Convective heat transfer to water near the critical region in a horizontal square duct

Numerical analysis has been carried out to investigate forced convective heat transfer to water near the critical region in a horizontal square duct. Near the critical point convective heat transfer in the duct is strongly coupled with large variation of thermophysical properties such as density and specific heat. Buoyancy force parameter has also severe variation with fluid temperature and pressure in the duct. There is flow acceleration along the horizontal duct resulted from fluid density decrease due to the heat transfer from the wall. Local heat transfer coefficient has large variation along the inner surface of the duct section and it depends on pressure. Nusselt number on the center of the bottom surface also has a peak where bulk fluid temperature is higher than the pseudocritical temperature and the peak decreases with the increase of pressure. Flow characteristics of velocity, temperature, and local heat transfer coefficient with water properties are presented and analyzed. Nusselt number distributions are also compared with other correlations for various pressures in the duct.     

EXPERIMENTAL STUDIES ON FLOW IN CONVERGENT AND DIVERGENT DUCTS OF RECTANGULAR CROSS SECTION

This paper describes the experimental examination of the pressure drop and heat transfer of the flow in convergent and divergent ducts of rectangular cross section. The aspect ratio based on the dimensions of the large end of the duct was 0⋅1. It has been found that at a given convergent or divergent angle pressure drop decreases while heat transfer increases with increasing Reynolds number. Along a given duct of small convergent angle, pressure drop increases while heat transfer decreases along the duct. However, heat transfer may increase near the downstream end of ducts of high convergent angle. At a given Reynolds number, both pressure drop and heat transfer increase with increasing convergent angle. As for flow in divergent ducts, the effects of Reynolds number on pressure drop and heat transfer are somewhat similar to those of flow in a convergent duct. © 1997 by John Wiley & Sons, Ltd.     

Transient convective heat transfer to water near the critical region in a vertical tube

Numerical analysis has been carried out to investigate transient forced convective heat transfer to water near the critical region in developing flow through a vertical tube. With large variations of thermophysical properties such as density, specific heat, viscosity, and thermal conductivity near the thermodynamic critical point, heat transfer in the tube is strongly coupled with fluid flow. Buoyancy force parameter has also large variation with fluid temperature and pressure in the tube. Time dependent characteristics of fluid velocity, temperature, and heat transfer coefficient with water properties are presented and analyzed. Transient Nusselt and Stanton number distributions along the tube are also compared for various pressures in the tube. Because of heat transfer from the wall transition behavior from liquid-like phase to gas-like phase of heat transfer coefficient occurs when the fluid passes through pseudocritical temperature region in the tube. Turbulent viscosity ratio also has steep variation near the pseudocritical temperature close to the wall.     

MIXED CONVECTION HEAT AND MASS TRANSFER IN RADIALLY ROTATING RECTANGULAR DUCTS

The present work investigates mixed convection heat and mass transfer in the entrance region of radially rotating rectangular ducts with water film evaporation along the porous duct watts. Mechanisms of secondary vortex development in the ducts under various conditions are examined by a vorticity-velocity numerical method. Emphasis is placed on the rotation effects, including both Coriolis and centrifugal buoyancy forces, and the mass diffusion effect on the flow structure and heat transfer characteristics. Results are presented in particular for an air-water vapor system under various conditions. Predicted results show that the effects of liquid film evaporation along the porous duct walls on the mixed convection neat transfer are rather substantial. The magnitude of the evaporative latent heal transfer may be 10 times greater than that of sensible heat transfer. The predictions also demonstrate that the distributions of Nu, Sh?z?, and fRe are closely related to the emergence, disappearance, growth, and decay of the rotating-induced secondary vortices. Additionally, a higher Nu?z? is found for a rectangular duct with a larger aspect ratio ( γ = 2) due to the relatively stronger secondary flows.     

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.     

Numerical study of convective heat transfer in T‐bifurcating channel

A numerical study of a three‐dimensional turbulent flow in a rectangular T‐bifurcating duct was performed. It focused on the analysis of heat transfer in the branching duct at 90 to the main flow. Including separation and reattachment phenomena, the flow seemed to be anisotropic. The closure system of the full set of Navier–Stokes equations governing the flow was based on the on one point statistical modeling using a low Reynolds number second‐order full stress transport model. For several aspect ratios, results show that in addition to the recirculation zone in the branching duct close to the upstream side; pairs of streamwise vortices were generated downstream of the junction zone with their centers moving towards the symmetry plane. The effect of the aspect ratio of the branching section in enhancing this phenomenon and flow rate effect on the heat transfer were particularly analyzed in this paper.     

Fitting the duct to the “body” of the convective flow

This paper is a proposal to design flow structures with maximal heat transfer rate per unit volume, by shaping each duct so that it fits optimally on the body of the convective flow. Optimally shaped ducts can be assembled into larger constructs. Two examples are given. In the first, a heat-generating strip is cooled inside a duct of rectangular cross-section. The duct geometry has two degrees of freedom, which can be selected so that the fixed duct volume packs a maximum of heat transfer rate. In the second example, the duct is a tube with isothermal internal surface, and the flow is sufficiently slow so that boundary layers do not form inside the duct. Once again, the duct aspect ratio can be optimized for maximal heat transfer rate density. Further improvements can be sought by endowing the duct geometry with more degrees of freedom.     

带有横向微沟槽的矩形通道内超临界液化天然气换热强化特性模拟研究

提出了一种用于超临界液化天然气换热的微小通道换热器整体性能提高的被动式强化技术并进行了数值模拟验证和设计优化。在普通的矩形微小通道内利用3D激光打印技术在壁面加工横向圆弧形微沟槽以强化换热能力。首先对圆弧形微沟槽的槽深、槽宽和相邻两槽道中心距等几何尺寸进行了优化计算,然后讨论了在使用强化技术后工质温度在跨越临界温度的120.000～250.000 K的换热强化和流动特性,进一步考察了工质温度、质量流量(雷诺数)和进口压力对传热系数(努塞尔数)、摩擦因子和综合效益系数的影响。此外,通过微沟槽附近的局部流动特性分析强化换热机理,数值模拟结果表明带有横向微沟槽的紧凑式换热器的综合换热效益得到30%左右增加,显示了优异的换热强化综合效果。     

矩形冷却通道内超临界RP-3航空煤油对流传热数值研究

对超临界压力下RP-3航空煤油在内截面宽为4mm、高为4mm、固体壁面厚为1mm、加热段长度为500mm的水平矩形冷却通道内的对流传热特性进行了数值模拟研究。分析了通道内速度场的分布规律,讨论了热流密度、压力、进口温度对传热的影响。计算结果表明:当主流温度处于拟临界温度附近时,流体物性参数变化剧烈,导致传热系数降低,传热出现恶化。在超临界压力下,较低的热流密度、增大压力、降低进口流体温度或提高质量流速均有利于改善冷却通道内的传热性能。     

Investigation on the characteristics and mechanisms of unusual heat transfer of supercritical pressure water in vertically-upward tubes

The heat transfer characteristics of supercritical pressure water in a vertically-upward optimized internally-ribbed tube was investigated experimentally to study the mechanisms of unusual heat transfer of supercritical pressure water in the so-called large specific heat region. The experimental parameters were as follows. The pressure at the inlet of the test section ranged from 22.5 to 29.0 MPa, and the mass flux of the fluid was from 650 to 1200 kg/m² s, and the heat flux on the inside wall of the tube varied from 200 to 660 kW/m². According to experimental data, the characteristics of heat transfer enhancement and also the heat transfer deterioration of supercritical pressure water in the large specific heat region was analyzed and based on the comparison and analysis of the current major theories that were used to explain the reasons for unusual heat transfer to occur, the mechanisms of heat transfer enhancement and deterioration were discussed, respectively. The enhanced heat transfer was characterized by the gently changing wall temperature, the small temperature difference between the inside-tube-wall and the bulk fluid and the high heat transfer coefficient in comparison to the normal heat transfer. The deteriorated heat transfer could be characterized by the sharply increasing wall temperature, the large temperature difference and a sudden decrease in heat transfer coefficient in comparison to the normal heat transfer. The heat transfer enhancement of the supercritical pressure water in the large specific heat region was suggested to be a result of combined effect caused by the rapid variations of thermophysical properties of the supercritical pressure water in the large specific heat region, and the same was true of the heat transfer deterioration. The drastic changes in thermophysical properties near the pseudocritical points, especially the sudden rise in the specific heat of water at supercritical pressures, might result in the occurrence of the heat transfer enhancement, while the covering of the heat transfer surface by fluids lighter and hotter than the bulk fluid made the heat transfer deteriorated eventually and explained how this lighter fluid layer formed.     

Laminar flow of viscoelastic fluids in rectangular ducts with heat transfer: A finite element analysis

A numerical study on the laminar flow and heat transfer behavior of viscoelastic fluids in rectangular ducts is conducted using the finite element approach. A Criminale-Ericksen-Fibley relation is applied to describe the viscoelastic character of the fluid, and a hydrodynamically and thermally fully developed flow with the H1 thermal boundary condition is considered. The finite element procedure employed yields essentially mesh-independent predictions with a fairly moderate computational effort. Computed results are presented and discussed in terms of the secondary flow field, the temperature field, the friction factor and the Nusselt number. In particular it is shown that the presence of a secondary flow markedly alters the temperature field and results in a substantial heat transfer enhancement with all duct aspect ratios considered.     

Further finite element analyses of fully developed laminar flow of power-law non-Newtonian fluid in rectangular ducts: Heat transfer predictions

Forced convection heat transfer to hydrodynamically and thermally fully developed laminar flow of power-law non-Newtonian fluid in rectangular ducts has been studied for the H1 and T thermal boundary conditions. The solutions for the velocity and temperature fields were obtained numerically using the finite element method with quartic triangular elements. From these solutions, very accurate Nusselt number values were determined. Computations were performed over a range of power-law indices and duct aspect ratios.     

Investigation of heat transfer and bubble dynamics in a boiling thin liquid film flowing over a rotating disk

Nucleate boiling heat transfer and bubble dynamics in a thin liquid film on a horizontal rotating disk were studied. A series of experiments were conducted to determine the heat transfer coefficient on the disk. At low rotation and flow rates, vigorous boiling increased the heat transfer coefficients above those without boiling. Higher rotational speeds and higher flow rates increased the heat transfer coefficient and suppressed boiling by decreasing the superheat in the liquid film. The flow field on the disk, which included supercritical (thin film) flow upstream of a hydraulic jump, and subcritical (thick film) flow downstream of a hydraulic jump, affected the type of bubble growth. Three types of bubble growth were identified. Vigorous boiling with large, stationary bubbles were observed in the subcritical flow. Supercritical flow produced small bubbles that remained attached to the disk and acted as local obstacles to the flow. At low rotational rates, the hydraulic jump that separated the supercritical and subcritical regions produced hemispherical bubbles that protruded out of the water film surface and detached from the disk, allowing them to slide radially outward. A model of the velocity and temperature of the microlayer of water underneath these sliding bubbles indicated that the microlayer thickness was approximately 1/25th of that of the surrounding water film. This microlayer is believed to greatly enhance the heat transfer rate underneath the sliding bubbles.     

带有横向微沟槽的矩形紧凑式通道换热器内超临界液化天然气工质换热强化特性模拟研究

提出了一种用于超临界液化天然气换热的微小通道换热器整体性能提高的被动式强化技术并进行了数值模拟验证和设计优化。在普通的矩形微小通道内利用3D激光打印技术在壁面加工横向圆弧形微沟槽以强化换热能力。首先对圆弧形微沟槽的槽深、槽宽和相邻两槽道中心距等几何尺寸进行了优化计算,然后讨论了在使用强化技术后工质温度在跨越临界温度的120K-250K范围内的换热强化和流动特性,进一步考察了工质温度、质量流量（雷诺数）和进口压力对换热系数（努塞尔数）、摩擦因子和综合效益系数的影响。此外,通过微沟槽附近的局部流动特性分析强化换热机理,数值模拟结果表明带有横向微沟槽的紧凑式换热器的综合换热效益得到30%左右增加,显示了优异的换热强化综合效果     

Bifurcated three-dimensional forced convection in plane symmetric sudden expansion

Simulations of bifurcated three-dimensional laminar forced convection in horizontal duct with plane symmetric sudden expansion are presented to illustrate the effects of flow bifurcations on temperature and heat transfer distributions. The stable bifurcated flow that develops in this symmetric geometry leads to non-symmetric temperature and heat transfer distributions in the transverse direction, but symmetric distributions with respect to the center width of the duct in the spanwise directions for the Reynolds number of 400-800. A strong downwash develops at the corner of the step and a smaller reverse flow region develops adjacent to the lower stepped wall than the one that develops adjacent to the upper stepped wall. The downwash and the “jet-like” flow that develop near the sidewall create a strong swirling spanwise flow in the primary recirculating flow regions downstream from the sudden expansion. The magnitude of maximum Nusselt number that develops on the lower stepped walls is higher than the one that develops on the upper stepped wall. The locations of these maximum Nusselt numbers on the stepped walls are near the sidewalls and are upstream of the “jet-like” flow impingement regions. Results reveal that the locations where the streamwise component of wall shear stress is zero on the stepped walls do not coincide with the outer edge of the recirculation flow region near the sidewalls. Velocity, temperature, Nusselt number, and friction coefficient distributions are presented.     

Numerical Investigation of Jet Impingement Cooling of a Flat Plate with Carbon Dioxide at Supercritical Pressures

Confined round jet impingement cooling of a flat plate at constant heat flux with carbon dioxide at supercritical pressures was investigated numerically. The pressure ranged from 7.8 to 10.0 MPa, which is greater than the critical pressure of carbon dioxide, 7.38 MPa. The inlet temperature varied from 270 to 320 K and the heat flux ranged from 0.6 to 1.6 MW/m². The shear-stress transport turbulence model was used and the numerical model was validated by comparison with experimental results for jet impingement heating with hot water at supercritical pressures. Radial conduction in the jet impingement plate was also considered. The sharp variations of the thermal-physical properties of the fluid near the pseudocritical point significantly influence heat transfer on the target wall. For a given heat flux, the high specific heat near the wall for the proper inlet temperature and pressure maximizes the average heat transfer coefficient. For a given inlet temperature, the heat transfer coefficient remains almost unchanged with increasing surface heat flux at first and then decreases rapidly as the heat flux becomes higher due to the combined effects of the thinner high specific heat layer and the smaller thermal conductivity at higher temperature.     

Laminar mixed convection heat and mass transfer in vertical rectangular ducts with film evaporation and condensation

The investigation of mixed convection heat and mass transfer in vertical ducts with film evaporation and condensation has been numerically examined in detail. This work is primarily focused on the effect of film evaporation and condensation along the wetted wall with constant temperature and concentration on the heat and mass transfer in rectangular vertical ducts. The numerical results, including the distributions of dimensionless axial velocity, temperature and concentration distributions, Nusselt number as well as Sherwood number are presented for moist air mixture system with different wall temperatures and aspect ratios of the rectangular ducts. The results show that the latent heat transport with film evaporation and condensation augments tremendously the heat transfer rate. Better heat transfer enhancement related with film evaporation is found for a system with a higher wall temperature.     

NUMERICAL PREDICTION OF LAMINAR FORCED CONVECTION IN TRIANGULAR DUCTS WITH UNSTRUCTURED TRIANGULAR GRID METHOD

The flow and heat transfer characteristics of smooth triangular ducts with different apex angles of 15, 30, 60, and 90 under the fully developed laminar flow condition were predicted numerically using a finite volume method. The SIMPLE-like algorithm was employed together with an unstructured triangular grid method, where the grid was generated by a Delaunay method. The triangular grid was adopted instead of the traditional rectangular grid to fit better into the triangular cross section of the duct. Two kinds of boundary condition (uniform wall temperature and uniform wall heat flux) were considered. Comparison of the predictions with previous computational results indicated a very good agreement. Both the friction factor and Nusselt number (Nu) showed a strong dependence on apex angle of the triangular duct. When the apex angle was 60, the duct provided the highest steady-state forced convection from its inner surface to the airflow under the laminar flow condition.     

Optimum Aspect Ratio for Heat Transfer Enhancement in Curved Rectangular Channels

Enhanced heal transfer in curved rectangular channels depends on at least two geometric factors, the radius of curvature of the duct and the aspect ratio, which is the width / depth ratio of the duct. In this work, an expression for optimum aspect ratio is derived mathematically from a correlation that includes both aspect ratio and bend curvature parameters. Enhancement factors are developed that show optimal, near-optimal, and nonoptimal aspect ratios for curved rectangular ducts. Predicted enhancements are within 25% of published literature results for individual designs, two of which show heat transfer enhancement of 200% over that of a straight duct with turbulent flow. The theoretical maximum enhancement is shown to be about 480% over a straight-duct, turbulent-flow situation. This is not achievable in practice, but near-optimal solutions are achievable, yielding enhancements on the order of 200-300%     

Heat Transfer of Bingham Fluids in an Annular Duct with Viscous Dissipation

ABSTRACT

Analytical expressions for the velocity and temperature profiles in a fully-developed laminar Poiseuille flow through a concentric annular duct of a Bingham fluid with constant wall heat flux at the inner and outer wall, in the presence of viscous dissipation are deduced and presented. It is found that the proportion of the heat generated by viscous dissipation near the outer wall increases with an increase of the dimensionless flow parameter, and a decrease of the duct radius ratio. The Nusselt numbers are first calculated based on a single bulk temperature for the entire duct cross section. The possibility of performing calculations of the relevant parameters discussed in this work is available via the Supplementary Material as an Excel file. Also in this work a new approach is employed, where two different bulk temperatures are used, one for each side of the radial location in the temperature profile whose derivative is zero. With this new approach the Nusselt number behavior is free of either unphysical discontinuities or negative values. As a consequence, the Nusselt number values better reflect the actual heat transfer coefficient at the walls and are more comparable with the heat transfer inside ducts when the temperature profile is symmetric.