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•Steady and unsteady flow characteristics show different solution structure.•Linear stability is examined in terms of rotational parameter.•The impact of coriolis-centrifugal instability is comprehensively explored.•Vortex structures are greatly influenced by coriolis force.•Strong interaction between heating-induced buoyancy and centrifugal-coriolis forces.

•This study reveals a numerical investigation on non-rotating bent square channel flow.•Steady structure and stability have been investigated and illustrated exactly.•Transient behavior of the fluid flow is described broadly.•Influence of energy transfer throughout the duct is comprehensively exposed.•Effects of centrifugal force on flow instability and heat transfer are meticulously explored.

The fluid flow and heat transfer through a rotating curved duct has received much attention in recent years because of vast applications in mechanical devices. It is noticed that there occur two different types of rotations in a rotating curved duct such as positive and negative rotation. The positive rotation through the curved duct is widely investigated while the investigation on the negative rotation is rarely available. The paper investigates the influence of negative rotation for a wide range of Taylor number (10 ≤ Tr ≤ 2500) when the duct itself rotates about the center of curvature. Due to the rotation, three types of forces including Coriolis, centrifugal, and buoyancy forces are generated. The study focuses and explains the combined effect of these forces on the fluid flow in details. First, the linear stability of the steady solution is performed. An unsteady solution is then obtained by time-evolution calculation and flow transition is determined by calculating phase space and power spectrum. When Tris raised in the negative direction, the flow behavior shows different flow instabilities including steady-state, periodic, multi-periodic, and chaotic oscillations. Furthermore, the pattern variations of axial and secondary flow velocity and isotherms are obtained, and it is found that there is a strong interaction between the flow velocities and the isotherms. Then temperature gradients are calculated which show that the fluid mixing and the acts of secondary flow have a strong influence on heat transfer in the fluid. Diagrams of unsteady flow and vortex structure are further sketched and precisely elucidate the curvature effects on unsteady fluid flow. Finally, a comparison between the numerical and experimental data is discussed which demonstrates that both data coincide with each other.

•This study develops a computational framework for curved duct flow.•Solution structure, stability and transient behavior of the flow have been investigated.•Effects of Grashof number on steady and unsteady flow have been discussed explicitly.•Heat transfer as well as temperature gradients have been comprehensively explored.•The influence of Dean vortices on overall heat transfer has been shown.

Time-dependent flow investigation through rotating curved ducts is utilized immensely in rotating machinery and metal industry. In the ongoing exploration, time-dependent solutions with flow transition through a rotating curved square duct of curvature ratio 0.009have been performed. Numerical calculations are carried out for constant pressure gradient force, the Dean number Dn = 1000and the Grashof number Gr=100over a wide range of the Taylor number values –1500≤ Tr ≤ 1500for both positive and negative rotation of the duct. The software Code::Blocks has been employed as the second programming tool to obtain numerical solutions. First, time evolution calculations of the unsteady solutions have been performed for positive rotation. To clearly understand the characteristics of regular and irregular oscillations, phase spaces of the time evolution results have been enumerated. Then the calculations have been further attempted for negative rotation and it is found that the unsteady flow shows different flow instabilities if Tr is increased or decreased in the positive or in the negative direction. Two types of flow velocities such as axial flow and secondary flow and temperature profiles have been exposed, and it is found that there appear two- to four-vortex asymmetric solutions for the oscillating flows for both positive and negative rotation whereas only two-vortex for the steady-state solution for positive rotation but four-vortex for negative rotation. From the axial flow pattern, it is observed that two high-velocity regions have been created for the oscillating flows. As a consequence of the change of flow velocity with respect to time, the fluid flow is mixed up in a great deal which enhances heat transfer in the fluid.

A mathematical model is analyzed to study Taylor-heat flux effect on fluid flow and energy distribution through a curved duct (CD) of rectangular cross-section with bottom wall heated while cooling from the top. The dimensionless non-linear equations have been solved by adopting spectral-based computational algorithm. The system is rotated in the clockwise and anti-clockwise direction over the Taylor number -2000≤Tr≤2000and curvature 0.001≤δ≤0.5with a constant pressure gradient force along the axial direction. After a comprehensive investigation, four curves of steady solutions (SS) comprising with 2- to 12-vortex solutions have been found. To explore transient flow behavior, time-history analysis is performed justified by analysis of power-spectrum (PS) density. Results show that the transient flow endures “chaotic → steady-state → chaotic → multi-periodic → steady-state” for 0≤Tr≤2000. For -2000≤Tr<0, however, the flow experiences the path “chaotic → multi-periodic → chaotic → steady-state”. Effects of curvature on secondary vortices are obtained and displayed in the bar diagrams where it is seen that the number of secondary vortices declines as δrises. The ongoing study demonstrates that convective heat transfer (CHT) is considerably exacerbated effectively by the chaotic phenomena than other physically realizable solutions. Furthermore, an assessment between the numerical and experimental data has been given, and a good agreement is observed.