1. Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER CHAPTER 8 Internal flow

2. Heat Transfer Su Yongkang School of Mechanical Engineering # 2 Internal Flow Heat Transfer Where we’ve been …… Introduction to internal flow, basic concepts, energy balance. Where we’re going: Developing heat transfer coefficient relationships and correlations for internal flow roro

3. Heat Transfer Su Yongkang School of Mechanical Engineering # 3 Internal Flow Heat Transfer KEY POINTS THIS LECTURE Convection correlations –Laminar flow –Turbulent flow Other topics –Non-circular flow channels –Concentric tube annulus

4. Heat Transfer Su Yongkang School of Mechanical Engineering # 4 Convection correlations: laminar flow in circular tubes 1. The fully developed region from the energy equation,we can obtain the exact solution. for constant surface heat flux for constant surface temperature Note: the thermal conductivity k should be evaluated at.

5. Heat Transfer Su Yongkang School of Mechanical Engineering # 5 Convection correlations: laminar flow in circular tubes 2. The entry region for the constant surface temperature condition thermal entry length

6. Heat Transfer Su Yongkang School of Mechanical Engineering # 6 Convection correlations: laminar flow in circular tubes 2. The entry region(cont’d) for the combined entry length For values of All fluid properties evaluated at the mean T

7. Heat Transfer Su Yongkang School of Mechanical Engineering # 7 Convection correlations: turbulent flow in circular tubes A lot of empirical correlations are available. For smooth tubes, the fully developed flow Heating: Cooling: For rough tubes, coefficient increases with wall roughness. For fully developed flows Consider the entry length For liquid metals, see textbook p461. or Short tubes

8. Heat Transfer Su Yongkang School of Mechanical Engineering # 8 Internal convection heat transfer coefficient (summary) 1.For laminar and fully developed flow (§8.4.1): i.q” constant: ii.Ts constant: 2.For laminar flow in entry region (before fully developed flow, §8.4.2: i.Ts constant : ii.Combined entry length with full tube: 3.For turbulent and fully developed (§8.5) i.Heating ii.Cooling All fluid properties evaluated at the mean T Eq. 8.53 Eq. 8.55 Eq. 8.56 Eq. 8.57 Eq. 8.60

9. Heat Transfer Su Yongkang School of Mechanical Engineering # 9 Example: Oil at 150 ℃ flows slowly through a long, thin- walled pipe of 30-mm inner diameter. The pipe is suspended in a room for which the air temperature is 20 ℃ and the convection coefficient at the outer tube surface is 11W/m 2.K. Estimate the heat loss per unit length of tube.

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11. Heat Transfer Su Yongkang School of Mechanical Engineering # 11 Internal Flow Heat Transfer (summary) If constant heat flux, mean fluid temperature can be computed directly from the pipe area and inlet temperature For constant wall temperature (such as if phase change occurs on outer pipe surface), mean fluid temperature will asymptotically approach the wall surface temperature, Ts Log mean temperature difference Use appropriate correlation equations for convection heat transfer based on flow conditions (laminar vs. turbulent, fully developed?). Evaluate fluid properties at mean fluid temperature

12. Heat Transfer Su Yongkang School of Mechanical Engineering # 12 Example: Air at 1atm and 285 K enters a 2-m long rectangular duct with cross section 75 mm by 150 mm. The duct is maintained at a constant surface temperature of 400 K, and the air mass flow is 0.10 kg/s. Determine the heat transfer rate from the duct to the air and the air outlet temperature.

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14. Heat Transfer Su Yongkang School of Mechanical Engineering # 14 Additional Topic: Noncircular Tubes Use hydraulic diameter, D h For turbulent flow, reasonably good analysis using same equations as for circular tubes. For laminar flow, Nusselt number have been determined for various shapes (Table 8.1)

15. Heat Transfer Su Yongkang School of Mechanical Engineering # 15 Additional Topic: Concentric Tube Annulus Heat transfer analysis for both tube surfaces Flow in the inner tube computed using methods already presented Heat transfer for fluid in the tube annulus can involve heat transfer coefficient calculation on both inner and outer surface. Calculate using the hydraulic diameter Separate Nusselt # for inner and outer surface, for example Coefficients Nu ii, etc. from Tables 8-2, 8-3.

16. Heat Transfer Su Yongkang School of Mechanical Engineering # 16 Additional Topic: heat transfer enhancement Enhancement Increase the convection coefficient Introduce surface roughness to enhance turbulence. Induce swirl. Increase the convection surface area Longitudinal fins, spiral fins or ribs.

17. Heat Transfer Su Yongkang School of Mechanical Engineering # 17 Additional Topic: heat transfer enhancement Helically coiled tube Without inducing turbulence or additional heat transfer surface area. Secondary flow

18. Heat Transfer Su Yongkang School of Mechanical Engineering # 18 Keep up the good work!