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In order to have a precise knowledge on how pressure gradients and buoyancy force affect fluid flow and energy distribution in a bending channel, it is important to perform a comprehensive study on flow characteristics and heat transfer mechanisms that trigger out the transition of fluids into a turbulent state, subject to a sustained pressure gradient. The present paper explores a computational modeling on two-dimensional fluid flow and thermal characteristics in a bent square channel of strong curvature. The Newton–Raphson (N-R) iteration method is applied to obtain a bifurcation structure depending on the pressure-driven force, the Dean number (De), covering 0 < De ≤ 5000. As a consequence, four branches of asymmetric steady solutions are identified for each of the cases of the Grashof number, Gn (=1000, 1500, and 2000), where only the first branch is found to exhibit asymmetric two-vortex solutions while the remaining branches encompass twoto four-vortex solutions. The similarity and disparity in the branching structure are also demonstrated. Then, adopting the Adam–Bashforth (A-B) method together with Crank–Nicholson (C-N) formula, the unsteady solutions (US) have been explored, validated by power spectrum density (PSD) and phase space Within the realm of US, two- and three-vortex solutions are found and these solutions exhibit transitions from steady to chaotic behavior profoundly. Effects of the Grashof number with convective heat transfer (CHT) are also compared. By analyzing the Nusselt number (Nu), it is observed that in case of highly chaotic flow, CHT experiences substantial enhancement. This intensified CHT arises from increased turbulence and mixing, facilitating more efficient thermal energy exchange under such chaotic flow conditions. [ABSTRACT FROM AUTHOR]

This research aims to delve into the transient MHD flow over a porous plate having an inclination, with heat and mass diffusion by taking the radiative phenomenon into consideration. The flow controlling equations of continuity, momentum, energy, and concentration are developed using the boundary layer approximations. The radiative flux is described using a differential approximation. The governing time-dependent equations are brought into a conversion to create a system of non-dimensional partial differential equations (PDEs). Numerical schemes approaching the explicit finite difference method (EFDM) are employed to discretize and reckon the equations in dimensional agreement. Stability and convergence checking are prepared to ensure the converging restrictions of pertinent parameters. The profiles of velocity, concentration, and temperature have been illustrated graphically and discussed comprehensively. [ABSTRACT FROM AUTHOR]

The understanding of fluid flow and heat transfer (HT) through a rotating curved duct (RCD) is important for different engineering applications. The available literature improved the understanding of the fluid flow and HT through a large-curvature rotating duct. However, the comprehensive knowledge of fluid flow and HT through an RCD with small curvature is little known. This numerical study aims to perform fluid flow characterization and HT through an RCD with curvature ratio 0.001. The spectral based numerical approach investigates the effects of rotation on fluid flow and HT for the Taylor number -1000 ≤ Tr ≤ 1500. A constant pressure gradient force, the Dean number Dn = 100, and a constant buoyancy force parameter, the Grashof number Gr = 500 are used for the numerical simulation. Fortran code is developed for the numerical computations and Tecplot software is used for the post-processing purpose. The numerical study investigates steady solutions and a structure of two-branches of steady solutions is obtained for positive rotation. The transient solution reports the transitional flow patterns and HT through the rotating duct, and two- to four-vortex solutions are observed. In case of negative rotation, time-dependent solutions show that the Coriolis force exhibits an opposite effect to that of the curvature so that the flow characteristics exhibit various flow instabilities. The numerical result shows that convective HT is increased with the increase of rotation and highly complex secondary flow patterns influence the overall HT from the heated wall to the fluid. To validate the numerical results, a comparison with the experimental data is provided, which shows that a good agreement is attained between the numerical and experimental investigations. [ABSTRACT FROM AUTHOR]

The present work explores a spectral-based computational study on hydrothermal behavior of transient fluid flow with natural and forced convective heat transfer through a rotating curved rectangular duct of strong curvature. The outer wall of the duct is heated while the inner wall cooled, the other walls being thermally insulated. The system rotates about the vertical axis in the positive and negative direction for the Taylor number (-1000≤Tr≤1000) with a constant non-dimensional pressure gradient force, the Dean number Dn = 2000. Time-history analysis is performed and fluid characteristics are well determined by depicting the phase space of the time-history result. It is found that the chaotic flow turns into steady-state flow through multiperiodic and periodic oscillating flows, if Tr is increased either in the positive or in the negative direction. Streamlines of secondary flow and isotherms are obtained at some specific values of Tr, and it is found that the time-dependent flow consists of asymmetric 2- tomulti-vortex solutions. Vortex structure of secondary flows is obtained for physically realizable solutions and it is found that maximum 8-vortex is obtained for the chaotic solution while 2-vortex for the steady-state solution. Nusselt number as well as temperature gradient is calculated as an index of heat transfer, and it is found that convective heat transfer is significantly enhanced by the secondary flow; and the chaotic flow, which occurs relatively at small Tr, boosts heat transfer more effectively than the steady-state or other solutions. Finally, our numerical results have been validated with the experimental outcomes and it is found that there is a good agreement between the numerical and experimental investigations. [ABSTRACT FROM AUTHOR]

The present paper addresses numerical prediction of hydrodynamic instability with convective heat transfer through a rotating curved rectangular duct of curvature 0.1. The bottom wall of the duct is heated while cooling from the ceiling. Numerical calculations are carried out by using a spectral method and covering a wide range of the Taylor number 0 2000 ≤ Tr ≤ for the constant pressure gradient force, the Dean number, 1000 Dn = . First, solution structure of the steady solutions is investigated. As a result, three branches of asymmetric steady solutions with two- to ten-vortex solutions are obtained by using Newton-Raphson iteration method. Then unsteady solutions are obtained by time evolution calculations and flow transitions are well justified by obtaining the phase space and power spectrum of the solutions. It is found that chaotic flow turns into steady-state flow through periodic oscillating flow, if Tr is increased. Streamlines and isotherms are also obtained at several values of Tr, and it is found that the unsteady flow consists of two- to ten-vortex solutions. The present study shows that combined action of the centrifugal-Coriolis-buoyancy forces contribute to generate the vorticity. The present study exposes the role of secondary vortices on convective heat transfer, which shows that convective heat transfer is significantly enhanced by the secondary flow; and the chaotic flow, which occurs at small Tr but at large Dn, enhances heat transfer more effectively than the steady-state or periodic solutions. [ABSTRACT FROM AUTHOR]

The present paper investigates numerical simulation of fluid flow and heat transfer through a rotating curved square channel of curvature ratios ranging from 0.001 to 0.5. Crank-Nicolson and Adams-Bashforth methods together with the function expansion and the collocation methods are applied to obtain the numerical solution. The bottom wall of the channel is heated while cooling from the ceiling. The channel is rotated in the positive direction for the Taylor number 0 ≤ Tr ≤ 2000 and combined effects of the centrifugal, Coriolis and buoyancy forces are investigated. As a result, two branches of asymmetric steady solutions comprising with two- to multi-vortex solutions are obtained. Linear stability analysis shows that the flow is stable only for a small region 164.82 ≤ Tr ≤ 601.62 while unstable otherwise. In the unstable region, time-dependent solutions are obtained and flow transitions are well determined by obtaining power spectrum density of the solutions and it is found that the timedependent flow undergoes through various flow instabilities, if Tr is increased in the positive direction. The results clearly show the existence of multiple Dean vortices along the duct while axial velocity profile is related to the outer Dean vortices, the wall pressure is more influenced by the Dean vortices attached to the outer concave wall. The present study elucidates the role of secondary vortices on convective heat transfer which shows that convective heat transfer is significantly enhanced by the secondary flow; and the chaotic flow, which takes place at large Tr's, enhances heat transfer more efficiently than the steady-state or periodic solutions. This study also reveals that there is a sharp influence between the ardor-induced buoyancy force and centrifugal-Coriolis instability in the rotating curved channel that inspires fluids mixing and consequently enhances heat transfer in the fluid. Finally, our numerical results are compared with the experimental investigations, and it is found that there is a good agreement between the numerical and experimental data. [ABSTRACT FROM AUTHOR]

In this paper, a numerical study on centrifugal instability with convective heat transfer through a curved square duct is presented by using a spectral method, and covering a wide range of the Dean number (0< Dn ≤ 5000) for a tightly coiled square duct of curvature 0.5 The outer and bottom walls of the duct are heated while cooling from the inner and the ceiling. The main objective of this study is to expose combined effects of centrifugal and buoyancy forces on fluid flows through a curved channel. For this purpose, solution structure of the steady solutions is obtained first. As a result, four branches of symmetric/asymmetric steady solutions are obtained. Linear stability of the steady solutions is then investigated. It is found that only the first branch is linearly stable while the other branches are linearly unstable. Unsteady flow behavior, obtained by time evolution calculations, shows that the steady-state flow turns into chaotic flow via periodic and multiperiodic flows, if Dn is increased. Typical contours of secondary flow pattern, stream-wise velocity distribution and temperature profiles are obtained at several values of Dn and it is found that the flow consists of asymmetric two- to four-vortex solutions. The present study shows that convective heat transfer is significantly enhanced by the secondary flow; and the chaotic flow, which occurs at large Dn’s, enhances heat transfer more effectively than the steady-state or periodic solutions. Finally, a comparison between the numerical and experimental investigations has been made, and it is found that there is a good agreement between the numerical and experimental investigations. [ABSTRACT FROM AUTHOR]