Stability of natural convection in an inclined square duct with perfectly conducting side walls

We have performed three-dimensional linear stability analyses for natural convection in an inclined square duct. The duct is heated from the bottom, while the lateral walls are assumed to be perfectly thermal conducting. Three-dimensional transverse rolls whose axes are normal to the axis of the duct occur from the motionless state when the Rayleigh number exceeds a critical value and the duct is placed horizontally (θ = 0°). However, it is found that when the duct is placed inclined (θ = 0.01°), a two-dimensional longitudinal roll which is unchanged in the axis of the duct occurs and is stable if the Rayleigh number is small.     

Thermosolutal convective instability and viscous dissipation effect in a fluid-saturated porous medium

The combined effects of the double-diffusion and of the viscous dissipation on the convective instability in a fluid-saturated porous medium with a basic horizontal throughflow are investigated. A horizontal porous layer with an impermeable adiabatic lower wall and an impermeable isothermal upper wall is considered. The parallel boundary walls are assumed to have uniform, but unequal, concentrations of the solute. A linear stability analysis is carried out both numerically and by a first-order perturbation method. General disturbances having the form of oblique rolls are considered, reducing either to longitudinal rolls or to transverse rolls in the special cases of roll axes parallel or orthogonal to the basic flow direction, respectively. It is shown that the combined effects of viscous dissipation and mass diffusion may lead to the instability of the basic horizontal flow. Either the longitudinal rolls or the transverse rolls may be the preferred modes of instability depending on the value of the viscous dissipation parameter Ξ. The longitudinal rolls are the most unstable when Ξ < 61.86657.     

A CFD study of flow quantities and heat transfer by changing a vertical to diameter ratio and horizontal to diameter ratio in inline tube banks using URANS turbulence models

This paper reports the effect of changing the aspect ratio on the heat transfer and flow quantities over in-line tube banks. Two types of in-line arrangements were employed; square and non-square configurations. The models that were examined are a standard k-ε model, SST k-ω model, v2-f model, EB k-ε model and EB-RSM model. The closer results to the experimental data and LES were obtained by the EB k-ε and v2-f models. For the square pitch ratios, the solution has faced a gradual change from a strong asymmetric to asymmetric and then to a perfect symmetry. The strong asymmetric solution was found by the very narrow aspect ratio of 1.2. However, the behaviour of cases of 1.5 and 1.6 became less strong than that predicted in the case of 1.2. In the larger aspect ratio of 1.75, the flow behaviour is seen to be absolutely symmetric for all variables under consideration except Nusselt number. For the very large pitch ratio of 5, the flow has recorded maximum distributions for all parameters on the windward side of the central tube with a perfect symmetric solution around the angle of 180° while the vortex shedding frequency has recorded minimum value and the Strouhal number; therefore, has given the smallest value. However, for the non-square pitch ratio of constant transverse distance, the solution is still asymmetric for all parameters with merely one stagnation at the angle of 52° at the case of the 1.5 × 1.75 while by increasing the longitudinal distance to 2 and 5, the solution provided a comprehensive symmetry for all variables with two vortices are fully developed mirrored in shape on the leeward side of the central tube. On the contrary, for the non-square pitch ratio of constant longitudinal distance, the flow of the case of 1.75 × 1.5 provided two stagnation locations at around 52° and 308° with a very similar solution to the case square ratio of 1.75 for all variables whereas by increasing the transverse distance to 2 and 5, the solution recorded was not perfectly symmetric resulting in two different vortices and one stagnation position located at the leading edge of the cylinder provided by the case of 5 × 1.5. In terms of vortex shedding effect, the reduction in the Strouhal number at a constant transverse pitch is less steep than those at a constant longitudinal pitch.     

EFFECTS OF ASPECT RATIO ON VORTEX FLOW PATTERNS IN MIXED CONVECTION OF AIR THROUGH A BOTTOM-HEATED HORIZONTAL RECTANGULAR DUCT

Abstract

Buoyancy-induced vortex flow structures and the associated heat transfer were numerically investigated in a mixed convective airflow in a bottom-heated horizontal rectangular duct of different aspect ratios. The unsteady three-dimensional Navier-Stokes and energy equations were directly solved by a higher order upwind finite difference scheme. Results were presented in particular for Reynolds numbers ranging from 5 to 15, Rayleigh numbers up to 9000, and aspect ratios from 4 to 12. The predicted results clearly show significant differences in vortex structures induced in ducts with small and large aspect ratios. For an aspect ratio less than 6 the transverse vortex rolls are periodically generated in the duct entry and gradually transform into longitudinal rolls when moving downstream. The resulting vortex flow eventually evolves to a time periodic state with the upstream and downstream portions of the duct dominated by the transverse rolls and longitudinal rolls, respectively. For a large aspect ratio (A > 9) the transverse rolls prevail in the duct core, with two to three longitudinal rolls existing near each sidewall. The flow oscillation in the region dominated by the transverse rolls is much higher than that dominated by the longitudinal rolls. At high Ra the flow becomes chaotic in time, and the duct is filled with unstable irregular vortex rolls.     

Linear stability analysis of Poiseuille–Bénard–Marangoni flow in a horizontal infinite liquid film

We present the first linear stability analysis of a Poiseuille–Bénard–Marangoni flow, which refers to a horizontal infinite liquid film flowing in one direction with uniform heating from below. This study concerns the two limiting cases of pure buoyancy effect (Ma = 0) and pure thermocapillary effect (Ra = 0). The stability thresholds of the flow and their variation with the control parameters (Biot, Reynolds and Prandtl numbers) are given and compared with those for a Poiseuille–Rayleigh–Bénard flow. The spatial structures of the flow are presented, and it is shown that the centers of the rolls are shifted upwards compared to the PRB case and that there is a loss of symmetry with respect to the vertical axis for the transverse rolls. These effects are directly linked to thermocapillary convection.     

A further investigation of effects of jet-disk separation distance on steady mixed convective vortex flow resulting from a confined impinging air jet

We extend our previous study [J.C. Hsieh, T.F. Lin, Effects of jet-to-disk separation distance on the characteristics of mixed convective vortex flow in an impinging air jet confined in a cylindrical chamber, Int. J. Heat Mass Transfer 48 (2005) 511–525] here to further investigate how the jet-disk separation distance H affects the mixed convective vortex flow resulting from a round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber. The experiment is conducted for the jet-disk separation distance varying from 40.0 to 60.0 mm and the jet flow rate is varied from 0 to 12.0 slpm (standard liter per minute) for the jet Reynolds number Re_j ranging from 0 to 1623. The temperature difference between the disk and the air injected into the chamber is varied from 0 to 25.0 °C for the Rayleigh number Ra ranging from 0 to 507,348. The data from the present study for the ratio H/D_j = 4–6 are compared with our previous study for H/D_j = 1–3. The results indicate that the critical jet Reynolds numbers for the onsets of the secondary and tertiary inertia-driven rolls and for the onset of the buoyancy-driven roll vary nonmonotonically with the jet-disk separation distance due to the complicate changes of the vortex flow structure with H. In the steady vortex flow, both the primary inertia-driven roll and the buoyancy-driven roll get larger at increasing jet-disk separation distance before they contact with each other for H/D_j = 1 and 2. But for H/D_j ≧ 3 the primary roll and buoyancy roll do not always grow at increasing H. Finally, empirical correlations are proposed for the critical conditions leading to the onsets of the inertia- and buoyancy-driven vortex rolls.     

Stationary transverse rolls and U-rolls in limiting low Reynolds number mixed convective air flow near the convective threshold in a horizontal flat duct

Combined experimental flow visualization and temperature measurement are carried out in the present study to explore the buoyancy driven vortex flow patterns in a limiting low Reynolds number mixed convective air flow through a bottom heated horizontal flat duct. In Particular, attention is paid to the flow approaching the natural convection limit (Re=0) for Re=1.0 and 2.0 with the Rayleigh number near the critical level for the onset of convection for 1200?Ra?4000. Results from the flow visualization have revealed two unfamiliar vortex flow patterns which were not seen in our earlier study [Int. J. Heat Mass Transfer 44 (4) (2001) 705]. One is characterized by the stable stationary transverse rolls in the duct entry and stable longitudinal rolls in the downstream. Another is in the form of U-rolls. The relations of these two patterns with those reported in the literature from analytical, numerical and experimental studies are discussed. Moreover, stable longitudinal rolls along with nonperiodic traversing waves, and mixed longitudinal and transverse rolls as well as irregular cells which appear in the higher Reynolds number for 3.0?Re?5.0 are also noted here. The temporal and spatial characteristics of the unfamiliar vortex flows are inspected in detail. In addition, the flow formation processes leading to the two unfamiliar vortex flow structures are also examined carefully. During the flow formation we noted merging of longitudinal and transverse rolls to form U-rolls, splitting of rolls into cells and the reverse process of cell integration into rolls, aside from the generation of the longitudinal and transverse rolls. Finally, a flow regime map is provided to delineate various vortex flow structures observed in this study and in the previous study (cf. the above-mentioned reference) driven by the slightly supercritical and subcritical buoyancies for 1.0?Re?5.0.     

Energy separation in the wake of a cylinder: Effect of Reynolds number and acoustic resonance

Energy separation is a spontaneous redistribution of total energy in a flowing fluid without external work or heat transfer. The energy separation mechanism in the vortex field behind an adiabatic circular cylinder in a cross flow of air is investigated. Time-averaged velocity and temperature measurements taken one diameter downstream of the cylinder (Re ～ 10⁵, M_∞ ～ 0.25) indicate flow reversal. The measured recovery temperature, expressed as distribution of energy separation factor indicates that energy separation is caused by the vortex flow in the wake, enhanced by acoustic excitation, and is insensitive to Reynolds number in the sub critical range studied.     

Vortex formation and heat transfer in turbulent flow past a transverse cavity with inclined frontal and rear walls

The process of vortex formation, distributions of pressure coefficients, and convective heat transfer in a turbulent flow past a cavity with a low aspect ratio and inclined frontal and rear walls were experimentally studied. The angle of wall inclination φ was varied in the interval from 30° to 90°. Visualization techniques were applied to trace the evolution of the flow with the angle φ as the transverse cavity became more open. Pressure fields in the longitudinal and transverse sections on the bottom wall of the cavity, and on its frontal and rear walls, were measured. The measured distributions of temperature in the longitudinal and transverse sections on the three heated walls, and the obtained thermographic fields over the whole heated surface, were used to calculate local and average heat-transfer coefficients. It is found that in the interval of wall inclination angles φ = 60–70° the flow in the cavity becomes unstable, with the primary vortex changing its structure from single-cellular to double-cellular. As a result, the distributions of static pressure and surface temperature across and along the cavity suffer dramatic changes. At smallest angles φ the flow re-attachment point gets displaced into the cavity to cause an abrupt growth of pressure and heat-transfer coefficients on the rear wall, which leads to a slight increase of the surface-mean pressure and heat transfer inside the cavity. At the angle of instability, φ = 60°, the local heat-transfer coefficient decreases markedly over the cavity span from the end faces of the cavity toward its center, and a most pronounced intensification of heat transfer is observed.     

Analysis of combined thermal and magnetic convection ferrofluid flow in a cavity

A numerical analysis of the magnetic gradient and thermal buoyancy induced cavity ferrofluid flow is conducted by a semi-implicit finite element method. The physical model for a square cavity containing two different temperature side walls and a magnet near bottom wall is described by mass, momentum and energy equations. Conditions for the fixed Prandtl number, Rayleigh number and different ferro-hydrodynamic interaction parameter are studied for 5 × 10⁸ ≤ β ≤ 1.6 × 10¹⁰. Results show the flow strength increases with the strengthening magnetic field. However, the side-wall heat transfer rate presents a decrease trend with the increase in magnetic field strength, for the magnet located near the bottom central area evokes the circulation to move toward the central portion. In summary, a proper choice of magnet strength and location can adjust the flow field and local heat transfer rate to fit the practical application.     

Three-dimensional thermocapillary–buoyancy flow of silicone oil in a differentially heated annular pool

In order to understand the characteristics of thermocapillary–buoyancy flow, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary–buoyancy flow of 0.65cSt silicone oil (Prandtl number Pr = 6.7) in an annular pool with different depth (d = 1–11 mm) heated from the outer wall (radius r_o = 40 mm) and cooled at the inner cylinder (r_i = 20 mm) with an adiabatic solid bottom and adiabatic free surface. Simulation conditions correspond to those in the experiments of Schwabe [D. Schwabe, Buoyant–thermocapillary and pure thermocapillary convective instabilities in Czochralski systems, J. Crystal Growth 237–239 (2002) 1849–1853]. Simulation results with large Marangoni number predict three types three-dimensional flow patterns. In the shallow thin pool (d = 1 mm), the hydrothermal wave characterized by curved spokes is dominant. In the deep pools (d ⩾ 5 mm) the three-dimensional stationary flow appears and this flow pattern corresponds to the Rayleigh-Benard instability, which consists of pairs of counter-rotating longitudinal rolls. When 2 mm ⩽ d ⩽ 4 mm, the hydrothermal wave and three-dimensional oscillatory flow coexist in the pool and travel along the same azimuthal direction with the same angular velocity. The critical conditions for the onset of three-dimensional flows were determined and compared with the experimental results. The characteristics of three-dimensional flows were discussed.     

Enhancement of air cooling in staggered array of electronic modules by integrating delta winglet vortex generators

This study is to experimentally investigate the heat transfer enhancement by delta winglet vortex generators in air cooling of a staggered array of rectangular electronic modules. The winglet vortex generators are placed in front of 3 × 5 modules with 20° attack angle. Each module has dimensions of 1.8 × 5.4 × 0.6 mm and each one generates heat at 2.5 W. The adiabatic heat transfer coefficients, the thermal wake functions including their correlations for the modules with and without the vortex generators are considered at different values of Reynolds number and the module density. It could be seen that the vortex generators could enhance the adiabatic heat transfer coefficients, reduce the thermal wake functions and the module temperatures significantly. The module temperatures predicted by the superposition of the convective effect due to the module heat generations and the module thermal wakes are fitted very well with the measured data.     

Transient natural convective heat transfer of a low-Prandtl-number fluid inside a horizontal circular cylinder with an inner coaxial triangular cylinder

A numerical study of transient natural convection of liquid gallium (Pr = 0.023) from a horizontal triangular cylinder to its coaxial cylindrical enclosure is performed. The aspect ratio is fixed at 2 and two positions of the inner triangular cylinder are considered. The development of the convective flow and heat transfer is shown via the time histories of the average Nusselt number over the outer circular wall for various Grashof numbers. Temporal phases of the flow development are identified as: initializing, developing, transitioning, and steady/quasi-steady state or oscillating. Typical flow patterns and temperature distributions at these phases are presented by means of streamlines and isotherms, respectively. Pitchfork bifurcation is present for both positions of the inner triangular cylinder when Gr ? 5 × 10⁴. The time-averaged Nusselt number over the outer circular cylinder, the flow development time, and the onset time of pitchfork bifurcation are predicted and scaled with the Grashof number. It is found that the time-averaged Nusselt number is apparently increased by horizontally placing the top side of the inner triangular cylinder for Gr ? 1 × 10⁵.     

Subcooled flow boiling heat transfer and associated bubble characteristics of FC-72 on a heated micro-pin-finned silicon chip

Experiments are conducted here to investigate subcooled flow boiling heat transfer and associated bubble characteristics of FC-72 on a heated micro-pin-finned silicon chip flush-mounted on the bottom of a horizontal rectangular channel. In the experiments the mass flux is varied from 287 to 431 kg/m² s, coolant inlet subcooling from 2.3 to 4.3 °C, and imposed heat flux from 1 to 10 W/cm². Besides, the silicon chips contain three different geometries of micro-structures, namely, the smooth, pin-finned 200 and pin-finned 100 surfaces. The pin-finned 200 and 100 surfaces, respectively, contain micro-pin-fins of size 200 μm × 200 μm × 70 μm (width × length × height) and 100 μm × 100 μm × 70 μm. The measured data show that the subcooled flow boiling heat transfer coefficient is reduced at increasing inlet liquid subcooling but is little affected by the coolant mass flux. Besides, adding the micro-pin-fin structures to the chip surface can effectively raise the single-phase convection and flow boiling heat transfer coefficients. Moreover, the mean bubble departure diameter and active nucleation site density are reduced for rises in the FC-72 mass flux and inlet liquid subcooling. Increasing coolant mass flux or reducing inlet liquid subcooling results in a higher mean bubble departure frequency. Furthermore, larger bubble departure diameter, higher bubble departure frequency, and higher active nucleation site density are observed as the imposed heat flux is increased. Finally, empirical correlations for the present data for the heat transfer and bubble characteristics in the FC-72 subcooled flow boiling are proposed.     

Experimental investigation of opposing mixed convection hear transfer in the vertical flat channel in a laminar–turbulent transition region

In this paper we present the results on experimental investigation of the local opposing mixed convection heat transfer in the vertical flat channel with symmetrical heating in a laminar–turbulent transition region. The experiments were performed in airflow (p = 0.1–1.0 MPa) in the range of Re from 1.5 × 10³ to 6.6 × 10⁴ and Gr_q up to 1 × 10¹¹ at the limiting condition q_w1 = q_w2 = const. The analysis of the results revealed significant increase in the heat transfer with increasing of air pressure (Gr number). Also sharp increase in heat transfer was noticed in the region with vortex flow in comparison with the turbulent flow region.     

Thermal performance of in-line diamond-shaped pin fins in a rectangular duct

This work experimentally studied the pressure drop and heat transfer of an in-line diamond-shaped pin-fin array in a rectangular duct by using the transient single-blow technique. The variable parameters are the relative longitudinal pitch (X_L = 1.060, 1.414, 1.979) and the relative transverse pitch (X_T = 1.060, 1.414, 1.979). The empirical formula for the heat transfer is suggested. Besides, the optimal inter-fin pitches, X_T = 1.414 and X_L = 1.060, are provided based on the largest heat dissipation under the same pumping power.     

A Bayesian approach for the simultaneous estimation of surface heat transfer coefficient and thermal conductivity from steady state experiments on fins

This paper explores the potential of the Bayesian approach to estimate multiple parameters from simple, inexpensive experiments on natural convection heat transfer from a vertical rectangular fin. A vertical fin of rectangular cross-section is placed on two heated horizontal aluminium blocks of size 250 × 75 × 10 (all in mm) that act as a horizontal base and hold the extended surface made up of mild steel of size 250 × 160 × 4 (all in mm). A heater is placed below the aluminium block and to restrict the heat flow, the bottom side of the heater is insulated with glass wool. Steady state experiments are carried out to obtain the temperature distribution for different levels of heating and temperatures on the fin are recorded with K-type thermocouples. Using data from these experiments, two critical parameters namely, the average heat transfer coefficient and the thermal conductivity of the extended surface are first individually and later simultaneously obtained using the Bayesian approach thereby obviating the need for sophisticated equipment. The above two parameters are correlated thereby making their simultaneous estimation very challenging. The Markov Chain Monte Carlo (MCMC) is used for the estimation without and with subjective priors on the two parameters. The uncertainties are obtained explicitly in the form of standard deviation. The addition of subjective priors is the hallmark of the Bayesian approach as it reduces the standard deviation of the estimates. This considerably helps regularizing the ill-posedness and becomes a necessity for estimating correlated parameters. A discussion on the optimum number of temperature measurements needed for estimating the parameters with a given accuracy using the Bayesian method is also presented.     

Visualization of flow patterns and bubble behavior during flow boiling in open microchannels

Flow boiling in microchannels is favored by the heat transfer community due to the high heat transfer rates that can be obtained with lower mass flow rates. However, the heat transfer rates for flow boiling in microchannels are impacted by flow reversals and flow instabilities. An open microchannel structure was recently proposed to reduce the impact of the flow boiling instabilities. Subcooled flow boiling experiments were conducted in open microchannels using deionized water. The open microchannels had 6 parallel channels with a 0.3 mm uniform thickness gap above them The channels were fabricated on a 6 mm × 40 mm copper block. The channels were 0.5 mm wide and 0.3 mm deep with 0.43 mm wide fins between them. Flow visualizations were performed with a high-speed CCD camera with the results showing that the flow regimes in the open microchannels differ from those in closed microchannels with stratified flow and no flow instability. Two types of confined bubbles were observed with characterizations of the effects of the bubbles on each other. The heat transfer mechanisms for flow boiling in open microchannels are also described.     

Effect of magnetic obstacle on fluid flow and heat transfer in a rectangular duct

The vortex dynamics behind various magnetic obstacles and characteristics of heat transfer are investigated using a three-dimensional model. In the numerical study, the magnet width (M_y) is alterable to investigate the instability, Strouhal number, wake structure behind various magnetic obstacles and percentage increment of the overall heat transfer for a wide range of constrainment factors (0.08 ≤ κ ≤ 0.26), Reynolds numbers (400 ≤ Re ≤ 900) and interaction parameters (9 ≤ N ≤ 15). For all constrainment factors, the fundamental frequency (f) is uniform for a particular value of Reynolds number. Downstream cross-stream mixing due to vortex shedding enhances the wall-heat transfer and the maximum value of percentage increment of the overall heat transfer (HI) is about 20.2%. However, the pressure drop penalty (ΔP_penalty) is not increasingly dependent on interaction parameter when Re and κ remain constant.     

Experimental study on heat transfer in square duct with combined twisted-tape and winglet vortex generators

The article presents an experimental investigation on thermal performance enhancement in a constant heat-fluxed square duct fitted with combined twisted-tape and winglet vortex generators. The experiments are carried out for the airflow rate through the tested square duct fitted with both the vortex generators for Reynolds number from 4000 to 30,000. The effect of the combined twisted tape and rectangular winglet inserts on heat transfer and pressure drop presented in terms of respective Nusselt number and friction factor is experimentally investigated. The characteristics of the combined twisted-tape and winglet include two twist ratios (Y = 4 and 5), three winglet- to duct-height ratios, (R_B = 0.1, 0.15 and 0.2), four winglet-pitch to tape-width ratios, (R_P = 2, 2.5, 4 and 5) and a single attack angle of winglet, α = 30°. The experimental results reveal that the Nusselt number and friction factor for the combined twisted-tape and V-winglet increase with increasing R_B but decreasing R_P. The inserted duct at R_B = 0.2, R_P = 2 and Y = 4 provides the highest heat transfer rate and friction factor but the one at R_B = 0.1, R_P = 2 and Y = 4 yields the highest thermal performance. The application of combined vortex-flow devices gives thermal performance around 17% higher than the twisted tape alone.