1. Introduction 1 Heat Transfer and Its Applications

2. Heat Exchange Insulation 2

3. Nature of heat flow Heat flows from the object at the higher temperature to that at the lower temperature. How it happens? 3

4. Conduction ( 热传导 ) Convection ( 对流传热 ) Radiation ( 热辐射 ) Three mechanisms : 4

5. Heat Transfer by Conduction 5

6. If a temperature gradient exists in a continuous substance, heat can flow unaccompanied by any observable motion of matter. Conduction Qualitative( 定性的 ) Quantitative( 定量的 ) 6

7. Heat transfer by conduction considering heat flow in homogeneous ( 均一的 ) isotropic( 孤立的 ) solids because in these there is no convection and the effect of radiation is negligible. Assumption: 7

8. Math. Model by Conduction According to Fourier ’ s law （傅里叶导热定 律）, the heat flux is proportional to the temperature gradient and opposite to it in sign. Where: q: heat transfer rate, W=J/s A: heat transfer area, m 2 dq/dA: heat transfer flux, W/m 2 T: temperature, K or o C x: distance, m dT/dx: temperature gradient, K/m k: thermal conductivity, W/(m∙K) (4.2-1) q x For one-dimensional heat flow 8

9. Thermal conductivity k The proportionality constant k is a physical property of the substance. The unit of k are W/(m∙ ℃ ) or W/(m∙K). For small ranges of temperature, k is constant For larger temperature ranges, k is approximated by (4.2-5) k vary over a wide range. They are highest for metals and lowest for finely powdered materials from which air has been evacuated ( 排空 ). 9

10. k of metal cover a wide range of values, from about 17W/m∙ºC for stainless steel ( 不锈钢 ) and 45W/m∙ºC for mild steel ( 低碳钢 ), to 380W/m∙ºC for copper and 415W/m∙ºC for silver For glass and most nonporous materials, the thermal conductivities are much lower, from about 0.35 to 3.5. For most liquid k is lower than that for solids, with typical values of about 0.17. k decreases by 3 ~ 4 %t for a 10 ºC rise in temperature, except water. Gases have the smallest thermal conductivities, with values as low as 0.007. For air at 0ºC, k is 0.024 W/m·ºC. conductor insulator 10

11. In metals ： thermal conduction results from the motion of free electrons. In solids ： poor conductor of electricity, produced by momentum transport In most liquids: thermal conduction results from momentum transfer between adjacent vibrating( 振动 ) molecules or atoms. In gases: conduction occurs by the random motion of molecules. conductor insulator 11

12. Steady-state conduction Conduction under the condition of constant temperature distribution is called steady-state conduction. In the steady state, T is a function of position only, and the rate of heat flow at any point is a constant. Heat flow into the tankHeat flow from the tank Limiting Condition 12

13. Since in steady state there can be neither accumulation nor depletion of heat within the slab, q is constant along the path of heat flow. T x q If x is distance from the hot side. For steady one-dimensional flow.Eq.(4.2-1) may be written (4.2-7) 13

14. Where x 2 -x 1 =B= thickness of layer of insulation T 1 -T 2 =ΔT=temperature drop across layer When k varies linearly with temperature, Eq.(4.2-5), still can be used rigorously by taking an average value k. Since the only variables in this Eq. are x and T, direct integration gives (4.2-8) 14

15. Equation (4.2-8) can be written in the form (4.2-9) Where R=B/k is thermal resistance between points 1 and 2. m 2 ∙ ℃ /W 15

16. Compound resistance in series 16

17. Compound resistance in series Consider a flat wall constructed of a series of layers, as shown in Fig.4.2 Assume that the layers are in excellent thermal contact, so that no temperature difference exists across the interfaces between the layers. Then, if ΔT is the total temperature drop across the entire wall ΔT= ΔT A + ΔT B +ΔT C 17

18. Where R A, R B and R C =resistance of individual layers R=overall resistance (4.2-11) (4.2-12) According to Eq.(4.2-8) 18

19. A flat furnace wall is constructed of 120-mm layer of sil-o- cel brick, with a thermal conductivity 0.08 W/(m· ℃ ) ， backed by a 150-mm of common brick, of conductivity 0.8 W/(m· ℃ ), the temperature of inner face of the wall is 1400 ℃, and that of the outer face is 200 ℃ Example 4.2 B A =0.12mB B =0.15m k A =0.08 W/(m∙ ℃ ) k B =0. 8 W/(m∙ ℃ ) T i =1400 ℃ T o =200 ℃ T2T2 19

20. (a)What is the heat loss through the wall, in W per square meter Example 4.2 B A =0.12mB B =0.15m k A =0.08 W/(m∙ ℃ ) k B =0. 8 W/(m∙ ℃ ) T 0 =1400 ℃ T 3 =200 ℃ T2T2 According to Eq.(4.2-9) 20

21. b)To reduce the heat loss to 600 W/m 2 by adding a layer of cork ( 软木 ) with k= 0.2 W/(m· ℃ ) on the outside of common brick, how many meters of cork are required? Example 4.2 B A =0.12mB B =0.15m k A =0.08 W/(m∙ ℃ ) k B =0. 8 W/(m∙ ℃ ) T i =1400 ℃ T o =200 ℃ T2T2 T3T3 B C =? m k C =0. 2 W/(m∙ ℃ ) According to Eq.(4.2-9) 21

22. Heat flow through a cylinder The inside radius of the cylinder is r i, the outside radius is r o, and the length of the cylinder is L. The temperature of outside surface is T o, and the that of inside surface is T i. The thermal conductivity of the material of which the cylinder is made is k. r i, T i r o, T 0 L Consider the hollow cylinder represented by Fig.4.3 22

23. It is desired to calculate the rate of heat flow outward for this case. At radius r from the center, the heat flow rate is q and the area through which it flows is A. At steady state the heat flow rate is constant. (4.2-13) Since heat flows only in the r direction, Eq. (4.2-7) becomes L r i, T i r o, T 0 r 23

24. Rearranging Eq(4.2-13) and integrating between limits gives (4.2-14) (4.2-17) (4.2-16)(4.2-15) L r i, T i r o, T 0 r the logarithmic ( 对数 ) mean 24

25. The logarithmic mean is less convenient than the arithmetic ( 算术 ) mean, and the latter can be used without appreciable error for thin-walled tubes, where r o /r i is nearly 1. The ratio of the logarithmic mean to the arithmetic mean is a function of r o /r i as shown in Fig4.3 96% (4.2-15) 25

26. Formula Derivation r0r0 r1r1 r2r2 k2k2 k1k1 1 2 26

27. r0r0 r1r1 r2r2 k2k2 k1k1 1 2 According to Eq.(4.2-14) Steady-state conduction Formula Derivation Heat loss per meter for multi-layer cylinder 27

28. A steel tube with dimension Ф60 ×3mm is backed by a 30-mm thick cork, with a thermal conductivity of 0.043 W/(m· ℃ ), and is followed by a 40-mm layer of some insulating material, of 0.07 W/(m· ℃ ). The temperature of the outer face of steel tube is -110 ℃, and that of the outer face of insulating material is 10 ℃. What is the heat loss per meter tube through the wall? Exercise 28

29. For steady one-dimensional conduction Summary (4.2-11) Conduction—If a temperature gradient exists in a continuous substance, heat can flow unaccompanied by any observable motion of matter. Additional formula Uniform units Draw schematic diagram 29

30. Problem 4.1 A layer of pulverized cork 152-mm thick is used as a layer of thermal insulation in a flat wall. The temperature of the cold side of the cork is 4.4 ℃, and that of the warm side is 82.2 ℃. The thermal conductivity of the cork at 0 ℃ is 0.036 W/(m · ℃ ), and that at 93.3 ℃ is 0.055 W/(m · ℃ ). The area of the wall is 2.32m 2. What is the rate of heat flow through the wall in watts? 30

31. Steps & traps 1 、 draw a schematic diagram 2 、 write out the known quantity and unify the units 3 、 analysis the relationship between the known’s and unknown’s 4 、 be careful with some details such as diameter, temperature dependent physical properties, average temperature 31

32. Problem 4.3 A tube of 60-mm outer diameter (OD) is insulated with a 50- mm layer of silica foam, for which the conductivity is 0.055 W/(m · ℃ ), followed with a 40-mm layer of cork with a conductivity of 0.05 W/(m · ℃ ). If the temperature of the outer surface of the pipe is 150 ℃ and the temperature of the outer surface of the cork is 30 ℃, calculate the heat loss in watts per meter of pipe. 32

33. Problem 4.5 The outer diameter of a steel tube is 150mm. The tube wall is backed by two insulating layers to reduce the heat loss. The ratio of thermal conductivity of two insulating materials is k 2 /k 1 =2 and both insulating materials have the same thickness 30mm. If the temperature difference between pipe wall and outer surface of insulating material is constant, which insulating material should be backed inside to enable less heat loss? 33