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1、 外文文献原文Optimization of a central-heating radiator Cihat Arslanturk and A. Feridun OzgucDepartment of Mechanical Engineering, Faculty of Engineering, Ataturk University, 25240 Erzurum, TurkeyFaculty of Mechanical Engineering, Istanbul Technical University, Gumussuyu, 80191 Istanbul, TurkeyAbstractAn
2、approximate analytical model has been used to evaluate the optimum dimensions of a central-heating radiator. The radiator problem is divided into three one-dimensional fin problems and then the temperature distributions within the fins and heat-transfer rate from the radiator are obtained analytical
3、ly. The optimum geometry maximizing the heat-transfer rate for a given radiator volume and the geometrical constraints associated with production techniques, and thermal constraints have been found. The effects of geometrical and thermal parameters on the radiators performance are presented.Keywords
4、: Central heating; Optimization; Radiators1. IntroductionRadiators are the most popular central-heating emitters. As the radiator is hotter than the air surrounding it, a certain amount of heat is transferred to the air and thus the water exists at a lower temperature. Of the various designs availab
5、le usually equipped with convection fins to improve their heat output, are common in domestic, business and industrial environments. The use of central-heating radiators is the main form of domestic heating in the homes. Although radiators are known as radiator, most of their output is by natural co
6、nvection. Since the average surface temperature of a central-heating radiator is generally less than 80C, the contribution of radiative transfer to the total heat transfer is smaller than that of the natural convection heat transfer. Because of the low surface temperatures, radiation heat transfer t
7、erm in the energy balance equations can be linearized in the thermal analysis of such a radiator. In the present paper, assuming that the predominant modes of heat transfer are conduction and convection, and the effect of the radiation is ignored, an approximate mathematical model is constructed for
8、 finding temperature distribution and heat transfer rate.The design and optimization of these radiators or fins and fin assemblies are generally based on two approaches and: one is to minimize the volume or mass for a given amount of heat dissipation, and the other is to maximize the heat dissipatio
9、n for a given volume or mass. The optimization problem considered here focuses on finding the optimum dimensions of a central-heating radiator maximizing the heat transfer rate for the given volume of the radiator material and geometrical and thermal constraints.2. Mathematical analysisConsider a ra
10、diator which is shown schematically in Fig. 1. Considering steady-state conditions and neglecting the temperature change across the thickness, we may assume that the temperature distribution in the radiator is one-dimensional, angular in the tube and axial in the fins. Assuming that the predominant
11、modes of heat transfer are conduction and convection and the effect of radiation is ignored, a linear mathematical model is considered. Due to the symmetric conditions, it is sufficient that quarter part of the radiator is taken into consideration as shown in Fig. 1. This suggests that the problem b
12、e investigated in terms of three domains for mathematical convenience. Full-size image (23K)Fig. 1.Schematic of the modelled radiator.For each part of the radiator, energy balance equations are given in the form of (1)Invoking the continuity of temperature and heat current at the junctions, boundary
13、 conditions of the governing equations can be expressed as: （2a）1(L1)=2(0) (2b) (2c) (2d) (2e) (2f) (3a) (3b)The solutions of the governing equations given in Eq. (1) are expressed as follows: (4) Using the well-known DittusBoelter correlation, the heat-transfer coefficient, hi, inside the tube is e
14、xpressed in terms of pipe radius for selected inner fluid velocity. hi=A(U)0.8(R)0.2 (5)The coefficient A in Eq. (5) can be calculated using thermo-physical properties of the inner fluid .Applying the boundary conditions given in Eqs. (2a), (2b), (2c), (2d), (2e) and (2f), the unknown coefficients C
15、j,1 and Cj,2 in Eq. (4) can be symbolically calculated.3. Optimization procedureThe objective here is to maximize the heat transfer rate for attaining the radiator volume fraction and held fix all other thermal parameters. The total heat transfer rate, i.e. objective function, is readily calculated
16、by applying Newtons law of cooling between the tube and the inner fluid as: (6)The radiators volume-fraction is expressed as an equality constraint. (7)Since the radiators frontal dimensions, which must be equal or less than due to the production technique, are restricted as can be seen in Fig. 1, t
17、he following equality constraints can be written: (8)For simplicity, selecting 1=2=3= and employing the equality constraints given in Eqs ,an objective function can be found with one independent variable of radiator tube radius, R. The value of R which maximizes the function is obtained by different
18、iating the function with respect to R and setting the result equal to zero and then solving the new resulting equation. 4.Results and discussionIt would be of interest to examine the effects of different parameters (such as tube radius, thicknesses of the fins, heat transfer and coefficients) on the
19、 temperature distributions. However, this would require providing too many examples. Therefore, only one example is presented that will show the temperature distribution within the fins and the tube wall. Fig. 2 shows the temperature distributions for a set of given thermal and geometrical parameter
20、s.Full-size image (36K)Fig. 2.Temperature distribution of the three radiator sections.The optimization procedure can be conducted by locating the geometrical and thermal conditions that yield the total heat transfer rate. However, the existence of such a value should first be checked. In Fig. 3, the
21、 dimensionless heat transfer rate is plotted versus tube radius for three inner fluid velocities. A clear maximum heat transfer rate is shown in Fig. 3. Note also that for higher inner fluid velocities, the maximum appears at higher radiuses.Full-size image (58K)Fig. 3.Heat transfer rate versus radi
22、ator tube radius for the given volume fraction and inner fluid velocity.The variations of maximum heat transfer rate and optimum dimensions as a function of radiator volume fraction are shown in Fig. 4 for three different environment temperatures. As expected, the increase of radiator volume fractio
23、n increases the maximum heat transfer rate and optimum tube diameter. Assuming that the flow inside the tube is turbulent flow, the well-known DittusBoelter equation was used in optimization calculations. The values of the optimum tube diameters presented in Fig. 4 have been used for checking the va
24、lidity of the aforesaid assumption. It has been seen that the inner fluid flow is turbulent for all cases in Fig. 4.Full-size image (42K)Fig. 4.The effects the inner fluid temperature on optimum dimensions and maximum heat transfer rate.The variations of maximum heat transfer rate and optimum tube r
25、adius as a function of radiator volume fraction for three different ambient fluid temperatures are shown in Fig. 5. It can be seen that the curves shown in Fig. 5 approach an asymptotic value of the heat transfer rate at the large values of radiator volume fraction. That the maximum heat transfer ra
26、te depends on ambient fluid temperature but the corresponding optimum tube radius does not depend on this parameter is also shown in Fig. 5.Full-size image (42K)Fig. 5.The effects the room temperature on optimum dimensions and maximum heat transfer rate.5. ConclusionsAn approximate analytical model
27、has been proposed for the optimum design of central-heating radiators in the present paper. The radiator problem has been divided into three one-dimensional fin problems. The problems have been solved to evaluate the temperature distributions within the fins using the boundary conditions of the radi
28、ator and the continuity of temperature and heat current at the junctions of the fins. The temperature differences have been used within the heat transfer rate from the radiator to the environment. The optimum radiator geometry maximizing the heat transfer rate has been obtained by using the approxim
29、ate analytical model. The present optimization technique can be extended to central-heating radiator with more complex geometry. 中文译文:优化集中供暖散热器 阿尔斯兰蒂尔克和厄兹居奇机械工程学院，阿塔图尔克大学， 25240埃尔祖鲁姆，土耳其 学院：机械工程，伊斯坦布尔技术大学， Gumussuyu ， 80191伊斯坦布尔 ，土耳其 摘要 ：近似解析模型已经被用来评估集中供暖散热器的最佳尺寸。散热器的问题是被分为三个一维的问题，然后温度分布和来自散热器的热传输速率
30、，得到了很好分析。优化热传输速率的几何最大限度，是为了给定散热器的数量和与生产技术相关的几何约束。并且对于热的限制，已经被发现。 现在介绍几何和热参数对散热器的性能的影响。 关键词：集中供热；优化；散热器 1 导言散热器是最受欢迎的集中采暖设备。作为散热器，它比周围的空气热，此时一定数额的热量转移到空气，从而水在较低的温度下存在。对各种可用的设计通常配备对流散热，以改善其热输出，这些设计普遍应用于国内商业、工业领域。对于集中供暖散热器的使用主要形式是国内的家居采暖。尽管散热器被称为散热器，但他们中的大部分是以自然对流的形式输出的。由于集中采暖散热器的平均表面温度一般情况下低于80，所以辐射传热
31、对于总热量的传输的贡献小于自然对流换热。由于表面温度较低，在对这种散热器的热分析中，对于辐射传热来说，在能量平衡方程中可以线性化。在本文中，假设的主要模型，传热是传导和对流，辐射对其的影响可以被忽略。为了测量温度分布和传热率，一种近似的数学模型被构建出来。设计和优化这些散热器或散热器片，一般是基于两种方法，一种是为了某一特定数量的散热，尽量减少其数量或质量；另一种是为了某一特定的数量或质量，最大限度的增大热耗散。这里考虑的优化问题的重点是：根据给定的散热器材料的数量和几何限制、热限制，以找到能最大限度的发挥热传递的集中采暖散热器的最佳尺寸。2 数学分析在图1中所显示的散热器，考虑到稳定状态的条
32、件和忽略温度在整个厚度边界层上的变化，我们可以假定温度在散热器管的中心线上的分布是一维的。假设关于传热是传导和对流，以及可以忽略辐射对其的影响，这个结论是正确的。那么线性数学模型即被认可。由于平衡的条件，散热器的一部分显示在图1中已经足够了。这表明，为了数学方便，这个问题在条款的三个领域内会被调查。Full-size image (23K) 图1 散热器示意图对于散热器的每个部分，能量平衡方程都以以下形式给出 (1)目前在联结点对温度和热的连续性的引用，边界条件的方程可表示为： （2a）1(L1)=2(0) (2b) (2c) (2d) (2e) (2f) (3a) (3b)该方程给出了均衡器
33、，（1）表示如下： (4)使用著名的Dittus-Boelter的相关性，为了选定内流速，传热系数、内管都以管半径的形式表示。hi=A(U)0.8(R)0.2 (5)在如（5）所示的系统图A里，可以计算出内部流体的热物理特性。运用边界条件给出了均衡器：(2a),(2b),(2c),(2d)和(2f),未知系数 Cj,1 和 Cj,2 也在表里， （4）可以粗略地计算。3 优化程序这里的目的是最大限度地发挥传热率，为了达到散热器的体积分数和举例来校核其他的热工参数。总传热率，即目标函数，很容易计算，应用管与管内流体之间的牛顿冷却定律，式为： (6)散热器的体积分数被表示为一个相同的约束。 (7)
34、散热器的正面尺寸，必须等于或者小于，由于生产技术，其正面尺寸受到限制，在图1中，以下等式约束可以写成： (8)为简单起见，选择1 = 2 = 3 = ，并应用相同的限制，给出了均衡器。一个客观的功能与一个独立的变量散热器管半径可以被发现，R。能最大限度地发挥功能的R的价值被认可，它通过鉴别设置的结果归于零的这种功能表示出来。然后解决新产生的方程。4 结果与讨论它将会对不同参数（如管半径、散热器片厚、传热系数）对温度分布影响的研究产生兴趣。不过，这需要举出太多的例子。因此，只有一个例子是介绍可以显示内部和管壁的温度分布。图2显示的温度分布是为了一组特定的热工参数和几何参数。Full-size i
35、mage (36K)图2 三个散热器部分的温度分布优化程序可以通过定位的几何条件和产生总传热率的热工条件进行。然而，这样一个价值的存在，首先要进行检查。在图3中，为了三个与两管半径相比之下内流体的速度，印次传热率被策划出来。图3中显示了一个明确的最高传热率，还应注意到，较高的内流体速度，最高出现在较高的半径。Full-size image (58K)图3 为了特定的体积分数和内流速的，在散热器管中心线上的传热速率为了三个不同的环境温度，最大的传热率和作为一种散热器体积分数功能的最佳尺寸的变化显示在图4。正如所料，增加散热器的体积分数会使传热率的最大限度和最佳管径也增加。假设该内管流体为湍流，著
36、名的Dittus-Boelter方程在优化计算中被应用。图4介绍了最佳管径的价值，已经被用于检查上述假设的有效性。在图4中可以看到，管内流体流动是湍流的所有情况。Full-size image (42K)图4 影响最佳尺寸和最高传热率的流体温度为了三种不同的环境流体温度，最大传热率和作为一种散热器体积分数功能的管半径的优化的变化在图5中显示。可以看出，该曲线显示在图5，在散热器体积分数的最大价值下的传热率的渐近值。即最高传热率，取决于环境流体温度，但相应的优化管半径并不取决与此参数，也显示于图5中。Full-size image (42K)图5 影响最佳尺寸的最高传热率的室温5 结论在本文中，
37、为了集中供暖散热器的优化设计，近似解析模型已被提出。散热器的问题，已分为三个一维的问题。为了评估散热器内温度分布，利用散热器的边界条件和连续性，该问题已经解决了。温度差异已被用于从散热器到环境的内部传热率中。通过使用近似解析模型，散热器最佳尺寸与最大限度传热率的优化已经获得。目前的优化技术，可以应用于集中采暖散热器与更复杂的几何形状。 Central Heating Radiator System Can Be Made To Be Efficient 集中供暖散热器系统，可以有效地利用 One of the oldest and most inefficient home heating s
38、ystem is the single loop central heating radiator system. In this system, a boiler heats water, usually in the homes basement and the hot water is pumped through a pipe to the inlet side of the radiators connected to the system. Water from that first radiator is then passed along to the next one in
39、the single loop central heating radiator system until it has traveled through them all, when it is returned to the boiler.The primary disadvantage to this system is that the radiator closest to the central heating radiator system gets much hotter than the last one in the line. In theory, there is no
40、 limit to the number of radiators that can be connected to the loop, but the further from the central heating radiator boiler they are, the less heat they will generate. Another design for the central heating radiator system has a separate water return line from each radiator. The feed line of the h
41、ot water is extended to all of the radiators in the loop, which is actually a separate loop for each radiator. As the water passes through the respective radiators, it goes into a return line that sends it back to the boiler. This provides a more even distribution of the hot water from the boiler. S
42、peed Is Not A Strength Of Radiated Heat.As the name implies, the heat generated in a central heating radiator system comes from the hot water in the radiators. Since there is no moving air there will be less dust flying around the house but there will also be no warm air being circulated. Once the r
43、adiator gets hot, the air around it is warmed through conduction. As the hot air rises and the cold air heads towards the floor, making lower areas in the room considerably colder than the ceilings, where no one usually sits.Some radiators in a central heating radiator system use metal deflectors on
44、 top of the individual radiators to deflect the heat down and away from the radiator, helping to move the warmer air around the room faster. Radiators can also cause burns if touched while the hot water is just arriving into the system.One of the big dangers with central heating radiator units is if all of the radiators are turned off and the boilers relief valve is not functioning, pressure can build up in the pipes causing them to burst from the pressure or worse, causing the boiler to break apart at the seams.待添加的隐藏文字内容2 Radiator散热器
