Analysis of laminar flow forced convection heat transfer with uniform heating in the entrance region of a circular tube

A new integral or boundary-layer solution for laminar flow heat transfer in the combined entrance region of a circular tube is presented for the case of constant wall heat flux. The solution is based on the hydrodynamic inlet-filled region concept originally proposed by Ishizawa (1966) and later adopted by Mohanty and Asthana (1978) to hydrodynamically developing flow through a circular tube. Unlike available boundary-layer solutions, the new analysis provides results which join smoothly and asymptotically to the fully developed values. Results for the Nusselt number were found to agree favorably with available numerical solutions.     

SIMULTANEOUS DEVELOPMENT OF VELOCITY AND TEMPERATURE PROFILES IN THE ENTRANCE REGION OF A PARALLEL PLATE CHANNEL: LAMINAR FLOW WITH UNIFORM WALL HEAT FLUX

Available boundary layer type solutions to the combined hydrodynamic and thermal entrance region problem are known to exhibit a discontinuity in the gradients of the velocity and temperature distributions in the entrance region. A new solution is presented which alleviates this shortcoming. The new solution is based on the hydrodynamic inlet-filled region concept originally proposed by Ishizawa (1966) and later adopted by Mohanty and Das (1982) to hydrodynamically developing flow in a channel. This concept is extended to the combined entry length problem by dividing the thermal entrance length into two lengthwise regions, a thermal inlet region and a thermally filled region. In the former, the effect of heat transfer between fluid and wall is confined within the thermal boundary layer developing along the wall. At the end of the thermal inlet region, the thermal boundary layers meet at the duct axis but the temperature profile is not yet developed. In the thermally filled region, the heat effects propagate throughout the entire cross section and the temperature profile undergoes adjustment in a fully thermal region to finally attain the fully developed form. A thermal shape factor is also introduced in the thermally filled region which ensures that all thermal quantities attain their fully developed values asymptotically. The new model is used to obtain solutions to the combined entry length problem for laminar flow through a parallel plate channel under the constant wall heat flux boundary condition. The analysis gives considerably better results for the local Nusselt number and thermal entrance length than previously available.     

内插不同形状涡产生器管内层流流动与传热特性的对比分析

内插扰流元件是一种可操作性强的管内强化传热方式,其强化传热机理主要是在管内诱导产生了二次流。在均匀壁温热边界条件下,对内插不同形状涡产生器管内层流流动与传热特性进行了数值分析。研究发现：在扭带基础上裁去部分面积相同的条件下,管内插等腰梯形涡产生器的换热能力最强,直角梯形涡产生器次之,矩形涡产生器的换热能力最差,管壁上的局部Nusselt数的峰值所在圆周位置及其大小与涡产生器形状有关,而不同形状的涡产生器对管内流动的阻力系数影响较小。插入涡产生器后,管内二次流强度参数Se和平均Nusselt数Nu均随Reynolds数Re的增大而增大,二者随Reynolds数Re的变化规律具有一致性。平均Nusselt数Nu与二次流强度参数Se呈幂函数相关,内插涡产生器管内的二次流强度决定了其对流换热强度。     

外凸式波节套管换热器壳程流动与传热机理的数值模拟

针对波节套管换热器壳程中的流动和传热机理进行了k-ε的数值模拟研究。采用六面体网格结合波节区域加密的特殊划分方法,进行了首层网格间距和主流区网格间距的无关性分析。数值模拟结果与经验公式进行对比,验证了数值模拟方法的准确性。对比分析了波节管和光管中流动和传热参数（速度、温度、湍动能和湍流耗散率）的性能差异,揭示了波节管的强化换热机理。同时,分析了波节管的局部Nusselt数和阻力降沿壁面的变化规律。结果表明流体在波节的去流侧形成了一个脱体旋涡,破坏了流体的速度边界层和温度边界层,同时使得其内部的摩擦阻力和热扩散能力明显提高,起到了明显的强化换热效应。     

Heat transfer in turbulent forced convection between parallel-plates

The thermal entry region heat transfer due to turbulent forced convection of a Newtonian fluid inside a parallel-plate duct maintained at constant uniform temperature is solved analytically and the local Nusselt numbers are determined with a high degree of accuracy up to the region very close to the inlet. The calculated local Nusselt numbers are compared with those obtained from a recently proposed empirical correlation.     

HEAT TRANSFER MEASUREMENTS FOR A SPHERE EXPOSED TO A THERMAL PLASMA FLOW

Experimental data are presented concerning heat transfer to a sphere immersed into an argon plasma flow. Transient method has been employed to measure the heat flux to the sphere. The temperature and velocity of the thermal plasma flow are about 104K and 102m/s, respectively, while the sphere diameter is 0.68 or 1.0 mm. In preliminary tests, the applicability of the transient method has been demonstrated, and a series of complicated factors which may affect the heat flux measurement have been studied including the diameter and the length exposed to the plasma flow of the thermocouple wires, radiation heat loss from the probe to the surroundings, etc. Experimental results show that the Nusselt number defined based on the LTE (local thermodynamic equilibrium) heat-conduction-potential always assumes a value greater than 2.0. Main error source of the experimental Nusselt numbers is the: plasma temperature measurement.     

缩放管内湍流对流换热(Ⅰ)场协同控制机理

通过对缩放管管内湍流对流换热的模拟研究,考察了热边界层厚度、湍流强度及时均速度与时均温度梯度之间夹角的变化规律,得出了影响对流换热强度的场协同作用沿流动方向的分布规律.通过讨论两种不同结构尺寸缩放管的换热情况,发现流体在收缩段可获得较好的场协同作用,增强换热能力,而在扩张段场协同作用的效果减弱.     

插入圆柱状丝网管对单相对流传热的强化

提出在传热管内插入圆柱状丝网管调控流场进而强化传热的方法。通过在管内同心插入圆柱状丝网管,将流通截面分成中心区和环隙区,流体流经丝网入口处时受到阻力较大,大部分流体流向环隙区,使得速度场受到调控。环隙区与中心区内冷热流体掺混,强化传热。为验证这一思想搭建强制对流换热实验台,以去离子水为工质,Reynolds数为2392～20175,热通量为50.18～282.88 kW·m^-2。通过对局部、平均Nusselt数及摩擦压降数据的研究,结果表明：同光管传热相比,插入丝网管后平均Nusselt数提高,传热强化系数为1.21～1.84,且最大强化系数发生在过渡流内。入口段强化效果明显,局部传热强化系数最高可达到2.64。而强化传热的同时摩擦压降增大6.1～10.6倍。同时对该结构的传热强化机理进行分析：流场受到丝网管的调控作用,进而强化传热。     

Impingement Heat Transfer for a Cluster of Laminar Impinging Jets Issuing from Noncircular Nozzles

Abstract:

Results of numerical simulation of the flow and heat transfer characteristics for a semi-confined cluster of laminar air jets impinging normally on a plane wall are presented. A central jet is surrounded by four equally spaced jets of the same configuration. Both circular and noncircular nozzles are considered. The nozzle footprint is displayed in the static pressure, temperature, and local Nusselt number contours on the impingement surface only for relatively short nozzle-to-surface distances. The heat transfer characteristics and performance of circular and noncircular nozzles are compared. It is observed that the Nusselt number based on property values at the jet temperature is relatively insensitive to the temperature difference between the jet and the impingement surface. Also, the local Nusselt numbers are independent of the thermal boundary condition; i.e., the values are nearly the same for both isothermal and uniform heat flux conditions at the target surface. Finally, Nusselt numbers for a single equivalent jet viz. one with the same area as the five nozzles in the cluster combined, are compared for the case of the circular jet.     

Axial conduction with boundary conditions of the mixed type

A method is proposed for obtaining nearly analytical solutions to laminar flow thermal entrance region problems with axial conduction when the wall boundary conditions are of the mixed type. The method involves the utilization of Green's functions and the solution of a Fredholm integral equation using the Wiener-Hopf procedure. The method is illustrated by obtaining expressions for the temperature field for laminar flow in a circular tube in the zero Peclet number limit for Robin-Dirichlet wall boundary conditions.     

并流多通道进出口管壳式换热器壳程传热性能比较

对一种新型并流多通道进出口结构的壳程轴流管壳式换热器壳程局部传热性能进行实验研究,在有分布挡板与无分布挡板的情况下,分别对进口段局部努塞尔数Nu的分布、局部平均Nu的分布、以及换热器整体的传热和阻力性能进行了比较与分析。研究结果揭示了壳程进口段的局部表面Nu的分布规律,并给出了合理的机理分析。结果表明,分布挡板不但能够有效促进壳程流场和局部Nu的均匀分布,而且能够提高整体传热性能,且阻力增加较小。     

Transient forced convection in the entrance region of a porous tube

The problem of transient forced convection in the entrance region of a cylindrical porous medium with developing thermal boundary layer is investigated. The hydrodynamic behaviour of the flow is assumed to be steady and fully developed, and both Darcian and non-Darcian effects on the flow are considered. Thermal transients are created by a step change in the temperature of the tube wall. The effect of different fluid and solid-matrix parameters on Nusselt number, thermal entrance length, total heat absorbed and mixing cup temperature are considered.     

THERMOHYDRAULICS OF LAMINAR FLOW THROUGH A CIRCULAR TUBE HAVING INTEGRAL HELICAL CORRUGATIONS AND FITTED WITH HELICAL SCREW-TAPE INSERT

The experimental friction factor and Nusselt number data for laminar flow through a circular duct having integral helical corrugations and fitted with a helical screw-tape insert are presented. Predictive friction factor and Nusselt number correlations are also presented. The thermohydraulic performance was evaluated. The major findings of this experimental investigation are that the helical screw-tape insert in combination with integral helical corrugations performs significantly better than the individual enhancement technique acting alone for laminar flow through a circular duct up to a certain value of the fin parameter. This research finding is useful in designing tubes carrying solar thermal mass of viscous oil in a parabolic trough solar collector used in environmentally sound and increasingly cost-effective solar thermal electric power plants. The result is also useful in designing heat exchangers used in process industries.     

Re-evaluation of the Nusselt number for determining the interfacial heat and mass transfer coefficients in a flow-through monolithic catalytic converter

The two-equation porous medium model has been widely employed for modeling the flow-through monolithic catalytic converter. In this model, the interfacial heat and mass transfer coefficients have been usually obtained using the asymptotic Nusselt and Sherwood numbers with some suitable assumptions. However, previously it seemed that there existed some misunderstanding in adopting these Nusselt and Sherwood numbers. Up to now, the Nusselt number based on the fluid bulk mean temperature has been used for determining the interfacial heat and mass transfer coefficients. However, the mass and energy balance formulations in the two-equation model indicate that the Nusselt number should be evaluated based on the fluid mean temperature instead of the fluid bulk mean temperature. Therefore, in this study, to correctly model the heat and mass transfer coefficients, the Nusselt number based on the fluid mean temperature was newly obtained for the square and circular cross-sections under two different thermal boundary conditions (i.e., constant heat flux and constant temperature at the wall). In order to do that, the present study employed the numerical as well as analytical method.     

CO2水合物浆在水平圆管中的传热特性

在CO₂水合物浆流动传热特性测试实验系统上,采用套管式电加热的方法对CO₂水合物浆进行了分解实验,并对CO₂水合物浆的流动传热特性进行了分析。对CO₂水合物浆的相变特性进行了研究,得到CO₂水合物浆的相变温度在8～12℃。研究了在固相体积分数为13.2%以及流速为0.45m/s的条件下CO₂水合物浆在内径为8mm的水平不锈钢管中的传热特性,计算得到CO₂水合物浆在不锈钢水平圆管中的对流传热系数为1500～1800 W/(m²·K),并且其在流动传热过程中呈现先增大随后趋向平稳的趋势,在水合物的相变区相应的对流传热系数表现最大。研究了分解加热功率对管壁温和对流传热系数的影响,发现加热功率对管壁温度的影响较强。在实际应用中可利用CO₂水合物浆的相变作用来增强传热,提高传热效率。     

环形通道内层流入口段换热及流体变物性的影响

采用SIMPLER算法对环形通道内二维定常轴对称入口段流动与换热进行了数值计算, 研究了两种边界条件下的层流流动与换热规律, 给出了不同Prandtl数以及半径比率下沿程Nusselt数的变化曲线,同时还给出了流体物性随温度变化对流动与换热的影响, 最后还拟合出了不同半径比率下平均Nusselt数的关联式.计算结果还表明,环形通道能强化传热,强化程度随半径比率减小而增大,且入口段的换热强化与其较高的径向速度有关.     

带V型折流板圆管中流动结构与传热的三维数值研究(英文)

A 3D numerical investigation has been carried out to examine periodic laminar flow and heat transfer character-istics in a circular tube with 45° V-baffles with isothermal wal . The computations are based on the finite volume method (FVM), and the SIMPLE algorithm has been implemented. The fluid flow and heat transfer characteristics are presented for Reynolds numbers ranging from 100 to 2000. To generate main longitudinal vortex flows through the tested section, V-baffles with an attack angle of 45° are mounted in tandem and in-line arrangement on the opposite positions of the circular tube. Effects of tube blockage ratio, flow direction on heat transfer and pressure drop in the tube are studied. It is apparent that a pair of longitudinal twisted vortices (P-vortex) created by a V-baffle can induce impingement on a wal of the inter-baffle cavity and lead a drastic increase in heat trans-fer rate at tube wall. In addition, the larger blockage ratio results in the higher Nusselt number and friction factor values. The computational results show that the optimum thermal enhancement factor is around 3.20 at baffle height of B=0.20 and B=0.25 times of the tube diameter for the V-upstream and V-downstream, respectively. ? 2014 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. Al rights reserved.     

Laminar Flow and Heat Transfer Characteristics in Jackets of Triangular Flow Channels

Laminar flow and heat transfer characteristics of jacketed vessel with triangular flow channels were numerically studied under hydrodynamically and thermally fully developed conditions. Constant heat flux at theheated wall was assumed. The numerical program code interms of vorticity, stream function, axial velocity com ponent and energy equations was written based on a finite volume method. Based on the numerical results, the flow and temperature field were given, and the effects of Dean and Prandtl numbers on flow and heat transfer were ex amined, and the correlations of flow resistance and mean Nusselt number were developed for the jacket. The results show that the structure of secondary flow is steady two vortices in the investigated range of dimensionless curvatureratio and Reynolds number. Two peaks of local Nusselt number increase significantly with Prandtl and Dean num ber increasing, but the local Nusselt numbers near two ends and at the center of the heated wall increase only slightly. The center and two ends of heated wall are the poor positions for heat transfer in the jacket. Compared with the outer half coil jacket at the same area of heated wall, curvature radius, Reynolds number and Prandtl number, e jacket of triangular flow chmnel has lower flow resistance and less mean Nusselt number.     

基于全息术的水平偏置椭圆管自然对流换热

采用全息术实验研究水平偏置椭圆管层流自然对流换热,分析了长轴从水平方向到竖直方向不同角度的换热规律,记录了无限大空间水平椭圆管偏置角为0°~90°的干涉图,通过反演椭圆管周围的温度场得到了椭圆管表面的局部和平均Nusselt数。实验结果表明,长轴从水平位置偏置到竖直位置时,换热逐渐增强;长轴位于水平位置和竖直位置时,换热最小值均位于椭圆管上方,最大值则位于椭圆管长轴附近。研究结果与文献中已有的数值和实验结果吻合较好,可为今后热管换热器的设计提供优化方向,也可为工程应用提供检测方法。     

不同外径组合转子过渡区强化传热性能实验研究

以60%甘油水溶液为管程介质,对内置螺旋开槽两叶片转子换热管过渡区内的强化传热综合性能进行了实验研究。在雷诺数范围为2800～6200之间对光管性能进行了实验验证,以保证实验结果的可靠性。同时,对比分析了转子外径对其强化传热性能的影响,研究结果表明：内置转子强化管的努塞尔数Nu较光管约提高了60%～200%,阻力系数较光管约增大了16%～32%,综合评价因子PEC值介于1.56～2.79之间。此外,内置转子强化管的努塞尔数、阻力系数以及PEC值均随着转子外径的增大而增加,这是由于较大的转子外径使得转子具有更强的扰流与减薄边界层的作用。