1. Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER CHAPTER 9 Free Convection

2. Heat Transfer Su Yongkang School of Mechanical Engineering # 2 Natural Convection Where we’ve been …… Up to now, have considered basic concepts of natural convection, the governing equations and laminar free convection on vertical surface. Where we’re going: Consider empirical correlations for natural convection.

3. Heat Transfer Su Yongkang School of Mechanical Engineering # 3 Empirical Correlations Typical correlations for heat transfer coefficient developed from experimental data are expressed as: Vertical Plate For an plate at constant Ts Rayleigh number For T For L

4. Heat Transfer Su Yongkang School of Mechanical Engineering # 4 Empirical Correlations (Cont’d) Vertical Plate (Cont’d) Alternative applicable to entire Rayleigh number range (for constant Ts) Vertical Cylinders Use same correlations for vertical flat plate if: Inclined Plate Eq 9.26 See Figure 9.7

5. Heat Transfer Su Yongkang School of Mechanical Engineering # 5 Empirical Correlations (Cont’d) Horizontal Plate Cold Plate (Ts < T  ) Hot Plate (Ts > T  )

6. Heat Transfer Su Yongkang School of Mechanical Engineering # 6 Empirical Correlations (Cont’d) Horizontal Plate (Cont’d) Define the characteristic length, L as Upper surface of heated plate, or Lower surface of cooled plate : Lower surface of heated plate, or Upper surface of cooled plate : Note: Use fluid properties at the film temperature

7. Heat Transfer Su Yongkang School of Mechanical Engineering # 7 Empirical Correlations (Cont’d) Long Horizontal Cylinder Very common geometry (pipes, wires) For isothermal cylinder surface, use general form equation for computing Nusselt # Constants for general Nusselt number equation Ra D C n Table 9.1 Eq 9.33

8. Heat Transfer Su Yongkang School of Mechanical Engineering # 8 Example: Heated Wire Given: Coil of wire in an electrical resistance baseboard heater Assume that the wire can be treated as a horizontal cylinder Wire is 1 mm in diameter Find: Heat loss to room per unit length of wire Using air properties at a film temperature of ºC

9. Heat Transfer Su Yongkang School of Mechanical Engineering # 9 Example: Heated Wire At a Rayleigh # of : C =, n= Compute Nusselt # and convection coefficient Rate of heat transfer to air is:

10. Heat Transfer Su Yongkang School of Mechanical Engineering # 10 Example: Determine the average convection heat transfer coefficient for the 2.5-m high vertical walls of a home having respective interior air and wall surface temperature of (a) 20 and 10 ºC and (b) 27 and 37 ºC.

11. Heat Transfer Su Yongkang School of Mechanical Engineering # 11

12. Heat Transfer Su Yongkang School of Mechanical Engineering # 12 Example: An electrical heater in the form of a horizontal disk of 400-mm diameter is used to heat the bottom of a tank filled with engine oil at a temperature of 5 ºC. Calculate the power required to maintain the heater surface at 70 ºC.

13. Heat Transfer Su Yongkang School of Mechanical Engineering # 13

14. Heat Transfer Su Yongkang School of Mechanical Engineering # 14 Natural (Free) Convection KEY POINTS OF FREE CONVECTION Natural or free convection is common phenomena, but generally has lower heat transfer rates than in forced convection for similar temperature differences Grashof number for free convection is similar to Reynolds number in forced convection Rayleigh number is used to account for relative impact of buoyancy and viscous forces acting as same time Most problems solved using equations derived from empirical data of the form: Evaluate fluid properties at the film temperature