Forced convection in slightly curved microchannels

To address the effects of curvature, initial conditions and disturbances, a numerical study is made on the fully-developed bifurcation structure and stability of the forced convection in curved microchannels of square cross-section and curvature ratio 5 × 10⁻⁶. No matter how small it is, the channel curvature always generates the secondary flow in the channel cross-plane which increases the mean friction factor moderately and the Nusselt number significantly. Unknown initial conditions of convection lead to the co-existence of multiple steady fully-developed flows of various structures. Ten solution branches (either symmetric or asymmetric) are found with eight symmetry-breaking bifurcation points and thirty-one limit points. Thus a rich solution structure exists with the co-existence of various flow states over certain ranges of governing parameters. Dynamic responses of the multiple steady flows to finite random disturbances are examined by the direct transient computation. It is found that possible physically realizable fully-developed flows under the effect of unknown disturbances evolve, as the Dean number increases, from a stable steady 2-cell state at lower Dean number to a temporal periodic oscillation, another stable steady 2-cell state, a temporal intermittent oscillation, and a chaotic temporal oscillation. There exist no stable steady fully-developed flows in some ranges of governing parameters. Both the mean friction factor and the mean Nusselt number are also obtained and analyzed with their correlating relations listed.     

Bifurcation and stability of combined free and forced convection in rotating curved ducts of square cross-section

A numerical study is made on fully developed bifurcation structure and stability of combined free and forced convection in a rotating curved duct of square cross-section. The solution structure is determined as the variation of a parameter indicating the magnitude of buoyancy force. Steady solution structure is very complicated. Flow and temperature fields on various solution branches are identified to be symmetric/asymmetric multi-cell patterns. Dynamic responses of multiple solutions to finite random disturbances are examined by direct transient computation. Five types of physically realizable solutions are identified numerically. They are stable steady 2-cell solution, stable steady multi-cell solution, periodic oscillation, chaotic oscillation and symmetry-breaking oscillation led by sub-harmonic bifurcation (period doubling). Among them, three kinds of stable steady solutions are found to co-exist within a range of parameters. In addition, temporal periodic and chaotic oscillations can also co-exist in another range of parameters. Furthermore, sub-harmonic bifurcation is identified to be another route to chaos. Spectral analysis is used to demonstrate the presence of additional frequencies for the case of sub-harmonic bifurcations. Results show that symmetry-breaking oscillation driven by sub-harmonic bifurcations appear to be identical with the mode observed in Lipps [J. Fluid Mech. 75 (1976) 113], McLaughlin and Orszag [J. Fluid Mech. 122 (1982) 123], and Gollub and Benson [J. Fluid Mech. 100 (1980) 449] for problem of free convection between flat horizontal plates.     

Laminar Forced Flow and Heat Transfer in Cross-Corrugated Triangular Ducts

The fluid flow and heat transfer characteristics in a cross-corrugated triangular channel are studied under laminar forced flow and uniform wall temperature conditions. Both the local and the periodic mean values of friction factor and wall Nusselt numbers in the hydro and thermally developing entrance region are investigated. It is found that at higher Reynolds numbers, recirculations in the lower wall valleys are a dominant factor for flow and heat transfer, while at lower Reynolds numbers, parallel flows in the upper wall corrugation are the predominant factor. Compared with a parallel flat plates duct, the Nusselt numbers in a cross-corrugated triangular duct can be enhanced, and can be even higher at higher Reynolds numbers. The growth of steady recirculations and the concomitant periodic disruption and thinning of the boundary layer promote enhanced transport of heat as well as momentum. Effects of heat transfer enhancement are more obvious under higher Reynolds numbers. Two correlations are proposed to predict the periodic mean values of Nusselt numbers and friction factors for Reynolds numbers from 10 to 2000.     

Effect of thermal buoyancy on vortex shedding past a circular cylinder in cross-flow at low Reynolds numbers

This paper demonstrates the vortex shedding process behind a heated cylinder in a cross-flow at low Reynolds numbers under the influence of thermal buoyancy. The simulations were performed using an SUPG-based finite element technique. The range of Reynolds numbers was chosen to be 10–45. The flow was steady in the absence of thermal buoyancy. The eddy length and the separation angle were computed for the steady separated flow in the above range of Reynolds numbers. The results were in agreement with those reported in the literature. The Nusselt number distribution around the heated cylinder was also computed in the above range of Reynolds numbers for forced convective flows. The results compared fairly well with available experimental results. The effect of superimposed thermal buoyancy in the same range of Reynolds numbers was studied for various Richardson numbers. The steady separated flows become unsteady periodic in the presence of superimposed thermal buoyancy. For the unsteady periodic flows, the Strouhal numbers were computed. The separation angles and average Nusselt number for such unsteady flows were found to vary with time.     

Stability of an oscillatory shear flow in a differentially heated vertical channel

The linear stability of an oscillatory shear flow in a differentially heated vertical channel was investigated numerically for Re = 1000 and Pr = 0.7. The Galerkin method is used to solve the disturbance momentum and energy equations. The results show that the least stable disturbance could be three-dimensional for higher flow oscillation frequency and larger flow oscillation amplitude, while it is two-dimensional in the isothermal oscillatory and heated steady channel flows. The flow oscillation acts to stabilize the flow at moderate and high oscillation frequencies, where the degree of stabilization increases with the oscillation amplitude; but, it acts to destabilize the flow and the amount of destabilization increases with the oscillation amplitude at low oscillation frequency. It is shown from the balance of disturbance kinetic energy budget that shear production is responsible for the flow instability. For the 2-D wave initiated instability, almost all the shear production is generated during a very short time interval at low oscillation frequency, while it is generated during most of the time of a cycle for the 3-D disturbance.     

Natural Convection in an Enclosure with a Partially Active Magnetic Field

Chaotic natural convection flow of a molten gallium in a square enclosure with the upper and lower surfaces being insulated was studied by two-dimensional numerical simulation. Constant temperatures are imposed along the left and right walls of the enclosure with a volumetrically heated enclosure. In addition, a nonuniform partially active magnetic field is applied in a vertical direction. The flux lines spread out into a fringing field so the effective cross-sectional area of the gap is larger than that of the pole face. A chaotic regime is considered under steady state boundary condition. This study was done for an internal Rayleigh number of 10⁷, external Rayleigh number of 10⁵, and Prandtl number of 0.024. The study covers various magnet pole effect widths of 1/4, 1/2, and 3/4 from enclosure width and the magnetic field strength ranges 0.0 ≤ B _o  ≤ 10 Tesla. The transport equations for continuity, momentum, and energy are solved. The numerical results are reported for the effect of the partially active magnetic field on the velocity vectors, counters of temperature, streamline, and heat transfer coefficient. The numerical study shows that a magnetic field is damping chaotic oscillation behavior and decreases the amplitude of oscillation. Also, at a certain magnetic field strength the chaotic flow tend to becomes periodic flow at certain amplitude and frequency, and at high magnetic field strength the flow in the square enclosure flow tends to become steady laminar flow with stable average Nusselt number values; so, the random oscillation behavior disappeared. The effect of a nonuniform magnetic field tends to push the fluid to flow away from magnetic field region.     

Fully-Developed Flow in a Furrowed Wavy Channel: Characterization of Unsteady Flow Regimes and Its Effect on Thermal-Hydraulic Performance

Numerical study is done at various Reynolds numbers (100–2000), for periodically fully developed flow and heat transfer in five geometrically different wavy channels. Time signal analysis is done to distinguish various unsteady flow regimes and a flow regime map is proposed; demarcating steady, two types of periodic as well as quasi-periodic, and chaotic flow regimes. Temporal variation of flow structure and Nusselt number as well as friction factor are presented – in the various unsteady regimes – and discussed for a unified cause-and-effect study. Effect of different flow regimes on the thermal-hydraulic performance of wavy as compared to plane channel is presented. Effect of Prandtl numbers (0.01–100) is also studied.     

Numerical modelling of wind and dust patterns around a full-scale paraboloidal solar dish

This study reports on numerical predictions of velocity and pressure fields, and dust particles trajectories in steady and unsteady flows around a full-scale paraboloidal solar dish. Calculations are performed for three wind speeds of 4.16, 9.72, and 15.2 m s⁻¹, and dish pitch angles from 0° to 180°. The flow field structure, lift and drag coefficients are calculated for each flow configuration. Using the predicted mean flow velocity field, analytical expressions for the aerodynamic coefficients, as a function of the pitch angle, are developed. The unsteady-state flow is characterised by formation of stable vortices behind the dish for most flow configurations, except at 60° and 150° pitch angles. At these angles vortex-shedding occurred with a strong flow oscillation extending downstream the dish. The calculations of dust particles trajectories provide a qualitative assessment of the deposition rate, dish orientation, and surface locations where dust accumulation is most likely to occur. The study also presents an initial assessment of the effectiveness of various windbreaks installed upstream of the dish in reducing aerodynamics drag.     

A UNIFIED ENGINEERING MODEL FOR STEADY AND QUASI-STEADY SHEAR-DRIVEN GAS MICROFLOWS

We analyze one-dimensional plane Couette flows in the entire Knudsen regime with the objective of modeling shear-driven rarefied gas flows encountered in various microelectromechanical system (MEMS) components. Using the linearized Boltzmann solutions available in the literature and hard sphere direct simulation Monte Carlo (DSMC) results, we develop a unified empirical model that includes analytical expressions for the velocity distribution and shear stress for steady plane Couette flows. We also present extension of this model to time-periodic oscillatory Couette flows. Comparisons between the extended model and ensemble averaged unsteady DSMC computations show good agreements in the quasi-steady flow limit, where the Stokes number (β) based on the plate separation distance and oscillation frequency is ≤ 0.25. Overall, the new model accurately predicts the velocity distribution and shear stress for steady and quasi-steady (β ≤ 0.25) flows in a wide Knudsen number range (K_n ≤ 12), and it is strictly valid for low subsonic flows with Mach number ≤ 0.3.     

Characteristics of vortex flow in a low speed air jet impinging onto a heated disk in a vertical cylindrical chamber

An experiment combining flow visualization and transient temperature measurement is carried out to investigate the characteristics of the mixed convective vortex flow resulting from a low speed air jet impinging onto a heated horizontal circular disk confined in a vertical adiabatic cylindrical chamber. Attention is focused on the conditions leading to the onset of the inertia and buoyancy driven vortex rolls and the effects of governing nondimensional groups on the steady and time dependent vortex flow. More specifically, experiments are conducted for the jet Reynolds number varied from 0 to 1082 and Rayleigh number from 0 to 18,790 for two different injection pipes. The results show that typically the steady vortex flow in the processing chamber consists of two inertia-driven and one buoyancy-driven circular vortex rolls. The secondary inertia-driven roll only appears at high jet Reynolds numbers. At low buoyancy-to-inertia ratio Gr/Re_j² the vortex rolls are steady and axisymmetric. But at certain high Gr/Re_j² the vortex flow becomes unstable and the vortex rolls are somewhat deformed. Besides, new vortex rolls can be induced by the additional thermal rising from the heated disk and the splitting of the primary inertia-driven roll. The temporal characteristics of the time periodic vortex flows are examined in detail. In the region dominated by the new rolls the flow oscillates significantly. Finally, empirical equations are proposed to correlate the oscillation frequency of the time periodic flow, and the size and location of the vortex rolls. Furthermore, the conditions for the onset of the buoyancy driven rolls are given. A flow regime map is provided to delineate the temporal state of the vortex flow.     

NUMERICAL SIMULATION OF TRANSIENT NATURAL CONVECTION FROM AN ISOTHERMAL CAVITY OPEN ON A SIDE

Numerical simulations are presented for buoyancy-induced flow and heat transfer in a square isothermal cavity open on a side. The vorticity-stream function formulation with improvised boundary conditions at the window of the cavity is employed. It is shown that flows at moderate to high Rayleigh numbers are periodic or unsteady. The interaction of the buoyant elements generated at the three sides and their entrainment characteristics are complex. The basic physical mechanisms underlying these complex flows are discussed in detail. Nusselt number data are provided for steady and unsteady flows.     

Numerical Study of Heat Transfer of a Porous-Block-Mounted Heat Source Subjected to Pulsating Channel Flow

A numerical analysis was conducted to investigate the convective characteristics of pulsating flow through a channel with a porous-block-mounted heat source. Comprehensive time-dependent flow and temperature data are calculated and averaged over a pulsation cycle in a periodic steady state. The impacts of the Darcy number, pulsating frequency and amplitude, and porous blockage ratio are documented in detail. The results indicate that the periodic alteration in the structure of recirculation flows, caused by both porous block and flow pulsation, has a direct impact on the flow behavior in the vicinity of the porous block and on the heat transfer rate from the heater.     

Periodically Fully Developed Heat and Fluid Flow Characteristics in a Furrowed Wavy Channel

Periodically fully developed two-dimensional (2D) flow in a furrowed wavy channel is investigated numerically at various Reynolds numbers (100–2123). For the laminar and transitional flow regime, the study is done for six geometrically different channels; corresponding to various nondimensional amplitude (0.05, 0.075, and 0.1) and wavelength (0.5 and 1). Critical Reynolds number—for the onset of periodic flow—decreases with increasing amplitude and wavelength. A flow regime map—demarcating steady and unsteady flow regime—is proposed. It is shown that the size of the vortex in streamlines and waviness in isotherms increase with increasing Reynolds number, amplitude and wavelength. The performance of wavy as compared to straight channel is studied with the help of ratio of Nusselt number, friction factor and area-goodness factor, and thermal-performance factor. With increasing Reynolds number, all these parameters remain almost constant in the steady regime and increase almost linearly in the unsteady regime. For the largest Reynolds number (close to 2000) studied here, the increase in the Nusselt number ratio—within the periodic flow regime—is 11.21% and 133% for the amplitude equal to 0.075 and 0.1, respectively, at a wavelength of 0.5; at a wavelength of 1.0, the increase is 101%, 134%, and 181% for the amplitude of 0.05, 0.075, and 0.1, respectively.     

Visualiztion of Unsteady Gas／Vapor Expansion Flows

INTRODUCTIONReleaseoflatentheataftercondensationofpureva-porsorinvaPor/carriergasmixturesleadstocomplexdynamicalinteractionsoftheflowwiththephasetran-sitionprocess.Infastexpansionflowstheformationoftheliquidphaseisdominatedbyhomogeneouscon-densation.If,asinmanyinternalflowsofwatervapor,thecoolingrateoftheexpansion-dT/dtisoftheor-der1"/ps,heterogeneouscondensationeffectscanbeneglected.TyPicalwatervaporcontentsinthesupplyleadtotransoniccondensationonsetMachnumbers,wheretheflowisnearthemaxi…     

Non-unique convection in a three-dimensional slot-vented cavity with opposed jets

This study aims to investigate multiple flow structures in a three-dimensional chamber with opposed jets. Numerical computations focus on the effect of inlet velocity on the air flow pattern, especially on multiple steady flow characteristics for Reynolds maintaining 10⁵. Three distinct branches of steady-state flows are found for this configuration. A complete study of stability of each branch is performed for varying velocity of the left inlet continuously between 0 and 3. The results are presented by stability diagrams showing the critical parameters corresponding to transition from one steady-state branch to the other state within multiple flow range. In parallel with numerical development, an experimental system was set up where adjustable flow rate was prescribed to produce variation of supplying jets. The corresponding vector flow fields, on a scale model, were measured by a laser-based particle image velocimetry (PIV) system. The multiple flow structures were validated both by numerical simulation and experimental investigation.     

Effect of water-based Al2O3 nanofluids on heat transfer and pressure drop in periodic mixed convection inside a square ventilated cavity

A numerical study of unsteady mixed convection flows through an alumina-water nanofluid in a square cavity with inlet and outlet ports due to incoming flow oscillation is performed. It is found that an oscillating velocity at the inlet port cased to creating a periodic variation in the fluid flow and temperature field in the cavity after a certain time duration. The influence of the nanoparticle on the flow and temperature fields has been plotted and discussed. The effect of the oscillation frequency is concealed in a dimensionless number which is the Strouhal number. It is observed that the heat transfer is enhanced for all the Strouhal and Richardson numbers investigated by adding the nanoparticle to the base fluid. It is also found that the performance of the nanoparticle on the enhancement of the heat transfer at higher Richardson numbers is less than that of lower Richardson numbers.     

Transient flow and heat transfer leading to periodic state in a cavity with inlet and outlet ports due to incoming flow oscillation

A finite-volume-based computational study of transient laminar flow and heat transfer (neglecting natural convection) leading to periodic state within a square cavity with inlet and outlet ports due to an oscillating velocity at the inlet port is presented. The inlet port is placed at the top of the left wall and the outlet port is positioned at the bottom of the right wall of the cavity. The inlet velocity varies sinusoidally with time for a range of dimensionless frequencies (St = 0.1, 0.5, 1, 2 and 10). The instantaneous Reynolds number also varies sinusoidally between 100 and 500 and Pr = 5. It takes more cycles for the temperature field to reach its periodic state in comparison to the corresponding flow field. For cases with higher Strouhal numbers, it takes more cycles to reach a periodic state. The throughflow stream undergoes cyclic growth and decay. The throughflow is in constant contact with the clockwise rotating primary vortex, which in turn interacts with two rotating vortices on the left wall. A counterclockwise rotating vortex at the top right corner also experiences periodic growth and decay. Minimal heat transfer is consistently observed on the left wall. In contrast, certain segments of the other three walls and the boundary of the throughflow are zones of active heat exchange. For St = 0.1, the mean Nusselt numbers on the four walls clearly exhibit large amplitudes of oscillation and periodicity. With St = 10, the amplitudes of oscillation on various walls are generally degraded. These behaviors are directly linked to the relation between the period of oscillation and the convection time scale. Regardless of the Strouhal number, heat transfer enhancement in comparison to the steady state case is consistently observed. The best heat transfer rate is realized when the Strouhal number is close to unity. This is the case when the period of the incoming stream resonates with the convection time scale.     

Free convective flow of heat generating/absorbing fluid between vertical porous plates with periodic heat input

This study investigates the free convective flow of heat generating/absorbing fluid between vertical parallel porous plates due to periodic heating of the porous plates. The analysis is performed by considering fully developed flow and steady-periodic regime. The momentum and energy equations, which arise from the definition of velocity and temperature, are written in dimensionless form. Separating the temperature and velocity fields into steady and periodic parts, the resulting second order differential equations are solved to obtain the expressions for velocity, temperature, skin friction and the rate of heat transfer. The effects of various flow parameters such as the suction/injection (s), heat source/sink (δ), Strouhal (St) and Prandtl (Pr) numbers on the skin friction coefficient, rate of heat transfer, velocity and temperature profiles are discussed with the aid of line graphs and contour maps.     

A Numerical Computation of Heat and Fluid Flow in L-Shaped Curved Channels

A numerical analysis of steady, hydrodynamically and thermally fully developed, incompressible laminar flow with constant physical properties is presented. Two different geometrical cases of L-shaped channels are considered: right-curved and left-curved. The solution of the discretized continuity, momentum, and energy equations was obtained by using an elliptic Fortran program based on the SIMPLE algorithm. Solutions are obtained for Dean number ranges from 4.1 to 210.6 with dimensionless radius of curvature of 100, and Prandtl number of 0.7. The secondary flow streamlines, the isotherms, average Nusselt numbers, and friction factors are presented depending on Dean number and L-shaped channel orientation. As a result, it is observed that the secondary flows resulting from centrifugal forces change the distribution of the velocity and the temperature fields. In addition, it is determined that channel orientation has a profound effect on the flow and temperature fields.     

A numerical study of heat transfer performance of oscillatory impinging jets

Enhancement of heat transfer to a planar surface by oscillating jets is presented in this work. Two jets from adjacent slots are made to oscillate with the same frequency but with a phase shift of π/2. The two nozzles are idealisation of an array of oscillating jets. A two-dimensional model is developed using finite element methods to investigate the heat transfer performance with respect to the oscillation frequency, geometric parameters and the flows with Reynolds number in the range of 0 < Re ? 1200. The computational results show that the oscillatory flow jets achieve approximately 100% improvement of heat transfer efficiency over conventional steady flow jets. It is shown that the periodic disruption of the boundary layer leads to this improvement. Further, the analysis shows the existence of a range of frequencies that are effective depending on the separation between the nozzles. The study shows that frequencies as low as 1 Hz are effective depending on the nozzle separation.