A Computational Modeling on Flow Bifurcation and Energy Distribution through a Loosely Bent Rectangular Duct with Vortex Structure

The present study investigates the non-isothermal flow and energy distribution through a loosely bent rectangular duct using a spectral-based numerical approach over a wide range of the Dean number $0<Dn\le 3000$. Unlike previous research, this work offers novel insights by conducting a grid-point-specific velocity analysis and identifying new bifurcation structures. The study reveals how centrifugal and buoyancy forces interact to produce steady, periodic, and chaotic flow regimes significantly influencing heat transfer performance. The Newton-Raphson method is employed to explore four asymmetric steady branches, with vortex solutions ranging from 2- to 12 vortices. Unsteady flow characteristics are analyzed exquisitely by performing time-advancement of the solutions and the flow regimes are shown as a percentage of total flow with longitudinal vortex generation. Axial flow, secondary flow, and temperature profiles have been depicted in accordance with Dn to wander the flow pattern, and it is predicted that the time-dependent flow (TDF) consists of asymmetric 2- to 10-vortex solutions. The significant findings of this study include the axial displacement of the circulations due to the influence of the time-varying temperature dispersal applied along the wall. Chaotic flows, which dominate the higher Dean number range, are shown to enhance heat convection due to increased fluid mixing. A detailed comparison with prior research demonstrates the advantages of this approach, particularly in capturing complex non-linear behaviors. The findings of this study provide practical guidelines for optimizing duct designs to maximize heat transfer and suggest future research directions, such as using nanofluids or studying Magneto-hydrodynamics in the same configuration.