Heat Transfer to Power-Law Fluids from a Heated Square Cylinder

Forced-convection heat transfer to power-law fluids from a heated square cylinder has been investigated numerically for the range of conditions 1 ≤ Re ≤ 45, 0.5 ≤ n ≤ 2.0 and 1 ≤ Pr ≤ 100 (the maximum Peclet number being 4,000). In this range of Reynolds number, the flow is known to be steady and two-dimensional. The variation of the local Nusselt number on the individual surfaces of the square cylinder and the representative isotherm plots, for both the constant-temperature and uniform-heat-flux boundary conditions prescribed on the surface of the square obstacle, are presented to elucidate the role of Reynolds number, Prandtl number, and power-law index on the heat transfer characteristics. Using the present numerical data, appropriate predictive correlations are obtained for estimating the value of the mean heat transfer coefficient in a new application.     

Dulong_Petit传热规律时加热气体的最优膨胀

给定初态内能、体积,末态体积以及过程时间时对Dulong-Petit传热规律[q ∝(△T)5/4]下加热气体膨胀的最优构型进行了研究,利用最优控制理论得出了最大膨胀功输出时膨胀过程的最优构型由两个瞬时绝热分支和一个E-L分支组成.给出了各分支之间转换点参数的求解方法,进行最优构型的数值计算,将得到的结果与线性唯象传热规律、牛顿传热规律和辐射传热规律下加热气体膨胀的最优构型进行了比较,结果表明,虽然4种传热规律时E-L弧部分的气体内能和体积随时间的增加都是逐渐增加的,且在整个E-L弧部分温度均低于外部热槽温度,但是不同传热规律时的E-L孤的形式是不同的,初始绝热过程的终点位置也不相同,故整个膨胀过程所做出的最大功也不相同.     

Investigation of Heat and Mass Transfer in a Lid-Driven Cavity Under Nonequilibrium Flow Conditions

Gaseous flow and heat transfer in a lid-driven cavity under nonequilibrium flow conditions is investigated using the direct simulation Monte Carlo method, from the slip to the free-molecular regime. The emphasis is on understanding thermal flow features. The impact of the lid velocity and various degrees of rarefaction on the shear stress and heat flux rates are analyzed. The role of expansion cooling and viscous dissipation on the heat transfer mechanism is investigated. Complex heat flow phenomena, such as counter-gradient heat transfer, are revealed by the simulations which the conventional Navier-Stokes-Fourier equations are not able to capture, even in the slip-flow regime.     

Analysis of Conduction and Radiation Heat Transfer in a Differentially Heated 2‐D Square Enclosure

Radiative heat transfer with and without conduction in a differentially heated 2‐D square enclosure is analyzed. The enclosure with diffuse gray boundaries contains radiating and/or conducting gray homogeneous medium. Radiatively, the medium is absorbing, emitting and scattering. On the south boundary, four types of discrete heated regions, viz., the full boundary, the left one‐third, left two third and middle one third, are considered. In the absence of conduction, distributions of heat flux along the south boundary are studied for the effect of extinction coefficient. In the presence of conduction, distributions of radiation, conduction and total heat fluxes along the south boundary are analyzed for the effects of extinction coefficient, scattering albedo, conduction–radiation parameter, and south boundary emissivity. Effects of these parameters on centerline temperature distribution are also studied. To assess the performance of three commonly used radiative transfer methods, in all cases, the radiative transfer equation is solved using the discrete ordinate method (DOM), the conventional discrete ordinate method (CDOM) and the finite volume method (FVM). In the combined mode problem, with volumetric radiative information known from one of the three methods, viz., DOM, CDOM, and FVM, the energy equation is solved using the finite difference method (FDM). In all cases, the results from FDM‐DOM, FDM‐CDOM, and FDM‐FVM are in good agreement. Computationally, all three sets of methods are equally efficient.     

R1234yf Flow Boiling Heat Transfer in a Rectangular Channel Heated from the Bottom

This paper presents some preliminary experimental measurements collected during flow boiling heat transfer of low global warming potential refrigerant R1234yf in an asymmetrically heated rectangular plain channel. The asymmetrical heating is the common boundary condition that occurs in many different applications, for instance, in almost all the electronic devices, which are now pushing the cooling demands to more and more greater requirements. From this standpoint, the analysis of the flow boiling heat transfer of efficient and eco-friendly refrigerants can open new frontiers to the electronic thermal management. The experimental measurements were carried out at the Department of Industrial Engineering of the University of Padova by imposing two different heat fluxes, 50 and 100 kW m^?2, at a constant saturation temperature of 30°C; the refrigerant mass velocity was varied between 50 and 200 kg m^?2 s^?1, while the vapor quality varied from 0.2 to 0.95. The developed measuring technique permits to estimate the flow boiling heat transfer coefficient and the critical value of vapor quality at the onset of the dryout.     

多孔介质中高温气体非稳态渗流传热数值计算

针对水平导管中填充颗粒物料层内的高温气体参流传热现象，考虑渗流与传热的相互作用并采用局部非平衡假设建立多孔介质中的瞬态渗流传热物理数学模型。研究不同情况下填充物料中的渗流速度和气固温度分布。计算结果表明，高温热气体对水平导管中移动颗粒料层的热渗透主要发生在渗流入口端区域，随着渗流时间延长，热渗透深度沿导管推进。增大入口渗流速度以及减小出料速度，将导致物料温度沿导管慢速下降，热渗透深度扩大，热渗透作用区域内的物料温度水平提高。在热渗透作用区域，孔隙率对流场和温度场有很大的影响。研究对于高温反应器的颗粒输运和给料器的设计与运行有一定的参考作用。     

Flow and Heat Transfer Phenomena Across Two Confined Tandem Heated Triangular Bluff Bodies

Confined flow and heat transfer phenomena across two long triangular bars in tandem arrangement in a horizontal channel have been studied for the range of Reynolds number (Re) = 1–40, Prandtl number (Pr) = 0.71–50 and gap ratio (S/B) = 1–4 for a fixed blockage ratio of 25%. The average Nusselt number of the first triangular cylinder is found to be larger than the corresponding value for the second triangular cylinder in the tandem configuration. Heat transfer correlations in terms of the Colburn j_h factor have been established in the steady regime.     

The Effect of a Blockage on Forced Convection Heat Transfer From a Heated Square Cylinder to Power-Law Fluids

Forced convection heat transfer characteristics of a long, heated square cylinder blocking the flow of a power-law fluid in a channel is numerically investigated in this study. In particular, the role of the power-law index n, Reynolds number Re, Prandtl number Pr, and blockage ratio β(=B/H) on the rate of heat transfer from a square cylinder in a channel has been studied over the following ranges of conditions: 0.5 ≤ n ≤ 1.8, 60 ≤ Re ≤ 160, β = 1/4, 1/2, and 0.7 ≤ Pr ≤ 50. A semi-explicit finite-volume method is used on a nonuniform collocated grid arrangement. The third-order QUICK and the second-order central difference schemes are used to discretize the convective and diffusive terms, respectively, in the momentum and energy equations. Irrespective of the type of behavior of fluid (different values of n), the average Nusselt number increases as the blockage ratio increases. Similar to the unconfined flow configuration, the average Nusselt number increases monotonically with Reynolds and Prandtl numbers for both values of the blockage ratio and for all values of power-law index considered here. Further insights into the heat transfer phenomenon are provided by presenting isotherm contours in the vicinity of the cylinder for a range of values of the Reynolds number, Prandtl number, and power-law index for the two values of β considered in this work.     

Enhancement of Heat Transfer with Porous/Solid Insert for Laminar Flow of a Participating Gas in a 3-D Square Duct

In recent years, porous or solid insert has been used in a duct for enhancing heat transfer in high temperature thermal equipment, where both convective and radiative heat transfer play a major role. In the present work, the study of heat transfer enhancement is carried out for flow through a square duct with a porous or a solid insert. Most of the analyses are carried out for a porous insert. The hydrodynamically developing flow field is solved using the Navier–Stokes equation and the Darcy–Brinkman model is considered for solving the flow in the porous region. The radiative heat transfer is included in the analysis by coupling the radiative transfer equation to the energy equation. The fluid considered is CO₂ with temperature dependent thermophysical properties. Both the fluid and the porous medium are considered as gray participating medium. The increase in heat transfer is analyzed by comparing the bulk mean temperature, Nusselt number, and radiative heat flux for different porous size and orientation, Reyonlds number, and Darcy number.     

Numerical Investigation of Convective Heat Transfer in Unsteady Laminar Flow Over a Square Cylinder in a Channel

Unsteady laminar flow past a heated square cylinder mounted inside a plane channel was investigated numerically. The blockage ratio was chosen as 1/8 and the Reynolds number based on the mean flow velocity and chord length of the square cylinder was selected as less than 200, for which the two-dimensional behavior of the flow is assured. The time-averaged Nusselt number as well as some integral parameters such as drag coefficient, recirculation length, and Strouhal number were obtained and compared with literature. Results show a nearly linear increase in recirculation length and decrease in drag coefficient with increasing Reynolds number for the steady flow regime. There is an increase in the total Nusselt number and drag coefficient with a Reynolds number for unsteady flow regime, where vortex shedding is observed from the cylinder. A correlation was obtained for the variation of the total Nusselt number with the Reynolds number.     

烧结余热回收竖式炉内气体流动和传热的数值模拟

运用数值模拟的方法,通过求解非线性联立的质量、动量、能量及组分守恒偏微分方程组,借助多物理场祸合软件Comsol和模拟软件FLUENT模拟出竖式炉内气体流动,换热特性以及料层阻力特性。模拟结果表明:冷却段高度是影响竖式炉内气固流动换热的因素之一,高度增加,烧结矿温度降低,冷却风的温度升高,空气出口携带火用值先增加后趋于平缓,气固比也影响着竖式炉内气体流动和换热,气固比增加,烧结矿的出口温度和循环空气的平均出口温度逐渐降低,热空气携带的火用值先增加后减小;竖式炉直径也是影响因素之一,但相比于冷却高度和气固比影响不是很大。由模拟的结果给出的冷却段高度为7 m,气固比1 400 m~3/t,竖式炉直径12 m时,竖式炉炉内的气固换热最强,与现场实际的结构参数和操作参数比较吻合。     

Analysis of Thermal Nonequilibrium Inverse Heat Transfer in a Porous Channel

This article is concerned with the one-dimensional transient inverse heat conduction between two parallel plates filled with a porous medium under a nonthermal equilibrium condition between the solid and the fluid phases. The estimation of transient heat flux using the conjugate gradient method (CGM) along with the differential adjoint equations has been carried out under nonthermal equilibrium conditions between two phases. Derivation of the adjoint differential equations in the case of nonthermal equilibrium and calculation of gradient function from coupled adjoint equations are presented in detail here. The transient wall heat flux imposed on the porous boundary is estimated using the aforementioned method, and results show that sensor locations and existing error in the measured data have important effects on the calculated heat flux. Nonetheless, accurate heat flux estimation is quite achievable.     

单面加热竖直窄通道内环状流沸腾传热特性

基于汽芯的动量方程和液膜的质量和动量方程,建立了单面均匀热流竖直窄通道内环状流沸腾传热模型,利用数值法对方程组进行求解,得出了环状流区域的液膜厚度,并进一步预测了环状流两相沸腾传热系数。研究表明:模型预测的两相沸腾传热系数比Mahmound关联式计算值偏小;将不同工况下的291组环状流两相沸腾传热系数实验值与模型预测值进行对比,平均绝对误差为12.7%。     

通道中串列倒转柔性体的运动与传热

为研究柔性结构运动对通道换热性能的影响,采用任意拉格朗日-欧拉(Arbitrary Lagrangian-Eulerian, ALE)法,对通道中串列布置的倒转柔性体进行数值模拟。研究不同长宽比的柔性体在抗弯刚度系数相同时的拍动状态、流场特性以及对通道换热性能的影响。结果表明：随抗弯刚度系数变化柔性体存在稳定模式、大幅度拍动模式和偏转拍动模式3种运动模式;随抗弯刚度系数减小,小长宽比柔性体的拍动状态变化具有滞后性;大长宽比柔性体在净换热量提升上更有优势,在合理的机械能损失范围内拥有更高的热效率系数,相较小长宽比通道,平均净换热量提高了3.87倍,最高热效率系数可达1.3;在实际工程应用中,应采用大长宽比并处于大幅度拍动模式下才能有效提升通道内传热性能。     

Effect of Thermal Buoyancy on the Two-Dimensional Upward Flow and Heat Transfer Around a Square Cylinder

The effect of aiding/opposing buoyancy on the two-dimensional upward flow and heat transfer around a heated/cooled cylinder of square cross section is studied in this work. The finite-volume-based commercial computational fluid dynamics (CFD) software FLUENT is used for the numerical simulation. The influence of aiding/opposing buoyancy is studied for Reynolds and Richardson numbers ranges of 50 to 150 and –1 to 1, respectively, and the blockage parameters of 2% and 25%. The flow exhibits unsteady periodic characteristics in the chosen range of Reynolds numbers (except for Reynolds number of 50 and blockage parameter of 25%) for the forced convective cases (Richardson number of 0). However, the vortex shedding is observed to stop completely at some critical value of Richardson number for a particular Reynolds number, below which the shedding of vortices into the stream is quite prominent. Representative streamlines and isotherm patterns for different blockage parameters are systematically presented and discussed. The critical Richardson and average Nusselt numbers are plotted against the Reynolds and Richardson numbers, respectively, to elucidate the role of thermal buoyancy on flow and heat transfer characteristics. It is observed that the vortex shedding frequency (Strouhal number) increases with increased heating and suddenly reduces to zero at the critical Richardson number. The critical Richardson number is again found to increase with Reynolds number for a particular blockage ratio, and the higher the blockage ratio, the less is the critical Richardson number. The results obtained from the commercial solver are extensively validated with the available numerical results in the literature and an excellent agreement is observed.     

Heat Transfer Characteristics during Mist Cooling on a Heated Cylinder

Mist cooling is expected to contribute to better steel products because it enables uniform and moderate cooling in steel-making processes. In this study, experimental data were obtained to understand the mist cooling process in a high-temperature cylinder. The wetting phenomenon on the cylinder surface was also observed with an installed CCD camera. Comparing these results with those from previous investigations, we found that our cooling curve corresponded to two distinct heat transfer regimes in mist cooling. A simplified model from the analysis was introduced to simulate the cooling curve in each heat transfer regime. The estimated cooling curves by this model agreed with the experimental data in one regime and had a similarity in the other regime.     

Analysis of Flow and Heat Transfer in a Parallelogram Non‐Uniformly Heated Enclosure Filled with Porous Medium

The flow and heat transfer in a parallelogram enclosure filled with a porous medium is analyzed numerically. The heated bottom wall has a sinusoidal temperature distribution and side walls cooled isothermally while the upper wall is well insulated. Dimensionless Darcy law and energy equations are solved using the finite difference method along with the corresponding boundary condition. Computations were carried out for four inclination angles of side walls (γ = 45°, 60°, 75°, 90°) with different Rayleigh numbers (100≤Ra≤1000) and their effects on the flow field and heat transfer are discussed. It is found that the inclination angle has a significant effect on flow pattern and heat transfer and an increase in the angle leads to a decrease in the strength of the right vortex. The study also revealed that as the Rayleigh number increases at γ = 45°, another (third) vortex develops along the left wall and its strength enhances with Rayleigh number. At the end, a correlation is extracted from the numerical data which represents the relation between the Nusselt number, inclination angle, and the Rayleigh number. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; 39(7): 497–506, 2010; Published online in Wiley Online Library ( wileyOnlinelibrary.com ). DOI 10.1002/htj.20312     

A Multidomain Chebyshev Pseudo-Spectral Method for Fluid Flow and Heat Transfer from Square Cylinders

A simple multidomain Chebyshev pseudo-spectral method is developed for two-dimensional fluid flow and heat transfer over square cylinders. The incompressible Navier-Stokes equations with primitive variables are discretized in several subdomains of the computational domain. The velocities and pressure are discretized with the same order of Chebyshev polynomials, i.e., the P_N-P_N method. The Projection method is applied in coupling the pressure with the velocity. The present method is first validated by benchmark problems of natural convection in a square cavity. Then the method based on multidomains is applied to simulate fluid flow and heat transfer from square cylinders. The numerical results agree well with the existing results.     

Analysis of Heat Transfer and Flow Characteristics for the Arrangement of Piezoelectric Fan on Heated Cylinder

Piezoelectric fans are an effective device for heat transfer enhancement in low convective regions due to their low power consumption, low noise, and operational simplicity. This study performs a numerical and experimental investigation into the effects of a piezoelectric fan on the velocity and temperature fields near a cylindrical heat source with a constant heat flux on the sidewalls and upper flat surface. In performing the investigation, the blade is placed at various locations along the cylindrical axis and is arranged such that it vibrates in either the vertical direction or the horizontal direction. The results show that the airstream induced by the vibrating fan covers a broader area of the heated surface when the blade vibrates in the vertical direction, and therefore yields a better heat transfer performance than that achieved when the fan vibrates in the horizontal direction. In addition, it is found that the maximum heat transfer augmentation ratio is obtained at dimensionless fan positions ranging from 0.6 to 0.75, and has values of 1.94, 1.53, and 1.44 given dimensionless fan tip clearances of 0.5, 1.0, and 1.5, respectively. Finally, it is shown that while the numerical results underestimate the effect of the vibrating piezoelectric fan in enhancing the heat transfer performance by around 1–14%, a good qualitative agreement is observed between the numerical and experimental results.