Physical quantity Length Area Volume Velocity Density Force Mass Pressure Energy, heat Heat ﬂow Heat ﬂux per unit area Heat ﬂux per unit length Heat generation per unit volume Energy per unit mass Speciﬁc heat Thermal conductivity Convection heat-transfer coefﬁcient Dynamic Viscosity Kinematic viscosity and thermal diffusivity Symbol L A V v ρ F m p q q q/ A q/ L q ˙ q/m c k h μ ν, α SI to English conversion 1 m = 3.2808 ft 1 m2 = 10.7639 ft2 1 m3 = 35.3134 ft3 1 m/s = 3.2808 ft/s 1 kg/m3 = 0.06243 lbm /ft3 1 N = 0.2248 lbf 1 kg = 2.20462 lbm 1 N/m2 = 1.45038 × 10−4 lbf /in2 1 kJ = 0.94783 Btu 1 W = 3.4121 Btu/h 1 W/m2 = 0.317 Btu/h · ft2 1 W/m = 1.0403 Btu/h · ft 1 W/m3 = 0.096623 Btu/h · ft3 1 kJ/kg = 0.4299 Btu/lbm 1 kJ/kg · ◦ C = 0.23884 Btu/lbm · ◦ F 1 W/m · ◦ C = 0.5778 Btu/h · ft · ◦ F 1 W/m2 · ◦ C = 0.1761 Btu/h · ft2 · ◦ F 1 kg/m · s = 0.672 lbm /ft · s = 2419.2 lbm /ft · h 1 m2 /s = 10.7639 ft2 /s English to SI conversion 1 ft = 0.3048 m 1 ft2 = 0.092903 m2 1 ft3 = 0.028317 m3 1 ft/s = 0.3048 m/s 1 lbm /ft3 = 16.018 kg/m3 1 lbf = 4.4482 N 1 lbm = 0.45359237 kg 1 lbf /in2 = 6894.76 N/m2 1 Btu = 1.05504 kJ 1 Btu/h = 0.29307 W 1 Btu/h · ft2 = 3.154 W/m2 1 Btu/h · ft = 0.9613 W/m 1 Btu/h · ft3 = 10.35 W/m3 1 Btu/lbm = 2.326 kJ/kg 1 Btu/lbm · ◦ F = 4.1869 kJ/kg · ◦ C 1 Btu/h · ft · ◦ F = 1.7307 W/m · ◦ C 1 Btu/h · ft2 · ◦ F = 5.6782 W/m2 · ◦ C 1 lbm /ft · s = 1.4881 kg/m · s 1 ft2 /s = 0.092903 m2 /s

Important physical constants

Avogadro’s number Universal gas constant N0 = 6.022045 × 1026 molecules/kg mol R = 1545.35 ft · lbf/lbm · mol · ◦ R = 8314.41 J/kg mol · K = 1.986 Btu/lbm · mol · ◦ R = 1.986 kcal/kg mol · K Planck’s constant Boltzmann’s constant h = 6.626176 × 10−34 J · sec k = 1.380662 × 10−23 J/molecule · K = 8.6173 × 10−5 eV/molecule · K Speed of light in vacuum Standard gravitational acceleration c = 2.997925 × 108 m/s g = 32.174 ft/s2 = 9.80665 m/s2 Electron mass Charge on the electron Stefan-Boltzmann constant me = 9.1095 × 10−31 kg e = 1.602189 × 10−19 C σ = 0.1714 × 10−8 Btu/hr · ft2 · R4 = 5.669 × 10−8 W/m2 · K4 1 atm = 14.69595 lbf/in2 = 760 mmHg at 32◦ F = 29.92 inHg at 32◦ F = 2116.21 lbf/ft2 = 1.01325 × 105 N/m2

Basic Heat-Transfer Relations

Fourier’s law of heat conduction: ∂T qx = −kA ∂x Characteristic thermal resistance for conduction = x/kA Characteristic thermal resistance for convection = 1/hA Overall heat transfer = Toverall / Rthermal Convection heat transfer from a surface: q = hA(Tsurface − Tfree stream ) q = hA(Tsurface − Tﬂuid bulk ) Forced convection: Nu = f(Re, Pr) Free convection: Nu = f(Gr, Pr) ρux ρ2 gβ Tx3 Gr = μ μ2 x = characteristic dimension Re = for exterior ﬂows for ﬂow in channels (Chapters 5 and 6, Tables 5-2 and 6-8) (Chapter 7, Table 7-5) Pr = cp μ k

General procedure for analysis of convection problems: Section 7-14, Figure 7-15, Inside back cover. Radiation heat transfer (Chapter 8) energy emitted by blackbody Blackbody emissive power, = σT 4 area · time energy leaving surface Radiosity = area · time energy incident on surface Irradiation = area · time Radiation shape factor Fmn = fraction of energy leaving surface m and arriving at surface n Reciprocity relation: Am Fmn = An Fnm Radiation heat transfer from surface with area A1 , emissivity large enclosure at temperature T2 (K): 4 4 q = σA1 1 (T1 − T2 ) 1,

and temperature T1 (K) to

LMTD method for heat exchangers (Section 10-5): q = UAF Tm

where F = factor for speciﬁc heat exchanger; Tm = LMTD for counterﬂow double-pipe heat exchanger with same inlet and exit temperatures Effectiveness-NTU method for heat exchangers (Section 10-6, Table 10-3): Temperaure difference for ﬂuid with minimum value of mc = Largest temperature difference in heat exchanger UA NTU = = f(NTU, Cmin /Cmax ) Cmin See List of Symbols on page xvii for deﬁnitions of terms.

Heat Transfer

McGraw-Hill Series in Mechanical Engineering CONSULTING EDITORS Jack P. Holman, Southern Methodist University...