第九章 热传导
英文习题
1. Heat generation in a hair dryer
The resistance wire of a 1200W hair dryer is 80cm long and has a diameter of D=0.3cm. Determine the rate of heat generation in the wire per unit volume, in W/cm, and the heat flux on the outer surface of the wire as a result of this heat generation.
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2. Heat loss through double-pane window Consider a 0.8-m-high and 1.5-m-wide double-pane window consisting of two 4-mm-thick layers of glass (k=0.78 W/m.℃) separated by a 10-mm-wide stagnant air space (k=0.026 W/m℃). Determine the steady rate of heat transfer through this double-pane window and the temperature of its inner surface for a day during which the room is maintained at 20℃ while the temperature of the outdoors is -10℃. Take the convection heat transfer coefficient on the inner and outer surfaces of the window to be h1 =10 W/m.℃, where includes the effects of radiation.
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3. Equivalent thickness for contact resistance
The thermal contact conductance at the interface of two 1-cm-thick aluminum plates is measured to be 11 000 W/m℃. Determine the thickness of the aluminum plate whose thermal resistance is equal to the thermal resistance of the interface between the plates (Fig.9-2).
FIGURE 9-1
FIGURE 9-24. Heat loss through a composite wall
A 3-m-high and 5-m-wide wall consists of long 16-cm×22-cm cross-section horizontal bricks (k=0.72 W/m.℃) separated by 3-cm-thick plaster layers (k=0.22 W.m.℃). There are also 2-cm-thick plaster layers on each side of the brick and a 3-cm-thick rigid foam (k=0.026 W/m.℃) on the side of the wall, as shown in Fig.9-3. The indoor and outdoor temperatures are 20℃ and -10℃, and the convection heat transfer coefficients on the inner and the outer sides are h1=10 W/m.℃ and h2=25 W/m.℃, respectively. Assuming one-dimensional heat transfer and disregarding radiation, determine the rate of heat transfer through the wall.
FIGURE 9-32
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5. Heat transfer to a spherical container
A 3-m internal diameter spherical tank made of 2-cm-thick stainless steel (k=15 W/m.℃) is used to store iced water at T∞1=0 ℃. The tank is located in a room whose temperature is T∞2=22 ℃. The walls of the room are also at 22℃. The outer surface of the tank is black and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. The convection heat transfer coefficients at the inner and the outer surfaces of the tank are h1=80 W/m.℃ and h2=10 W/m.℃, respectively. Determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at 0℃ that melts during a 24-h period.
FIGURE 9-42
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6. Heat loss from an insulated electric wire
A 3-mm-diameter and 5-m-long electric wire is tightly wrapped with a 2-mm-thick plastic cover whose thermal conductivity is k=0.15 W/m.℃. Electrical measurements indicate that a current of 10 A passes through the wire and there is a voltage drop of 8 V along the wire. If the insulated wire is exposed to a medium at T∞=30℃ with a heat transfer coefficient of h=12 W/m.℃, determine the temperature at the interface of the wire and the plastic cover in steady operation. Also determine whether doubling the thickness of the plastic cover will increases or decrease this interface temperature. 2
FIGURE 9-5FIGURE 9-67. Effect of fins on heat transfer from steam pipes
Steam in a heating system flows through tubes whose outer diameter is D1=3 cm and whose walls are maintained at a temperature of 120℃. Circular aluminum fins (k=180 W/m.℃) of outer diameter D2=6 cm and constant thickness t=2 mm are attached to the tube, as shown in Fig.9-6. The space between the fins is 3 mm, and thus there are 200 fins per meter length of the tube. Heat is transferred to the surrounding air at T∞=25℃ with a combined heat transfer coefficient of h=60 W/m.℃. Determine the increase in heat transfer from the tube per meter of its length as a result of adding fins.
FIGURE 9-72
8. Temperature measurement by thermocouples
The temperature of a gas steam is to be measured by a thermocouple whose junction can be approximated as a 1-mm-diameter sphere, as shown in Fig. 9-7. The properties of the junction are k=35 W/m.℃, ρ=8500 kg/m, and Cp=320 kJ/kg.℃, and the convection heat transfer coefficient between the junction and the gas is h=210 W/m.℃. Determine how long it will take for the thermocouple to read 99 percent of the initial temperature difference.
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9. Cooling of a long stainless steel cylindrical shaft
A long 20-cm-diameter cylindrical shaft made of stainless 304 comes out of an oven at a uniform temperature of 600℃. The shaft is then allowed to cool slowly in an environment chamber at 200℃ with an average heat transfer coefficient of h=80 W/m.℃. Determine the temperature at the center of the shaft 45 min after the start of the cooling process. Also, determine the heat transfer per unit length of the shaft during this time period.
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10. Cooling of a short brass cylinder
A short brass cylinder of diameter D=10 cm and height H=12 cm is initially at a uniform temperature T1=120℃. The cylinder is now placed in atmospheric air at 25℃, where heat transfer takes place by convection, with a heat transfer coefficient of h=60 W/m.℃. Calculate the temperature at (a) the center of the cylinder and (b) the center of the top surface of the cylinder 15 min after the start of the cooling.
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11. Heat transfer from a short cylinder
Determine the total heat transfer from the short brass cylinder (ρ=8530 kg/m, and Cp=0.380 kJ/kg.℃) discussed in problem 10.
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工程热力学与传热学
第九章 热传导 习题
习 题
1. 2. 3. 4. 5. 6. 7. 8. 9.
写出导热傅立叶定律表达式的一般形式，说明其适用条件及式中各符号的物理意义。 写出直角坐标系三个坐标方向上傅立叶定律表达式。 为什么导电性能好的金属导热性能也好？
一个具体导热问题的完整数学描述应包括哪些方面？ 何谓导热问题的单值性条件，它包含哪些内容？
试说明在什么条件下平板和圆筒壁的导热可以按一维导热问题处理。 试用传热学观点说明冰箱为什么要定期除霜。
为什么有些物体要加装肋片？加肋一定会使传热量增加吗？ 试说明影响肋片效率的主要因素。
10. 什么是接触热阻？接触热阻的主要影响因素有哪些？ 11. 什么是非稳态导热的正规状况阶段？有什么特点？
12. 写出傅立叶数Fo及毕渥数Bi的表达式，并说明他们的物理意义/
13. 试以第三类边界条件下无限大平板的非稳态导热为例，说明傅立叶数Fo和毕渥数Bi对平板内温度分布的影响。
14. 什么叫做非稳态导热的集总参数法？其使用条件是什么？ 15. 简要说明数值计算导热问题的有限差分法的基本思想与步骤。 16. 是否差分网格划分的越细越好？为什么？
17. 炉墙由一层耐火砖和一层红砖构成，厚度都为250mm，热导率分别为0.6W/（m.K）和0.4 W/（m.K），炉墙内，外壁面温度分别维持700℃和80℃不变。（1）试求通过炉墙的热流密度；（2）如果用热导率为0.076 W/（m.K）的珍珠岩混凝土保温层代替红砖层，并保持通过炉墙的热流密度及其他条件不变，试确定该保温层的厚度。
18. 有一炉墙，厚度为20cm，墙体材料的热导率为1.3 W/（m.K），为使散热损失不超过1500W/m2，紧贴墙外壁面加一层热导率为0.1 W/（m.K）的保温层。已知复合墙壁内外两侧壁面温度分别为800℃和50℃，试确定保温层的厚度。
19. 热电厂有一外径为100mm的过热蒸汽管道（钢管），用热导率λ=0.04 W/（m.K）的玻璃棉保温。已知钢管外壁面温度为400℃，要求保温层外壁面温度不超过50℃，并且每米长管道的散热损失要小于160W，试确定保温层的厚度。
20. 某过热蒸汽管道的内，外直径分别为150mm和160mm，管壁材料的热导率为45 W/（m.K）。管道外包两层保温材料：第一层厚度为40mm，热导率为0.1 W/（m.K）；第二层厚度为50mm，热导率为0.16 W/（m.K）。蒸汽管道内壁面温度为400℃，保温层外壁面温度为50℃。试求：（1）各层导热热阻；（2）每米长蒸汽管道的散热损失；（3）各层间的接触面温度。
21. 热电偶的热接点可以近似地看作球形，已知其直径为d=0.5mm，材料的密度ρ=8500kg/m3，比热容c=400J/（kg..K），热电偶的初始温度为25℃，突然将其放入120℃的气流中，热电偶表面与气流间的表面传热系数为90W/（m2.K）试求：（1）热电偶的时间常数；（2）热电偶的过余温度达到初始过余温度的1%时所需的时间。
22. 将初始温度为80℃，直径为20mm的紫铜棒突然横置于温度为20℃，流速为12m/s的风道中冷却，5min后紫铜棒的温度降为34℃。已知紫铜棒的密度ρ=8950kg/m3，比热容c=380J/(kg.K)，热导率λ=390W/（m.K），试求紫铜棒表面与气流间对流换热的表面传热系数。
23. 将一块厚度为5cm，初始温度为250℃的大平板突然放置于温度为20℃的气流中，钢板壁面与气流间对流换热的表面传热系数为100W/（m2.K），已知钢板的热导率λ=47W/（m.K），热扩散率a=1.47×10-5m2/s。试求：（1）5min后钢板的中心温度和距壁面1.5cm处的温度；（2）钢板表面温度达到150℃时所需的时间。
习题课
一维稳态导热
24. 1. 厚2cm的壁，由平均导热系数为1.3W/(m.℃)的材料构成，用平均导热系数为0.35W/(m.℃)
的材料做壁的隔热层，使每平方米热损失不超过1830kW。假设加隔热层后，壁的内外表面温度分别为1300℃和30℃。试求隔热层厚度。
25. 一建筑物的墙壁由如图所示的空心砖砌成。设该
混凝土导热系数为0.8W/(m.K)，空气当量导热系数为h1?10W/(m2.K)0.28W/(m.K)。设温度只沿墙壁厚度X方向发生变化，tf1?25?C室内温度为25℃，表面传热系数为10 W/(m2.K)，室外空气温度为 -10℃，表面传热系数为20 W/(m.K)。求通过每块砖的导热量。
26. 外径5cm的不锈钢管，外面包扎着6.4mm厚的石棉隔热层，导热系数为0.166 W/(m.K)，再外面包扎着2.5mm厚的玻璃纤维隔热层，导热系数为0.0485 W/(m.K)。管壁温度为315℃，隔热层外表面温度为38℃。试计算石棉-玻璃纤维交界面的温度。
27. 如图所示的墙壁，其导热系数为50 W/(m.K)，厚度为50mm， 在稳态情况下墙壁内一维温度分布为 t = 200 – 2000 x2 。式中x 的单位为m。
试求（1）墙壁两侧表面的热流密度；
（2）壁内单位体积的内热源生成热。
28. 蒸汽管道的外直径d1=30mm，准备包两层厚度都是15mm的不同材料的热绝缘层。a种材料的导热系数λ
a = 0.04 W/(m.K)，b
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７５mm７５mm７５mmh2?20W/(m2.K)tf2??10?Ct f1 h1０７５mmt f2 h2xt??50W/(m.K)t?200?2000x2??50mm0δx种材料的导热系数λb = 0.1W/(m.K)。若温差一定，试问从减少
热损失的观点看下列两种方案：（1）a在里层，b在外层（2）b在里层，a在外层，哪一种好，为什么？
一维非稳态导热
29. 用热电偶测量气罐中气体的温度。热电偶的初始温度为20℃，与气体表面的传热系数为10 W/(m2.K)。热电偶近似为球形，直径为0.2mm。试计算插入10s后，热电偶的过余温度为初始过余温度的百分之几？要使温度计过余温度不大于初始过余温度的1%，至少需要多长时间？已知热电偶焊丝的λ= 67W/(m.K)，ρ=7310kg/m, c=228J/(kg.K)。
30. 一直径为0.5mm的热电偶，其材料的密度为ρ= 8930kg/m, 比热c = 400J/(kg.K)。初始温度为25℃，当被突然放于表面传热系数为95 W/(m2.K)，温度为120℃的气流中。试问热电偶的过余温度为初始过余温度的1% 及0.1% 时需要多少时间？这时热电偶指示的温度是多少？
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