APPENDIXES

Convection Heat Transfer, Fourth Edition. Adrian Bejan© 2013 John Wiley & Sons, Inc. Published 2013 by John Wiley & Sons, Inc.

A

CONSTANTS ANDCONVERSION FACTORS

CONSTANTS

Universal ideal gas constant P. R = 8.314 kJ/kmol · KPatm = 1.9872 cal/mol · KPatm = 1.9872 Btu/lbmol · ◦RPatm = 1545.33 ft · lbf/lbmol · ◦R

Boltzmann’s constant k = 1.38054 × 10−23 J/K

Planck’s constant h = 6.626 × 10−34 J · sSpeed of light in vacuum c = 2.998 × 108 m/s

Avogadro’s number N = 6.022 × 1023 molecules/mol

Stefan–Boltzmann constant σ = 5.669 × 10−8 W/m2 · K4

Patm = 0.1714 × 10−8 Btu/h · ft2 · ◦R4

Atmospheric pressure Patm = 0.101325MPa

Patm = 1.01325 bar

Patm = 1.01325 × 105 N/m2

Ice point at 1 atm Tice = 0◦C = 273.15 K

Gravitational acceleration g = 9.807m/s2

Patm = 32.17 ft/s2

Calorie 1 cal = 4.187 J

Mole 1mol = sample containing 6.022 × 1023

elementary entities (e.g.,molecules); also abbreviatedas 1 gmol, or

609

610 A CONSTANTS AND CONVERSION FACTORS

1mol = 10−3 kmol

= 10−3 kgmol

= 1

453.6lbmol

Natural logarithm ln x = 2.30258 log10x

log10x = 0.4343 ln x

Important numbers e = 2.71828

π = 3.14159

1◦ = 0.01745 rad

CONVERSION FACTORS

Acceleration 1m/s2 = 4.252 × 107 ft/h2

Area 1 in2 = 6.452 cm2

1 ft2 = 0.0929m2

1 yd2 = 0.8361m2

1 mi2 = 2.59 km2

1 hectare = (100m)2

1 acre = 4047m2

Density 1 kg/m3 = 0.06243 lbm/ft3

1 lbm/ft3 = 16.018 kg/m3

Energy 1 kJ = 737.56 ft · lbf= 0.9478 Btu

= 3.725 × 10−4 hp · h= 2.778 × 10−4 kW · h

1 Btu = 1055 J

= 778.16 ft · lbf= 3412.14 kW · h= 2544.5 hp · h

1 cal = 4.187 J

1 erg = 10−7 J

Force 1 lbf = 4.448N

= 0.4536 kgf

1 dyne = 10−5 N

CONVERSION FACTORS 611

Heat flux 1W/m2 = 0.317 Btu/h · ft21 Btu/h · ft2 = 3.154W/m2

Heat transfer coefficient 1W/m2 · K = 0.1761 Btu/h · ft2 · ◦F= 0.8598 kcal/h · m2 · ◦C

1 Btu/h · ft2 · ◦F = 5.6786W/m2 · KHeat transfer rate 1 Btu/s = 1055W

1 Btu/h = 0.2931W

1 hp = 745.7W

1 ft · lbf/s = 1.3558W

Kinematic viscosity (ν),thermal diffusivity (α),mass diffusivity (D)

1m2/s = 104 cm2/s

= 104 stokes

= 3.875 × 104 ft2/h

= 10.764 ft2/s

Latent heat, specific energy,specific enthalpy

1 kJ/kg = 0.4299 Btu/lbm= 0.2388 cal/g

1 Btu/lbm = 2.326 kJ/kg

Length 1 in = 2.54 cm

1 ft = 0.3048m

1 yd = 0.9144m

1 mile = 1.609 km

Mass 1 lbm = 0.4536 kg

1 kg = 2.2046 lbm

= 1.1023 × 10−3 U.S. ton

= 10−3 tonne

1 oz = 28.35 g

Mass transfer coefficient 1m/s = 1.181 × 104 ft/h

1 ft/h = 8.467 × 10−5 m/s

Power 1 Btu/s = 1055W = 1.055 kW

1 Btu/h = 0.293W

1W = 3.412 Btu/h

= 9.48 × 10−4 Btu/s

1 HP = 0.746 kW

= 0.707 Btu/s

612 A CONSTANTS AND CONVERSION FACTORS

Pressure, stress 1 Pa = 1N/m2

1 psi = 6895N/m2

1 atm = 14.69 psi

= 1.013 × 105 N/m2

1 bar = 105 N/m2

1 torr = 1mmHg

= 133.32N/m2

1 psi = 27.68 in H2O

1 ft H2O = 0.4335 psi

Specific heat, specificentropy

1 kJ/kg · K = 0.2388 Btu/lbm · ◦F= 0.2389 cal/g · ◦C

1 Btu/lbm · ◦F = 4.187 kJ/kg · KSpeed 1 mi/h = 0.447m/s

= 1.609 km/h

1 km/h = 0.278m/s

= 0.622 mi/h

1m/s = 3.6 km/h

= 2.237 mi/h

Temperature 1 K = 1◦C1 (K) = (9/5)◦FT (K) = T(◦C) + 273.15

T (◦C) = 5/9[T(◦F) − 32]

T (◦F) = T(◦R) − 459.67

Temperature difference �T (K) = �T (◦C)= 5/9 �T (◦F)= 5/9 �T (◦R)

Thermal conductivity 1W/m · K = 0.5782 Btu/h · ft · ◦F= 0.01W/cm · K= 2.39 × 10−3 cal/cm · s · ◦C

1 Btu/h · ft · ◦F = 1.7307W/m · KThermal resistance 1 K/W = 0.5275◦F/Btu · h

1◦F/Btu · h = 1.896 K/W

Viscosity (µ) 1N · s/m2 = 1 kg/s · m= 2419.1 lbm/ft · h= 5.802 × 10−6 lbf · h/ft2

1 poise = 1 g/s · cm

DIMENSIONLESS GROUPS USED IN THIS BOOK 613

Volume 1 L = 10−3 m3 = 1 dm3

1 in3 = 16.39 cm3

1 ft3 = 0.02832m3

1 yd3 = 0.7646m3

1 gal (U.S.) = 3.785 L

1 gal (imperial) = 4.546 L

1 pint = 0.5683 L

Volumetric heat generationrate

1 Btu/h · ft3 = 10.35W/m3

1W/m3 = 0.0966 Btu/h · ft3

DIMENSIONLESS GROUPS USED IN THIS BOOKa

Bejan number Be = (�PL2)/µα

Biot number Bi = hL/ksBoussinesq number Bo = (gβ �T H3)/α2

Eckert number Ec = U2/(cP �T)

Fourier number Fo = αt/L2

Graetz number Gz = D2U/αx = ReD Pr (D/x)

Grashof number Gr = (gβ �T H3)/ν2

Lewis numberb Le = α/D = Sc/Pr

Mass transfer Rayleigh numberb Ram = (gβc �ρiH3)/νD

Mass transfer Stanton number Stm = hm/U

Nusselt number Nu = hL/kfPeclet number Pe = UL/α = Re Pr

Porous medium Bejan numberc Be = (�P K)/µα

Porous medium Peclet numberc Pe = UL/α

Porous medium Prandtl numberc Pr = (ν/α)(H/bK)

Porous medium Rayleigh number,Darcy flowc

Ra = (KgβH �T)/αν

Porous medium Rayleigh numberbased on heat flux, Darcy flow

Ra* = Kgβq′′H2/ανk

Prandtl number Pr = ν/α = Sc/Le

aSubscripts: (·)s = solid, (·)f = fluid.bD is the mass diffusivity (m2/s).ck and α are properties of the fluid-saturated porous medium.

614 A CONSTANTS AND CONVERSION FACTORS

Rayleigh number Ra = gβ�TH3/αν

Rayleigh number based on heatflux

Ra* = gβq′′H4/ανk

Reynolds number Re = UL/ν

Schmidt numberb Sc = ν/D = Le Pr

Sherwood numberb Sh = hmL/D

Stanton number St = h/ρcPU = Nu/Re Pr

Stefan number Ste = (cf �T)/hsfTurbulent Prandtl number Prt = εM/εH