Heat transfer & heat exchangers - Lecture 3: Thermal design

Nội dung text: Heat transfer & heat exchangers - Lecture 3: Thermal design

1. Lecture 3 THERMAL DESIGN
2. Convection Newton’s law ∆ 푞 = 푅 1 푅 = ℎ ℎ = , 푅푒, 푃
3. General 푞 = 푈∆ 1 푈 = σ 푅 표푛 + 푅 표푛푣 + 푅
4. General 푞 2 1 1 푤1 푤2 2 − 푄 = 1 2 1 1 1 + ln 2 + 2 퐿 1ℎ1 2 퐿 1 2 퐿 2ℎ2
5. Overall heat transfer coefficients Physical situation 푼 푾Τ ℃ Brick exterior wall, plaster interior, uninsulated 2,55 Frame exterior wall, plaster interior, uninsulated 1,42 Frame exterior wall, plaster interior with rock–wool insulation 0,40 Plate–glass window 6,20 Double plate–glass window 2,30 Steam condenser 1100 – 5600 Feed water heater 1100 – 8500 Freon–12 condenser with water coolant 280 – 850 Water–to–water heat exchanger 850 – 1700
6. Critical thickness of insulation 푞 ℎ ∞ 1 1 1 2 ∞ 2 2 − − 푄 = 1 2 = 2 ∞ 1 1 ln 2 2 퐿 1 2 2퐿ℎ 2 퐿 1 − ∞ Insulation 푄 = 1 1 layer ln 2 + 1 2ℎ
7. Critical thickness of insulation 푄 푄 푄표 푄표 2 𝑖푛푠 2 = 𝑖푛푠 • 2 : insulation decreases heat transfer
8. Fouling factors Type of fluid Fouling factor ℃Τ푾 Sea water, below 125oF 0,09 × 10−3 Sea water, above 125oF 2 × 10−3 Treated boiler feed water above 125oF 0,2 × 10−3 Fuel oil 0,9 × 10−3 Quenching oil 0,7 × 10−3 Alcohol vapors 0,09 × 10−3 Steam, non–oil–bearing 0,09 × 10−3 Industrial air 0,4 × 10−3 Refrigerating liquid 0,2 × 10−3
9. Overall heat transfer coefficient 1 2 For cylinder 푈 = = 퐿 σ 푅 1 1 푅 푊Τ ℃ σ + σ ln 𝑖,표 푡 + σ 표 푙𝑖푛 𝑖ℎ𝑖 𝑖 𝑖,𝑖푛 𝑖 If based on outside area 표 = 2 표 푡 1 푈 = 표 푅 2 1 표 푡 표 푡 표 푡 표 푡 𝑖푛, 푊Τ ℃ + + ln + 푅표 푡, + ℎ표 푡 𝑖푛ℎ𝑖푛 𝑖푛 𝑖푛 If based on inside area 𝑖 = 2 𝑖푛 1 푈 = 𝑖 푅 2 1 𝑖푛 𝑖푛 표 푡 𝑖푛 표 푡, 푊Τ ℃ + + ln + 푅𝑖푛, + ℎ𝑖푛 표 푡ℎ표 푡 𝑖푛 표 푡
10. Pure double pipe ℎ1 ℎ1 ℎ2 1 2 ℎ2 1 2 1 2 1 2 Parallel flow Counter flow
11. Pure double pipe Integration from “section 1” to “section 2” 푄 = ℎ ℎ ℎ1 − ℎ2 푄 = 2 − 1 ℎ − 1 1 ln 2 2 = −푈 + ℎ1 − 1 ℎ ℎ ℎ − ℎ − ℎ − then, ln 2 2 = −푈 1 2 + 2 1 ℎ1 − 1 푄 푄 − − − or, 푄 = 푈 ℎ2 2 ℎ1 1 = 푈 ∆ − 퐿 ln ℎ2 2 ℎ1 − 1 ∆ − ∆ where, ∆ = 𝑖푛 퐿 ∆ ln ∆ 𝑖푛
12. Non double pipe 푄 = 푈 ∆ 퐿 is a correction factor
13. Non double pipe 1 shell pass – 2 tube passes 1 shell pass – 2푛 tube passes (error 2%) 1 − 푃 2 ln 1 − 푅푃 푅 + 1 = for 푅 ≠ 1 2 − 푃 푅 + 1 − 푅2 + 1 푅 − 1 ln 2 − 푃 푅 + 1 + 푅2 + 1 2푃 = for 푅 = 1 2 − 푃 2 − 2 1 − 푃 ln 2 − 푃 2 + 2
14. Non double pipe 푛(1 shell pass – 2 tube passes) 푛: number of shells Τ for 푅 ≠ 1 1 − 푃′ 1 − 푅푃 1 푛 ln 푅2 + 1 − 1 1 − 푅푃′ 1 − 푃 = 푃′ = ′ 2 1 − 푅푃 1Τ푛 2 − 푃 푅 + 1 − 푅 + 1 − 푅 푅 − 1 ln 1 − 푃 2 − 푃′ 푅 + 1 + 푅2 + 1 for 푅 = 1 2푃′ 푃 = 푃′ = 2 − 푃′ 2 − 2 푃 − 푛푃 + 푛 1 − 푃′ ln 2 − 푃′ 2 + 2
15. 1 1 Non double pipe 푡2 푡1 Divided flow shell – 2 tube passes 2 − 푅 = 1 2 푡2 − 푡1 1.0 0.9 factor 푅 = 15 10 6 8 . . 0 0 20 0.8 0.7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 푡 − 푡 푃 = 2 1 1 − 푡1
16. Non double pipe single pass cross flow exchangers and both fluids unmixed 1.0 factor 0.9 1 0.8 푡1 푡2 2 0.7 − 푅 = 1 2 0.6 푡2 − 푡1 푡 − 푡 푃 = 2 1 1 − 푡1 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
17. Non double pipe For phase change (evaporation & condensation), constant temperature, 푃 = 0 or 푅 = 0, so = 1
18. Effectiveness 휀 and Number of Transfer Units 푈
19. Pure double pipe Parallel flow Counter flow ℎ1 ℎ1 ℎ2 1 2 ℎ2 1 2 1 2 1 2 푄 푡 = ℎ ℎ1 − ℎ2 푄 푡 = ℎ ℎ1 − ℎ2 = 2 − 1 = 1 − 2
20. Pure double pipe Counter flow For energy balance 푄 푡 = ℎ ℎ1 − ℎ2 = 1 − 2 − − If < 휀 = 1 2 = 1 2 ℎ − ℎ1 − 2 ℎ1 2 ℎ ℎ − ℎ ℎ − ℎ If < 휀 = 1 2 = 1 2 ℎ ℎ − ℎ ℎ1 − 2 ℎ1 2 ∆ 𝑖푛𝑖 푙 𝑖 휀 = ∆ ,푒 ℎ 푛 푒
21. Pure double pipe Parallel flow ℎ,𝑖푛 ,표 푡 ,𝑖푛 ℎ,표 푡 푄 1 2 푄 = ℎ ℎ,𝑖푛 − ,𝑖푛 푄 = 𝑖푛 ℎ,𝑖푛 − ,𝑖푛
22. Pure double pipe Parallel flow For energy balance ℎ ℎ1 − ℎ2 = 2 − 1 2 − 1 If < ℎ 휀 = ℎ1 − 1 ℎ − 1 1 Design equation ln 2 2 = −푈 + ℎ1 − 1 ℎ Temperature elimination
23. Pure double pipe Parallel flow 푈 Therefore, ln 1 − 1 + 휀 = − 1 + ℎ ℎ ln 1 − 1 + 𝑖푛 휀 = − 푈 1 + 𝑖푛 푈 Number of Transfer Units 푈 푈 = indicates the size of heat exchanger 𝑖푛
24. Pure double pipe Parallel flow Counter flow 100 100 𝑖푛Τ = 0 % % 휀 휀 0.25 80 80 0.50 60 0.75 60 Effectiveness Effectiveness Effectiveness Effectiveness 1.00 40 40 20 20 푈 푈 0 0 1 2 3 4 5 1 2 3 4 5
25. Non double pipe 1 shell pass – 2푛 tube passes 2 shell passes – 4푛 tube passes 100 100 𝑖푛Τ = 0 % % 휀 휀 0.25 80 80 0.50 0.75 60 60 Effectiveness Effectiveness Effectiveness Effectiveness 1.00 40 40 20 20 푈 푈 0 0 1 2 3 4 5 1 2 3 4 5
26. Summary Flow geometry 휺 푵푻푼 Double pipe 1 − 푒 − 1 + − ln 1 − 1 + 휀 Parallel flow 휀 = = 1 + 1 + 1 − 푒 − 1 1 휀 − 1 Counter flow 휀 = = ln 1 − 푒 − 1 − 1 휀 − 1 휀 Counter flow = 1 휀 = = + 1 1 − 휀 Cross flow 푒 − 0,78 − 1 Both fluids unmixed 휀 = 1 − 푒 −0,22 1 휀 = Both fluids mixed 1 1 + − 1 − 푒 − 1 − 푒 − 1 − 푒 푒 − − 1 ln 1 − 휀 mixed, 𝑖푛 unmixed 휀 = = − ln 1 + 푒 − − 1 − ln 1 + ln 1 − 휀 unmixed, 𝑖푛 mixed 휀 = 1 − 푒 =
27. Design equation 휀 = 푈, 푈 푈 = = 𝑖푛 𝑖푛 푄 = 휀푄 𝑖푛 ℎ,𝑖푛 − ,𝑖푛
28. Off–Design problems • Fluid properties • Flow rate Process • Area, specification design • Overall heat transfer coefficient • Temperature Design • Heat load