A depth understanding of fluid flow past a curved duct having rectangular cross-section with different aspect ratios (

Rotating flow and consequent heat conduction through the curved duct have been drawn considerable interest to the researchers for their vast applications not only in the field of fluids engineering (cooling and heating systems) and aviation engineering [

In a curved duct, centrifugal force is produced due to the duct’s curvature, resulting in a lateral rotating vortex acting in the axial direction. In the bending domain, these vortices have the properties of spiraling motion known as secondary flow [

Time-dependent solution structures of the fully developed flow were investigated first by Yanase et al. [

One of the most features of fluid flow over a curved channel is heat conduction between two walls. Dean flow can help to transport energy and consequently increase heat transfer between two side walls. Chandratilleke et al. [

The hydro-thermal efficiency of coupled rotating cylinders with partially porous system in the bifurcation duct was investigated by Kolsi et al. [

Alsabery et al. [

In a fixed orthogonal coordinate system, the unsteady flow of an incompressible Newtonian fluid in a curved pipe with fixed curvature is studied. A rectangular shape cross-section is considered, where the height and width are 2

All the dimensional quantities are converted into the non-dimensional component by employing the representative length (_{0} = _{0} = ^{2}/_{0,} and _{0}, where _{0}^{2}

A unique variable

where,

The dimensionless parameters

where, _{n} = 1500,

The governing

where,

where

where

For evaluating the time-dependent results, both Crank-Nicolson and Adams-Bashforth schemes with

Before starting the investigation, the proposed model was validated comprehensively with published numerical modeling conducted by Mondal et al. [

The speed of rotation of the duct affects heat transfer through the Nusselt number. In order to measure the effect of rotation on heat generation, the Nusselt number was calculated and compared with the experimental results conducted by Becker et al. [

10 | 20 | 0.36057358 | 180.0593 | |

14 | 28 | 0.36089734 | 180.2898 | |

16 | 32 | 0.36090702 | 180.4822 | |

18 | 36 | 0.36090845 | 180.5019 | |

20 | 40 | 0.36090815 | 180.5231 | |

10 | 30 | 0.14077384 | 131.9530 | |

14 | 42 | 0.14087560 | 131.8759 | |

16 | 48 | 0.14063302 | 131.4308 | |

18 | 54 | 0.14090892 | 131.4209 | |

20 | 60 | 0.14070839 | 131.4035 |

To explore the effect of

After a certain rotational speed, the time evolution curve will shift into the periodic or multi-periodic oscillating flow. The flow patterns are irregular in shape, while the oscillation and amplitude of the oscillation are lower than low rotational speed (

Nusselt number (

where

Note that, if the fluid free-stream temperature and the wall-surface temperature vary, a thermal boundary layer develops near the vicinity of the wall and due to the energy exchange resulting from the temperature variation between the walls, a temperature profile is formed. As a temperature difference between the outer and inner walls is applied, a thermal boundary layer is developed for both heated and cooled walls, which contributes to the characterise the flow nature. To measure such nature of the unsteady fluid flow for the steaming motion in the bending channel

The calculated values of the time-averaged Nusselt number (_{c} = 671.23 ^{-2} and for heating wall _{h} = 819.74 ^{-2}). It is also mentioned that the variation of viscosity at the cooling bending wall is dampening the secondary flow and the vortex construction due to the energy gradient between these two side walls. Along the vertical centerline, the temperature management of fluid contributes to altering the density of the fluid due to the heated wall, and the fluid gets accelerated to travel. Consequently, heat is transferred to the low-temperature region. The rate of temperature distribution on the flow domain is analyzed to get a clear insight about the advection of the curved channel, as presented in

The temperature distribution of the outer and inner walls has been analyzed by calculating the temperature gradient of the flow domain (see

The present computational study has been performed to characterize fluid flow and energy distribution through a rotating bent rectangular channel of aspect ratio 2 and 3. The effect of rotational parameters on fluid flow for a constant pressure gradient is investigated by analysing Dean-vortex formation, temperature contour, and axial flow distribution for low to high-speed of rotation. The numerical code has been developed to optimize the present model by validating existing experimental and computational studies, and found excellent agreement. The overall calculation is performed for a variable wall temperature, and an adiabatic condition is employed at the upper and the lower walls of the bending channel. The following conclusions have been drawn from the present study:

Time-dependent solutions followed by phase-space analysis of the solutions exhibit that the transitient flow endures in the scenario ‘c

The numerical results report that maximum 10-vortex solution is attained for aspect ratio 2, while 13-vortex for aspect ratio 3. The study shows that 6- to 10-vortex solutions are available for the periodic solution, while 5- to 13-vortex for the chaotic solution. The chaotic regime of the flow exhibits maximum number of Dean vortices.

The study illustrates that higher temperature difference occurs for lower

Gradual increase of the Nusselt number at the high and low temperatured walls happens because of the effect of Coriolis force to maintain the constant heat flux into the computational domain.

The current study shows that there arises a strong interaction between the heating-induced buoyancy force and the centrifugal-Coriolis instability in the rotating bending channel that stimulates fluid mixing and thus increases heat transfer in the fluid.

The present study investigates effects of various forces,

The authors would like to thank Dr. Saidul Islam, Scholarly Teaching Fellow, University of Technology Sydney, for his contribution to formatting the manuscript.

_{0}