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94
CHAPTER S
1958: Gmd
Table 2. Approximate Unit Conductances fob Thermal Convection, fob^ Y
Several Flow Systems (Concluded)
Heat Transfer Equation* and its Limits oi Application
Fobced Convection
9 Same as Case 7.
General Equation (Laminar Flow) -"(?)"()"
For (y) < 500.000
irmf
mT Same as Case 7.
he (*) "
(up)wEquationfor Air
(Laminar Flow) Ip, = 0.0562(70"
For (2?) < 500.000
3"|jg
i
i 1
Free Convection
ii
Equation for Air /AI\0M
10* < JVGr < 10*
' Heat'Transfer
95
g = body force per unit mass, feet per hour per hour. (For static system on earth, g = 32.2 X 3600' feet per hour per hour.)
G = 3600 Ump = mass flow.per unit cross-sectional area normal to flow, pounds per (hour) (square foot of flow cross-section).
jVGr =, Grashof modulus, dimensionless (Nar = D'ptp&lg/fft).
hc -- average unit thermal convective conductance from the leading edge of
surface to the position x, Btu per (hour) (square foot) (Fahrenheit degree).
hex = local unit thermal convective, conductance, at the position x from the
leading edge of surface, Btu per. (hour) (square foot) (Fahrenheit degree).
k = thermal conductivity, Btu per (hour) (square foot) (Fahrenheit degree per foot thickness).
I = a dimension of the system, feet,
m = a subscript denoting mean.
P = pressure, atmospheres.
Pe = pressure (atmospheric) atmospheres.
t = temperature, Fahrenheit.
T = temperature, Fahrenheit, absolute.
u -- fluid velocity, feet per second.
V = volume, cubic feet.
y
x = a dimension of the system, feet.
P = coefficient of cubical expansion (ft = y1 (^dfV)p)i for perfect gases p = 1/T.
M = difference between wall and fluid temperatures, Fahrenheit degrees..
p = fluid viscosity, pounds per (hour) (foot).
`.
p = density, pounds per cubic foot.
" = infinity, referring the quantity to a point not directly affected by the phenomenon in question.
I Free convection past a heated horizontal cylinder.
T1 hj
I Free convection past a single vertical sur-| face.
7777-7777-'
U--- i
| Free convection past a heated horizontal surface (face up).
(...,,
'V/'
Equation for Air
* om= ()"" (*y-
!0> < WGr < 10>
>'=om(B'u(7y''
10* < VGr < 10
Equation for Air
C/ P\#M
*- 8 k) \t)
10* < Nqt < 10'
Equation for Air
* - -239 (/?P;)\,M /vAtI)V-"
HP < NGi < 10'
Free convection past a heated horizontal
I:surfaoe (face do.wn).
* Fluid properties should be evaluated at the arithmetic mean fluid temperature, tt -- (t surface -f- tfloig
divided by 2.
-Si*
b These expressions are suitable approximations to longitudinal flow in other than right circular cylinders
speroctvioidnesd, tthheehhyyddrraauulilcicddiaiammeeteterrisiseeqmuapllotoyefdouarsttihmeescothneducirtodeism-eeencstiioonnalpaarreaamdeitveidr.edFboyr nthoen-wciercttueldarpeHgB
eter.
' S
0 For low rates of heat transfer by free convection the exponent decreases towards zero, and for higjgB
rates, increases towards 0.33. The above equations employing an exponent equal to 0.25 are applicable ins*
intermediate range indicated.
2n
NOMENCLATURE AND DIMENSIONS FOR TABLE 2
cp = heat capacity at constant pressure, Btu per (pound) (Fahrenheit degrCsS
D = cylinder diameter, feet.
g|
/ = subscript denoting film.
Table 3. Radiation Factors or Emissivities, t* For the determination of factor Fe in Equation S
Class
Surfaces
Fraction of Black-Body Radiation
At 50-100F At 1000 F
Absorptivity FOB
Solar
Radiation
I A small hole in a large box, sphere, furnace, or
I enclosure.................................................................... | Black non-metallic surfaces such as asphalt, car 0.97 to 0.99 0.97 to 0.99
0.97 to 0.99
bon, slate, paint, paper....................................... I Red brick and tile, concrete and stone, rusty steel
0.90 to 0.98
0.90 to 0.98
0.85 to 0.98
and iron, dark paints (red, brown, green,etc.).. Yellow and buff brick and stone,' firebrick, fire
0.85 to 0.95
clay.............................................................................
| White or light-cream brick, tile, paint or paper, 0.85 to 0.95
0.75 to 0.90 0.70 to 0.85
0.65 to 0.80 0.50 to 0.70
plaster, whitewash...................................f............... Window glass................................................................ I Bright aluminum paint; gilt or bronze paint.... 1 Dull brass, copper, or aluminum; galvanized
0.85 to 0.95 0.90 to 0.95 0.40 to 0.60
0.60 to 0.75
0.30 to 0.50 Transparent* 0.30 to 0.50
9 10
steel; polished iron.................................................. Polished brass, copper, monel metal....................... 0.20 to 0.30 0.30 to 0.50 i Highly polished aluminum, tin plate, nickel, 0.02 to 0.05 0.05 to 0.15
| chromium...............
0.02 to 0.04 0.05 to 0.10
0.40 to 0.65 0.30 to 0.50
0.10 to 0.40
' Emissivities of other materials may be found in Reference 4. * Reflects about 8 percent.
ifoouurrtthn powers of the absolute surface temperatures (7Y -- 2Y)- The pro portionality factor (oFaFe) may be conveniently separated into three
parts (excepting in some problems involving interreflections, where it is not possible to divide the product (FaFe) into separate terms):
a = the Stefan-Boltzmann radiation constant = 1730 X 10-'* Btu per (hour) (square foot) (Fahrenheit degree absolute temperature to the fourth power).
Fa = the geometrical factor which is dimensionless and S 1. This factor accounts
for the shape and relative position of the two surfaces. The value of Fa - 1
may be used in the cases of large parallel planes, long concentric cylinders or
smaller bodies in large enclosures.
,
fE - the emissivity factor which is also dimensionless and 1. this lactor ac
counts for the absorption and emission characteristics of the surfaces for the