HEAT TRANSFER CHAPTER 9 Free Convection 们au Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 1 HEAT TRANSFER CHAPTER 9 Free Convection
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 were going Consider empirical correlations for natural convection Heat Transfer Su Yongkang School of Mechanical Engineering
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
Empirical Correlations Typical correlations for heat transfer coefficient developed from experimental data are expressed as hl CRa L k L RO G 8B(T,-T)L3 AL=ori 1/4 For T n=1/3 For L Rayleigh number Vertical plate For an plate at constant Ts Coordinales or recommended curve 1 ⊥.9 2.63 3.89 6.03 0.5 Logo NuL, 1.5 33.1 108 14 501.0 11 1.0 .2 Log1o rar Heat Transfer Su Yongkang School of Mechanical Engineering
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 ( ) 3 Pr g T T L Ra Gr s L L − = = Log10RaL Log10NuL n L CRaL k hL Nu = = Rayleigh number = = 1/ 3 1/ 4 n n For T For L
Empirical Correlations(Contd Vertical Plate(Contd Alternative applicable to entire Rayleigh number range(for constant Ts) 0.387Ra16 E 0.825+ 9/68/27 9.26 +(0.492/Pr) Vertical cylinders Use same correlations for vertical flat plate f D≈35 ≥ 1/4 L Inclined plate 7 See figure 9.7 d Heat Transfer Su Yongkang School of Mechanical Engineering
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 2 8/ 27 9/16 1/ 6 1 (0.492/ Pr) 0.387 0.825 + = + L L Ra Nu 1/ 4 ~ 35 GrL L D Eq 9.26 See Figure 9.7
Empirical Correlations(Contd Horizontal plate Cold plate Plate, T, (ST Plate, T Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 5 Empirical Correlations (Cont’d) Horizontal Plate Cold Plate (Ts T)
Empirical Correlations(Contd Horizontal Plate( contd Define the characteristic length, L as L P Upper surface of heated plate, or Lower surface of cooled plate: N=0.54Ra 104≤Rar≤10 0.15Ra 1/3 L 0′≤Rar≤10 Lower surface of heated plate, or Upper surface of cooled plate: Nu1=0.27Ra14(05≤Ra,≤100 Note Use fluid roperties at the pI T+t filmtemperature Heat Transfer Su Yongkang School of Mechanical Engineering
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 : ( ) ( ) 1/3 7 11 1/ 4 4 7 0.15 10 10 0.54 10 10 = = L L L L L L Nu Ra Ra Nu Ra Ra ( ) 1/ 4 5 10 NuL = 0.27 RaL 10 RaL 10 Note: Use fluid properties at the film temperature 2 + = T T T s f P A L s
Empirical Correlations(Contd ong Horizontal Cylinder Very common geometry(pipes, wires) For isothermal cylinder surface, use general Plume form equation for computing nusselt E hD 9.33 =CRa k Boundary Constants for general lay Nusselt number equation Rap 10-10-10 2 0.6750.058 Table9.110-2-10 02 0.148 102-10 0.8500.188 0.4800.250 0 0.1250.333 Heat Transfer Su Yongkang School of Mechanical Engineering
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 RaD C n 10 -10 0.125 0.333 10 -10 0.480 0.250 10 -10 0.850 0.188 10 -10 1.02 0.148 10 -10 0.675 0.058 7 12 4 7 2 4 2 2 10 2 − + − − Table 9.1 Eq 9.33 n D CRaD k hD Nu = =
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 T=120°C T=20C Find: Heat loss to room per unit length of wire USing air properties at a film temperature of T+t =709 Heat Transfer Su Yongkang School of Mechanical Engineering
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 120 C Ts = 20 C T = 70 2 = + = T T T s f
Example: Heated Wire At a rayleigh of Compute Nusselt# and convection coefficient TD hD CRap k Rate of heat transfer to air is q=hD(Ts-Too) W/m of length Heat Transfer Su Yongkang School of Mechanical Engineering
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: q = hD(Ts -T ) W/m of length ( ) 3 g T T D Ra s D − = n D CRaD k hD Nu = =
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 10C and (b)27 and 37C KNOWN: Interior air and wall temperatures; wall height. FIND:(a) Average heat transfer coefficient when T=20'C and Ts =10C, (b) Average heat transfer coefficient when Too=27C and Ts =37'C SCHEMATIC A、 Wall height 3 L-257 =20 G=27℃ a win nTer condITion 6 Summer condition ASSUMPTIONS:(a) Wall is at a uniform temperature, (b) Room air is quiescent. mk=005Wm.=209×10mr010(30K1amn==3279 62 10°K,v=16539×10mk=20027Wx=22820m=076 ANALYSIS: The appropriate correlation for the average heat transfer coefficient for free convection Heat Transfer Su Yongkang School of Mechanical Engineering
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
