工程熱力學(xué)與傳熱學(xué)（雙語）第9章習(xí)題課

1、--- Chapter 9 Conduction ---,Tutorial,Heat Transfer,1. 如圖所示的墻壁，其導(dǎo)熱系數(shù)為50 W/(m.K)， 厚度為50mm，在穩(wěn)態(tài)情況下墻壁內(nèi)一維溫度 分布為 t = 200 – 2000 x2 。式中x 的單位為m。 試求 （1）墻壁兩側(cè)表面的熱流密度； （2）壁內(nèi)單位體積的內(nèi)熱源生成熱。,2. 有一鍋爐圍墻由三層平壁組成，內(nèi)層是厚度δ1=0.2

2、3m， λ1=0.63W/(m.K) 的耐火粘土磚；外層是厚度δ3=0.25m， λ3=0.56W/(m.K)的紅磚層；兩層中間填以厚度δ2=0.1m， λ2=0.08 W/(m.K)的珍珠巖材料。爐墻內(nèi)側(cè)與溫度為 tf1=520℃的煙氣接觸，其表面?zhèn)鳠嵯禂?shù)h1=35W/(m2.K)， 爐墻外側(cè)空氣溫度tf2=22℃，空氣側(cè)表面?zhèn)鳠嵯禂?shù) h2=15W/(m2.K)。 試

3、求（1）通過該爐墻單位面積的散熱損失； （2）爐墻內(nèi)外表面溫度及層與層交界面的溫度； （3）畫出爐墻內(nèi)的溫度分布曲線。,3. 一建筑物墻壁由如圖所示的空心磚砌成，空心磚尺寸 300mm×300mm×300mm。設(shè)該混凝土導(dǎo)熱系數(shù)為 0.8W/(m.K)，空氣當(dāng)量導(dǎo)熱系數(shù)為0.28W/(m.K)。設(shè)溫度 只沿墻壁厚度X方向發(fā)生變化，室內(nèi)溫度為2

4、5℃，表面?zhèn)?熱系數(shù)為10W/(m2.K)，室外空氣溫度為 -10℃，表面?zhèn)鳠?系數(shù)為20W/(m2.K)。 求通過每塊磚的導(dǎo)熱量。,4. 外徑5cm的不銹鋼管，外面包扎著厚度為6.4mm 的石棉隔熱層，導(dǎo)熱系數(shù)為0.166W/(m.K)， 再外面包扎著厚度為2.5mm的玻璃纖維隔熱層， 導(dǎo)熱系數(shù)為0.0485W/(m.K)。不銹鋼管外壁溫度 為315℃，隔熱層外表面溫度為38℃。

5、試計算石棉-玻璃纖維交界面的溫度。,5. 蒸汽管道的外直徑d1=30mm，準(zhǔn)備包兩層厚度 都是15mm的不同材料的熱絕緣層。a種材料的 導(dǎo)熱系數(shù)λa = 0.04W/(m.K)，b 種材料的導(dǎo)熱 系數(shù)λb= 0.1W/(m.K)。若溫差一定。 試問從減少熱損失的觀點看下列兩種方案： （1）a在里層，b在外層； （2）b在里層，a在外層。哪一種好，為什么？,6. 一高為30cm鋁制圓錐臺，頂面直

6、徑為8.2cm， 底面直徑為13cm；底面和頂面溫度各自均勻且 恒定，分別為520℃和120℃，側(cè)面（曲面）絕 熱。試確定通過此臺的導(dǎo)熱量（鋁的導(dǎo)熱系數(shù) 取為100W/(m.K)。,7. 圖中所示為純鋁制作的圓錐形截面。其圓形截面直徑為 D=ax1/2，其中a=0.5m1/2。小端位于x1=25mm處，大端 位于x2=125mm處，端部溫度分別為T1=600K和T2=400K， 周

7、側(cè)面隔熱良好。 （1）作一維假定，推導(dǎo)用符號形式表示的溫度分布T(x) 的表示式，畫出溫度分布的示意圖。 （2）計算傳熱熱流量Q。,8. 初始溫度為30℃，壁厚為9mm的火箭發(fā)動機(jī)噴管，外壁 絕熱，內(nèi)壁與溫度為1750℃的高溫燃?xì)饨佑|，燃?xì)馀c壁面 間的表面?zhèn)鳠嵯禂?shù)為1950W/(m2.K)。假定噴管壁可作為 一維無限大平壁處理，材料物性如下：ρ=8400kg/m3，

8、c=560J/(kg.K)，λ=24.6W/(m.K)。試確定 （1）為使噴管材料不超過材料允許溫度（1000℃）而能 允許的運行時間； （2）在允許時間的終了時刻，壁面中的平均溫度梯度與 最大溫度梯度。,9. 用熱電偶測量氣罐中氣體的溫度。熱電偶的初始溫度 為 20℃，與氣體表面的表面?zhèn)鳠嵯禂?shù)為10W/(m2.K)。 熱電偶近似為球形，直徑為0.2mm。

9、 試計算熱電偶插入10s后，其過余溫度為初始過余溫度 的百分之幾？要使熱電偶過余溫度不大于初始過余溫度 的1%，至少需要多長時間？ 已知熱電偶焊絲的λ= 67W/(m.K)，ρ=7310kg/m3, c=228J/(kg.K)。,10. 一直徑為0.5mm的熱電偶，其材料的密度ρ= 8930kg/m3, 比熱c= 400J/(kg.K)。初始溫度為25℃，被突然放于表面

10、 傳熱系數(shù)為95 W/(m2.K)，溫度為120℃的氣流中。 試問熱電偶的過余溫度為初始過余溫度的1%及0.1% 時 需要多少時間？這時熱電偶指示的溫度是多少？,11. A large window glass 0.5cm thick [λ=0.78W/(m.℃) ] is exposed to warm air at 25℃ over its inner surface, an

11、d the heat transfer coefficient for the inside air is 15W/(m2.K). The outside air is -15℃, and the heat transfer coefficient associated with the outside surface is 50W/(m2.K). Determine the temp of the

12、 inner and outer surface of the glass.,12. A steel tube[λ=15W/(m.℃)] of outside diameter 7.6cm and thickness 1.3cm is covered with an insulation material [λ=0.2W/(m.℃)] of thickness 2cm. A hot gas at 3

13、20℃ with a heat transfer coefficient of 200W/(m2.K) flows inside the tube. The outer surface of the insulation is exposed to cooler air at 20℃ with a heat transfer coefficient of 50W/(m2.K) 。Calcu

14、late (1) the heat loss from the tube to the air for a 5-m length of the tube. (2) the temp drops due to the thermal resistances of the hot gas flow, the steel tube, the insulation layer,

15、 and the outside air.,13. A Steam pipe with an outside radius of 4cm is covered with a layer of asbestos insulation [λ=0.15W/(m.℃) ] 1cm thick, which is in turn covered with fiberglass insulation [λ

16、=0.05W/(m.℃) ] 3cm thick. The outside surface of the steam pipe is at a temp of 330℃, and the outside surface of the fiberglass insulation is at 30℃. Determine the heat transfer rate per meter length

17、of the pipe and the interface temp between the asbestos and the fiberglass insulation.,Tutorial,One-Dimensional Unsteady State Conduction Problem,14. A steel plate [a=1.2×10-5m2/s,λ=43W/(m.℃), cp=465J/

18、(kg.℃) , ρ=7833kg/m3] of thickness 10cm, initially at a uniform temp of 240℃, is suddenly immersed in an oil bath at 40℃. The convection heat transfer coefficient between the fluid and the surface is 600W/

19、(m2.℃). (a) How long will it take for the center-plane to cool to 100℃? (b) What is the temp at a depth 3cm from the outer surface? (c) Calculate the energy removed from the plate during this time .,15. Using l

20、umped system analysis, determine the time required for a solid steel ball of radius R=2.5cm, λ=54W/(m.℃),ρ=7833kg/m3, and c=0.465kJ/(kg.℃) to cool from 850℃ to 250℃ if it is exposed to an air stre

21、am at 50℃ having a heat transfer coefficient h=100W/(m2.℃).,16. A Large aluminum plate [ λ=204W/(m.℃), ρ=2702kg/m3, and c=0.896kJ/(kg.℃) of thickness L=0.1m, that is initially at a uniform temperature of

22、 250℃ is cooled by exposing it to an air stream at temperature 50℃ . Using lumped system analysis, determine the time required to cool the aluminum plate to 100℃ if the heat transfer coefficient be

23、tween the air stream and the plate surface is h=80W/(m2.℃).,17. A 6-cm-diameter steel ball [λ=61W/(m.℃), ρ=7865kg/m3, and c=0.46kJ/(kg.℃) is at a temperature of 800℃. It is to be hardened by suddenly

24、dropping it into an oil bath at a temperature of 50℃. If the quenching occurs when the ball reaches a temperature of 100℃ and the heat transfer coefficient between the oil and the sphere is 500W/m2

25、.℃, determine how long the ball should be kept in the oil bath. If 100 balls are to be quenched per minute, determine the rate at which heat must be removed from the oil bath in order to maintain t

26、he bath temperature at 50℃.,18. A thermocouple is to be used to measure the temperature in a gas stream. The junction is approximated as a sphere with thermal conductivity of 25W/(m.℃), density of 9000k

27、g/m3, and specific heat of 0.35kJ/(kg.℃). The heat transfer coefficient between the junction and the gas is 250W/(m2.℃). Calculate the diameter of the junction if the thermocouple should measure 95

28、percent of the applied temperature difference in 3s.,19. The temperature of a gas steam is to be measured by a thermocouple whose junction can be approximated as a 1-mm-diameter sphere, The properties of

29、the junction are λ=35W/(m.℃), ρ=8500kg/m3, and cp=320kJ/(kg.℃), and the convection heat transfer coefficient between the junction and the gas is h=210 W/(m2.℃). Determine how long it will take fo