ABSTRACT
Equation for q00 D k @T @z
h kg
i diffusive flux D ˛ @.cpT /
Diffusivity ˛ m2=s
DAB
m2=s
Equation for total flux q00 D k @T @z„ƒ‚…
C cpT u„ ƒ‚ … convective
nA;z D DAB @cA
@z„ ƒ‚ … diffusive
C cAu„ƒ‚… convective
Convective transfer h W=m2 K D q00
coefficient
Overall
Heat Transfer Mass Transfer
Governing Equation @T @t C u@T
C rA
Q is the rate of heat rA is the rate of mass generation or generation or
absorption per disappearance per
unit volume unit volume
Boundary Conditions
T ˇˇˇ surface
= Ts cA
ˇˇˇ surface
= cA;s
surface temperature surface concentration
is specified, e.g., is specified, e.g.,
condensing steam later stages of drying
ˇˇˇ surface
D nA;s surface heat flux surface mass flux
is specified, e.g., is specified, e.g.,
ˇˇˇ surface
= h.T ˇˇˇ surface
T1/ D hm.cA ˇˇˇ surface
cA;1 / convection over surface convection over surface
Only one of these conditions at a surface
Quantity Symbol Value
Universal Gas Constant Rg 8:205 102 m3 atm/kmolK 8:314 102 m3 bar/kmolK 8.314 kJ/kmolK
Avogadro’s Number N 6:024 1023 molecules/mol Planck’s Constant h 6:625 1034 J s/molecule Boltzmann’s Constant 1:380 1023 J/Kmolecule Speed of Light in Vacuum co 2:998 108 m/s Stefan-Boltzmann Constant 5:670 108 W/m2 K4 Gravitational Acceleration (Sea Level) g 9.807 m/s2
Normal Atmospheric Pressure p 101,325 N/m2
To Convert From to Multiply by
Area
acre m2 4.046 856 103 acre ft2 4.356 000 104 ft2 m2 9.290 304 102 m2 ft2 1.076 391 101 cm2 m2 1.000 000 104 ft2 in.2 1.440 000 102 in.2 m2 6.451 600 104
Energy
Btu (international) kJ 1.055 056 Btu kcal 2.519 958 101 kcal kJ 4.186 800
kW h kJ 3.600 000 103 kW h Btu 3.413 103 hp h Btu 2.454 103 J ergs 1.000 000 107 eV J 1.602 19 1019 Btu ft-lbf 7.781 693 102 ft lbf kJ 1.355 818 103
Force
lbf N 4.448 222
dyne N 1.000 000 105
Length
angstrom m 1.000 000 1010 caliber m 2.540 000 104 fathom m 1.828 800
ft m 3.048 000 101 inch m 2.540 000 102 mile m 1.609 344 103 mile ft 5.280 103 yard m 9.144 000 101
Mass
carat kg 2.000 000 104 grain kg 6.479 891 105 lbm (pound mass) kg 4.535 924 101 kg lbm 2.204 622
kg slug 6.852 1 102 slug lbm 3.217 405 101 ton lbm 2.000 103 ton kg 9.071 847 102
Mass per Unit Volume (density)
lbm/ft 3 kg/m3 1.601 846 101
lbm/in. 3 kg/m3 2.767 990 104
lbm/gal kg/m 3 1.198 264 102
Power
Btu/h W (watt) 2.930 711 101 J/s W 1.000 000 erg/s W 1.000 000 107 ft lbf/s W 1.355 818 hp W 7.456 999 102 hp ft lbf/s 5.50 102 hp ft lbf/min 3.300 0 104 hp (boiler) Btu/h 3.347 14 104 hp (boiler) kW 9.809 50
Pressure
std atm kPa 1.013 25 102 std atm lbf/in.2 1.469 6 101 cm Hg (0ıC) kPa 1.333 22 in. Hg (32ıF) kPa 3.386 389 in. H2O (60
ıF) kPa 2.488 4 101 bar kPa 1.000 000 102 bar lbf/in.2 1.450 377 101 lbf/in.2 kPa 6.894 757
in. Hg (32ıF) lbf/in.2 4.911 542 101 ft H2O (60
ıF) lbf/in.2 4.330 943 101 ft H2O (60
ıF) kPa 2.986 08 dyne/cm2 kPa 1.000 000 104
Specific Heat
Btu/lbm ıF kJ/kg K 4.186 800 cal/g ıC Btu/lbm ıF 1.000 000
Thermal Conductivity
Btu/ft h ıF W/m K 1.730 6 279 101 cal/cm h ıC Btu/ft h ıF 6.719 69 102
Thermal Conductance
Btu/ft2 h ıF W/m2 K 5.674 466
Temperature ıC K TK = TıC + 273.15 ıF ıR TıR = TıF + 459.67 K ıR TıR = TK 1.8 ıC ıF TıF = (TıC + 273.15) 1.8 - 459.67 ıF ıC TıC = (TıF + 459.67)/1.8 - 273.15
Velocity
ft/s m/s 3.048 888 101 miles/h km/h 1.609 344
knot m/s 5.144 444 101
Viscosity
centipoise Pa s 1.000 000 103 lbm/ft s Pa s 1.488 164 lbf s/ft2 Pa s 4.788 026 101
Volume
acre ft m3 1.233 483 103 barrel (42 gal) m3 1.589 873 101 ft3 m3 2.831 685 102 in.3 m3 1.638 706 105 ft3 gallons 7.480 52
liter m3 1.000 000 103 gallons liter 3.785 412
gallons m3 3.785 412 103 gallons ft3 1.336 81 101 quart (U.S. liquid) m3 9.463 529 104 pint (U.S. liquid) liter 4.731 765 101
erf() erf() erf()
0.000 0.0000 0.850 0.7707 1.700 0.9838
0.025 0.0282 0.875 0.7841 1.725 0.9853 0.050 0.0564 0.900 0.7969 1.750 0.9867
0.075 0.0845 0.925 0.8092 1.775 0.9879
0.100 0.1125 0.950 0.8209 1.800 0.9891
0.125 0.1403 0.975 0.8321 1.825 0.9901
0.150 0.1680 1.000 0.8427 1.850 0.9911 0.175 0.1955 1.025 0.8528 1.875 0.9920
0.200 0.2227 1.050 0.8624 1.900 0.9928
0.225 0.2497 1.075 0.8716 1.925 0.9935
0.250 0.2763 1.100 0.8802 1.950 0.9942
0.275 0.3027 1.125 0.8884 1.975 0.9948
0.300 0.3286 1.150 0.8961 2.000 0.9953 0.325 0.3542 1.175 0.9034 2.025 0.9958
0.350 0.3794 1.200 0.9103 2.050 0.9963
0.375 0.4041 1.225 0.9168 2.075 0.9967
0.400 0.4284 1.250 0.9229 2.100 0.9970
0.425 0.4522 1.275 0.9286 2.125 0.9973 0.450 0.4755 1.300 0.9340 2.150 0.9976
0.475 0.4983 1.325 0.9390 2.175 0.9979
0.500 0.5205 1.350 0.9438 2.200 0.9981
0.525 0.5422 1.375 0.9482 2.225 0.9983
0.550 0.5633 1.400 0.9523 2.250 0.9985 0.575 0.5839 1.425 0.9561 2.275 0.9987
0.600 0.6039 1.450 0.9597 2.300 0.9989
0.625 0.6232 1.475 0.9630 2.325 0.9990
0.650 0.6420 1.500 0.9661 2.350 0.9991
0.675 0.6602 1.525 0.9690 2.375 0.9992
0.700 0.6778 1.550 0.9716 2.400 0.9993 0.725 0.6948 1.575 0.9741 2.425 0.9994
0.750 0.7112 1.600 0.9763 2.450 0.9995
0.775 0.7269 1.625 0.9784 2.475 0.9995
0.800 0.7421 1.650 0.9804
0.825 0.7567 1.675 0.9822
Note: erf./ D erf./ and erfc./ D 1 erf./
Figure B.1: Unsteady-state diffusion in a large slab. Before using in mass transfer for
m ¤ 0, refer to discussion in Section 13.2.5 on page 452. From Principles of Unit Operations by A. S. Foust et al., c 1960 by John Wiley & Sons, Inc. Reprinted by permission of John Wiley & Sons, Inc.
