HEATCOOL计划计算炉负载瞬态加热和冷却时间 （由约瑟夫· 巴恩斯 ）

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适当的热处理周期需要知道当一部分被充分加热知道，如果它被冷却速度不够快。 The time at temperature can be critical to the results of the heat treatment.在温度，时间可能是至关重要的热处理结果。 If not, it is critical to determine the optimum time to optimize production efficiencies and reduce costs.如果不是，它是关键，以确定优化生产效率和降低成本的最佳时机。 This time can be easily calculated using the HEATCOOL program discussed here.这个时候可以很容易地计算使用的HEATCOOL的方案讨论。


To calculate time to heat or cool a part involves many temperature-dependent variables, including thermal conductivity, heat-transfer film coefficients, part size and shape, surface environment, etc. If the part is small, the time can be solved assuming a uniform temperature distribution throughout the body.计算时间来加热或冷却的一部分，涉及许多随温度变化的变量，包括导热系数，传热膜系数，零件的尺寸和形状，地表环境等，如果一部分是小，时间可以假设一个统一的解决整个身体的温度分布。 This is calculated as heat transferred to or from the material equal to the increase or decrease in heat energy of the body during a differential time period, and it is in the form of an equation relating temperature differential ratios to exponential heat-transfer values:这是计算转让或从材料，等于在一个差时间的增加或减少体内的能量热的热，它是在一个与温度差比指数的传热值的方程的形式：

(TT ¥ )/(Ti-T ¥ ) = e(bt) where b = h A/( r V Cp) （特）/（钛- T¥）= E（BT） 日元 ，其中b = H /（R V茂）

The transient temperature distribution in the part can be solved by a partial differential equation using advanced mathematical techniques, but the solution normally requires infinite series that are difficult to deal with and time consuming to evaluate.在部分的瞬态温度分布可以由偏微分方程的方程，采用先进的数学技术可以解决，但解决方案通常需要无穷级数，是难以对付和耗时的评估。 If the part is large, the analysis becomes quite involved.如果部分大，分析变得相当复杂。 Transient-temperature heat-transfer charts developed by Schack, Newman, Gurney-Lurie, Heisler (1947) and Grober (1961) can be used but are difficult to read and subject to reading errors[1].瞬态高温传热沙克，纽曼，格尼，劳瑞，海斯勒（1947年）和Grober（1961）开发的图表可以使用，但难以阅读和受读取错误[1]。

Fourier's Law is the differential equation for heat conduction relating transient temperature distribution傅里叶定律是热传导微分方程有关的瞬态温度分布   q = (TT ¥ )/(Ti-T ¥ ) to location within the part (distance from the center X = x/L), including the Biot number (Bi = h L/k) and time tau ( t = a t/L²) as the dimensionless parameters. Q =（电汇¥钛- T）/（ 元 ）位置内的部分（从中心X = X / L的距离），包括Biot数（碧= H L / K）和时间头（T = A T / L，²）为无量纲参数。 The Biot number is the ratio of external convection and radiation heat transfer to internal heat conduction in a part. Biot数是外部对流和辐射传热部分在内部热传导的比例。 It is defined as the ratio of heat conducted to the rate of heat stored in a material.它被定义为进行热率材料中的热量比例。 Alpha ( a ) is the symbol for thermal diffusivity = heat conducted/heat stored = k/( r Cp) and represents how fast heat diffuses through a material.阿尔法（a）是热扩散的象征=热量进行存储/热= K /（CP）和代表如何快速通过材料的热扩散。 The Stefan-Boltzmann law (Q = 5.67-8 W/(m2 K4) A T4) is the rate of radiation that can be emitted from a surface. Stefan-Boltzmann定律（为Q = 5.67-8瓦/（平方米K4），一个T4）是可以从表面发出的辐射率。 Part configuration and surface emissivity are key factors for this mode of heat transfer.部分配置和表面发射这种传热方式的关键因素。

Additional equations in the program determine the nondimensional transient temperature distribution in a one-term approximation of the Fourier infinite series, including the Biot number and thermal-diffusivity parameters.在该计划的其他方程确定在一个长期的傅立叶无穷级数逼近，包括Biot数和热扩散参数的无量纲的瞬态温度分布。 They result in errors less than 2% for time t > 0.2, which is suitable for most heating and cooling projects encountered in industrial heating applications.他们在错误的结果时间 t> 0.2，这是适合大多数的加热和冷却项目，工业加热应用中遇到的不到2％。


HEATCOOL Program HEATCOOL计划

The program can be used to compute transient heating or cooling time of any load configuration in a vacuum chamber or in a chamber equipped with or without fan circulation.该方案可以用来计算在一个真空室或带或不带风扇的流通室配备任何负载配置瞬态加热或冷却时间。 The load can be a slab, rectangular bars, cylinders, spheres, coiled strip or small parts in a basket.负载可以是平板，矩形条，圆柱体，球体，螺旋钢带或一篮子的一小部分。 The time includes convection, radiation and conduction heat-transfer modes.时间包括对流，辐射和传导传热模式。

Recirculated gas flow at any velocity can be air, argon, carbon dioxide, carbon monoxide, endo-exothermic, flue gas, helium, hydrogen, methane, nitrogen, 90%N2/10%H2 or steam.循环气体流量在任何速度可以是空气，氩气，二氧化碳，一氧化碳，内放热，烟道气，氦气，氢气，甲烷，氮，90％N2/10％H2或蒸汽。 Gas properties programmed and computed at any input pressure include density, specific heat, thermal conductivity, viscosity, and Reynolds and Nusselt numbers.在任何输入压力计算编程和气体的特性包括密度，比热，导热系数，粘度，雷诺数和努塞尔数。 The convection and radiation heat-transfer coefficients are computed.对流和辐射传热系数计算。 Plant elevation is entered, and the barometric pressure is computed.输入植物海拔，气压计算。 Chamber pressure can be above or below atmospheric.腔压力可高于或低于大气。 Cooling can also be done in a liquid (quenching in water, oil, brine or synthetic) with agitation to enhance heat transfer.也可以进行冷却液体（水，油，盐水或合成淬火），搅拌，以强化传热。

Density, specific heat and thermal conductivity of 23 metals from aluminum to zirconium and five nonmetals are programmed. 23金属铝锆和五非金属的密度，比热和导热编程。 Other nonprogrammed metals and nonmetals can be entered.可以输入其他非程序的金属和非金属。 The thermal diffusivity and Biot numbers are computed for analysis of internal/external thermal resistances.热扩散和比奥数字为内部/外部热阻的分析计算。 Final temperatures are computed at the center and surface for slabs, cylinders and spheres.最终温度计算的中心和表面板，气瓶和领域。 Three equally spaced nodal temperatures from center to surface are also computed.三个等距节点从中心到表面温度计算。 For rectangular shapes, temperatures are computed at the center, each face, center of the long edge and extreme corner.形状为长方形，温度计算的中心，每个面，长边中心和极端角落。 It is important when heating materials required to meet critical temperature specifications to be sure all surfaces of the part do not exceed the set-point temperature.加热材料时，需要达到临界温度规格，以确保所有表面的一部分，不超过设定点的温度，这一点很重要。 Higher head temperatures can also be input above the final set-point temperature to decrease heating time, and the time saved is displayed.高等教育头温度也可以输入最终设定点温度以上，以减少加热时间，节省的时间显示。


Enlarge this picture 放大这张图片  
  

Figure 1 is a printout of a HEATCOOL metric units program for computing time to heat 12 460-mm (18-inch) x 610-mm (24-inch) x 3660-mm (144-inch) aluminum billets, with a head temperature set at 592°C (1097°F) or 10% above the final set-point temperature of 538°C (1000°F).图1是一个HEATCOOL公制单位计算时间的方案，以12×610毫米（24英寸）460毫米（18英寸）x 3660毫米（144英寸）铝合金坯料加热的打印输出，与头的温度在592°C（1097°F）或10％以上的最终设定点温度为538°C（1000°F）。 The billets are set on their small side with 150-mm (6-inch) space between so radiation is not viewed 100% between billets and the small bottom side is not available for convection or radiation heat transfer.其副作用小的钢坯150毫米（6英寸），所以辐射之间的空间并不被100％之间钢坯和小的底部是没有对流或辐射传热。 At the end of the head-temperature phase (5.29 hr), the center temperature reached 479°C (894°F) and the corner reached 509°C (948°F).在头部温度阶段（5.29小时），中心温度达到479°（894°F）和角落达到509°C（948°F）的。 This corner temperature is not included in the printout but is displayed for reference.在打印输出，但不包括这个角落温度显示参考。 If the corner exceeded the set point during the higher head-temperature phase, this would be displayed and corrective action recommended (decrease the center within temperature and/or the head temperature).如果在头温度越高阶段角落超过设定点，这将显示和建议纠正措施（降低温度和/或头部的温度范围内的中心）。 The time to heat the center to 532°C (990°F) is computed to be about 11.2 hours, and the head temperature is computed to save about 2.0 hours heating time for this particular load compared to heating without a head temperature.中心加热到532°C（990°F）计算约为11.2小时，头部温度计算，可节省约2.0小时加热时间相比无头温度加热到这个特殊的负载。


Conclusion 结论

The HEATCOOL program transforms these complicated equations and formulas into practical data and computes heat or cool time with ease. HEATCOOL方案转化为实际的数据这些复杂的方程和公式，并计算轻松地加热或冷却的时间。 It will save many hours in solving transient heating- and cooling-time projects.在解决短暂的加热和冷却时间的项目，这将节省很多时间。 Inclusion of preprogrammed values eliminates the need to consult outside references for many physical properties, thus saving tedious and time-consuming nonproductive work.预先设定值列入省去了许多物理性质，化学性质，咨询以外的参考，从而节省了繁琐和费时的非生产性工作。 Direct, straightforward selections are used.用直接，简单的选择。

Heating and cooling (metal and nonmetal) slabs, billets, cylinders and coils can be readily computed with the HEATCOOL program, and different temperatures and times can be quickly evaluated. IH （金属和非金属）加热和冷却板，钢坯，气瓶和线圈，可以随时计算与HEATCOOL方案，不同的温度和时间，可以快速评估。 希

For more information: Joseph D. Barnes, PE is a consulting engineer and principal of Barnes Associates, 900 Market St., Apt. 欲了解更多信息：约瑟夫D巴恩斯，PE是一个咨询工程师，巴恩斯，900市场街公寓主要。 301, Meadville, Pa. 16335; tel: 814-724-4615; e-mail: jdb@barnesjd.com; web: www.barnesjd.com 301米德维尔，宾夕法尼亚州16335电话：814-724-4615电子邮件：jdb@barnesjd.com;网址：www.barnesjd.com

Symbols: T=Temperature, h=heat-transfer film coefficient, Cp=specific heat, V=Volume, r=density, L=length, k=conductivity, K=degree Kelvin, W=watt, m=meter, A=area, t=time, Q=blackbody emissive power.标志：T =温度，H =传热膜系数，CP =比热，V =体积，R =密度，L =长度，K =电导率K =开氏度W =瓦，M =米=区，T =时间，Q =黑体发射功率。

Additional related information may be found by searching for these (and other) key words/terms via BNP Media SEARCH at www.industrialheating.com: thermal diffusivity, transient heating, heat transfer, thermal conductivity, convection, radiation, conduction 这些（和其他）关键词/通过在www.industrialheating.com法国媒体搜索范围：热扩散，瞬时加热，传热，热传导，对流，辐射，传导，可能会发现其他相关信息


SIDEBAR: Running the Numbers 侧边栏：运行数

When asked to put the HEATCOOL program to the test with actual measured plant data, an historic study run at Westinghouse was used.当被问及HEATCOOL计划与实际测量的工厂数据测试，一个历史性的研究在西屋运行的。 In this study, aluminum coils 36.75 inch OD x 20 inch ID x 36 inch wide and 2,669 pounds in weight had been heated.在这项研究中，铝线圈36.75英寸外径×20英寸内径×36英寸宽和2,669磅的体重已经加热。 All of the data from the test was entered into the HEATCOOL program, including the final coil temperature and the furnace set-point temperature.从测试的所有数据输入到HEATCOOL程序，包括最后的线圈温度和炉内温度设定点。

One of the advantages of the program is the capability to enter different percentages for each surface area of the coil as well as different gas velocities over each of these surfaces.该方案的优势之一是为每个线圈的表面面积，以及这些表面的每一个不同的气体速度的能力，进入不同的百分比。 The ID surface estimation for radiation was 20% of the ID surface area of 15.708 sq. ft. A very low air velocity (100 fpm) was estimated over this ID surface, since the flow is not in a radial direction through the coil.辐射的ID表面估计的15.708平方英尺一个非常低的气流速度（100英尺），估计这个ID表面，因为流量是通过线圈的径向方向的ID表面积的20％。 The actual test shows the maximum air velocity (passing coil) at 32.2 fps and the minimum velocity (before coil) at 21.7 fps.实际测试表明在32.2帧的最大空气速度（通过线圈），最低为21.7 fps的速度（前线圈）。 The average of these velocities (1600 fpm) was used for the air flowing past the OD and end surfaces.这些速度的平均值（1600 FPM）用于过去的外径和端面的空气流动。

The program computes the heating time at 5.81 hours.该方案计算加热时间为5.81小时。 The test shows the actual heating time to be 5.7 hours (after the coil reached 200°F at the end of purge).测试显示实际加热时间为5.7小时（线圈后达到吹扫结束在200℉）。 The program indicates the head temperature saved about 1.4 hours heating time vs. if the head temperature was not employed.该计划表明保存头的温度加热时间1.4小时，与如果头部温度不被聘用。 This is a significant saving and would be an important factor to consider when scheduling furnace time.这是一个显着的节能炉时间安排时，考虑的将是一个重要的因素。


Joseph Barnes 约瑟夫· 巴恩斯

Consulting Engineer, Meadville, Pa.宾夕法尼亚州米德维尔咨询工程师，


References 参考文献
1.. Yunus A. Cengel, Heat Transfer: A Practical Approach, McGraw-Hill, New York, 1998, pp. 234-238 1。 传热 Cengel尤努斯答：实际出发，麦格劳-希尔，纽约，1998年，第234-238