1. Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER CHAPTER 7 External flow

2. Heat Transfer Su Yongkang School of Mechanical Engineering # 2 Looking for a job?

3. Heat Transfer Su Yongkang School of Mechanical Engineering # 3 External Flow: Other Shapes Topic of the Day oven

4. Heat Transfer Su Yongkang School of Mechanical Engineering # 4 External Flow: Other Shapes Where we’ve been …… Empirical correlations and analytical solutions Where we’re going: Applications to other shapes (cylinders and spheres) Brief discussion on multiple objects (tube bundles) and jet impingement. Internal flow next ……….. Textbook Sections §7.4-7.8

5. Heat Transfer Su Yongkang School of Mechanical Engineering # 5 Historical Example Cooling of lead shot Molten lead

6. Heat Transfer Su Yongkang School of Mechanical Engineering # 6 Background – Flow Considerations Favorable pressure gradient Adverse pressure gradient Stagnation pointSeparation point Wake

7. Heat Transfer Su Yongkang School of Mechanical Engineering # 7 Background – Flow Considerations (Cont’d) Boundary layer transition Momentum of fluid in a turbulent boundary layer is greater, and thus separation occurs further along the object. Example How fast must a soccer ball travel to expect a turbulent boundary layer? But other factors also involved (surface roughness, wind, ball spin, etc.)

8. Heat Transfer Su Yongkang School of Mechanical Engineering # 8 Convection heat transfer for cylinder Complicated physics makes necessary using empirical (experimental) correlations of heat transfer coefficient and flow conditions. Local Nusselt number

9. Heat Transfer Su Yongkang School of Mechanical Engineering # 9 Convection heat transfer for cylinder (Cont’d) Generally want the overall average Nusselt number for heat transfer with the entire object. As with a flat plate, correlations developed from experimental data to compute Nu as a f(Re m,Pr n ) Overall Average Nusselt number All properties are evaluated at the freestream temperature, except Pr s which is evaluated at the surface temperature.

10. Heat Transfer Su Yongkang School of Mechanical Engineering # 10 Values for C and m Expect accuracy within  20% with these correlations The empirical correlation due to Hilpert Values of C and m are listed in Table 7.2. All properties are evaluated at the film temperature.

11. Heat Transfer Su Yongkang School of Mechanical Engineering # 11 Example: Heat Loss from Smokestack Given: Hot gas enters a exhaust stack shown at 150º C. Find: –Rate of heat loss from stack –  T of the exhaust gas T in = 150º C V = 1 m/s 2 m 20 m T  = 0º C V = 5 m/s Assume: Ignore radiation heat loss Steady state conditions Solution Method?

12. Heat Transfer Su Yongkang School of Mechanical Engineering # 12 Example: Heat Loss from Smokestack (Cont’d) Compute Reynolds # From table, Values of C and m From Table: C= 0.076 and m=0.7 Air properties (from Tables) Pr of freestream = 0.714 ; Pr s =0.705 T in = 150º C V = 1 m/s 2 m 20 m T  = 0º C V = 5 m/s

13. Heat Transfer Su Yongkang School of Mechanical Engineering # 13 Example: Heat Loss from Smokestack (Cont’d) Heat loss from stack Now for  T of stack gas at 150ºC From property table: Mass flow of stack gas: Temperature change of stack gas:

14. Heat Transfer Su Yongkang School of Mechanical Engineering # 14 Example: Assume that a person can be approximated as a cylinder of 0.3-m diameter and 1.8-m height with a surface temperature of 24 ℃. Calculate the body heat loss while this person is subjected to a 15-m/s wind whose temperature is -5 ℃.

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16. Heat Transfer Su Yongkang School of Mechanical Engineering # 16 Convection heat transfer with a sphere (§7.5) External flow and heat transfer relations are similar to those around a cylinder. Numerous correlations proposed from lab experiments, one being: All properties except are evaluated at. Special case: Free falling liquid drops

17. Heat Transfer Su Yongkang School of Mechanical Engineering # 17 Back to cooling of lead shot example How would you go about analyzing the cooling of molten lead drops in this case? Issues Free-fall velocity, terminal velocity Transient conduction in drop Phase change energy transfer Radiation heat transfer significant? Convection heat transfer coefficient

18. Heat Transfer Su Yongkang School of Mechanical Engineering # 18 Convection heat transfer with banks of tubes Typically, one fluid moves over the tubes, while a second fluid at a different temperature passes through the tubes. (cross flow) The tube rows of a bank are staggered or aligned. The configuration is characterized by the tube diameter D, the transverse pitch and longitudinal pitch.

19. Heat Transfer Su Yongkang School of Mechanical Engineering # 19 Convection heat transfer with banks of tubes (cont’d) For tube bundles composed of 10 or more rows

20. Heat Transfer Su Yongkang School of Mechanical Engineering # 20 Convection heat transfer with banks of tubes (cont’d) All properties are evaluated at the film temperature. Values for C and m. For Reynolds number If staggered and or Click for large

21. Heat Transfer Su Yongkang School of Mechanical Engineering # 21 Convection heat transfer with banks of tubes (cont’d) If a correction factor may be applied And values for are from table

22. Heat Transfer Su Yongkang School of Mechanical Engineering # 22 Convection heat transfer with banks of tubes (cont’d) More recent results have been obtained by Zhukauskas. All properties except are evaluated at the arithmetic mean of the fluid inlet and outlet temperatures. Values for C and m. If, a correction factor my be applied Values for C 2 Click for large

23. Heat Transfer Su Yongkang School of Mechanical Engineering # 23 Convection heat transfer with banks of tubes (cont’d) For aligned tubes, typically the convection coefficient of a row increases with increasing row number until the fifth row. For small values of, upstream rows shield downstream rows form much of the flow, and heat transfer is adversely affected. is undesirable. For the staggered array, heat transfer enhanced is favored by the more Tortuous flow.

24. Heat Transfer Su Yongkang School of Mechanical Engineering # 24 Convection heat transfer with banks of tubes (cont’d) For large change in temperature, the temperature difference in Newton’s law of cooling should be the log mean temperature difference. Where and are temperature of the fluid as it enters and leaves the bank. Where N is the total number of tubes in the bank and is the number of tubes in the transverse plane. The heat transfer rate per unit length of the tubes is

25. Heat Transfer Su Yongkang School of Mechanical Engineering # 25 Convection heat transfer with banks of tubes (cont’d) The power required to move the fluid across the bank is directly proportional to the Correction factor Friction factor Aligned tubes staggered tubes

26. Heat Transfer Su Yongkang School of Mechanical Engineering # 26 Example: A preheater involves the use of condensing steam at 100 ℃ on the inside of a bank of tubes to heat air that enters at 1 atm and 25 ℃. The air moves at 5 m/s in cross flow over the tubes. Each tube is 1 m long and has an outside diameter of 10 mm. The bank consists of 196 tubes in a square, aligned array for which mm. What is the total rate of heat transfer to the air? What is the pressure drop associated with the airflow?

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28. Heat Transfer Su Yongkang School of Mechanical Engineering # 28 External Flow: Summary and Review KEY POINTS External flow: Boundary layer develops freely, without constraints Turbulent convective heat transfer generally higher than laminar due to mixing effect within boundary layer Analytical solutions possible for simple cases (laminar flow over flat plate)

29. Heat Transfer Su Yongkang School of Mechanical Engineering # 29 External Flow: Summary (Cont’d) Difference in boundary layer growth for high and low Pr number fluids - impact on rate of heat transfer? More complicated shapes like cylinders, spheres, etc. solved using experimental correlations of heat transfer coefficient, geometry and flow conditions y x For large Pr (oils): Pr > 1000 y x For small Pr (liquid metals): Pr < 0.1

30. Heat Transfer Su Yongkang School of Mechanical Engineering # 30 Large photos for this lecture

31. Heat Transfer Su Yongkang School of Mechanical Engineering # 31 Large photos for this lecture

32. Heat Transfer Su Yongkang School of Mechanical Engineering # 32 Have a good time!