature difference is applied across the vertical sidewalls for the Grashof number Gr =1000, where the outer wall is heated and the inner wall cooled. The main concern of this paper is to investigate effects of aspect ratio on time-dependent solutions such as steady-state, periodic, multi-periodic or chaotic. To investigate non-linear behavior of the unsteady solutions, time evolution calculations are performed and flow transition between two types of solutions is determined by drawing the phase space of the time-dependent solutions. The study shows that if Dn is small, the flow is steady-state whether the flow is isothermal or non-isothermal. However, as Dn increases, the flow undergoes in the scenario 'steady-state ⃗ periodic ⃗chaotic'. Secondary flow patterns, axial flow distribution and temperature profiles on the unsteady flow characteristics are also obtained and it is found that the time-dependent flow consists of asymmetric two- to eight-vortex solutions. Distribution of the time dependent solutions is shown in the Dean number vs. vortex-structure plane for both isothermal and non-isothermal flows. Finally, our numerical results are validated with the experimental investigations obtained so far. [ABSTRACT FROM AUTHOR]