N
i
N
, exp log
CO2 H2O CO2 H2O
cc
cc
N
M NM
00 1
0
L
MOM
L
(p . p / t )/ p a 2 56 0
4-74 Section 4
1999 by CRC Press LLC
(4.3.32)
where the compensates for overlap effects between H2O and CO2 bands, and the and are
calculated from Equation (4.3.30).
If
1
0
,
4-58 Section 4
1999 by CRC Press LLC
Note that 90% of all blackbody emission takes place at wavelengths of T > 2200 mK and at all
wavelengths T < 9400 mK. This implies that for typical high-temperature heat transfer applications
in the range betwe
Sd
SS
S
d
TT
d
dL
T
22
2
2
212
h
h
Nc
16
1
4-40 Section 4
1999 by CRC Press LLC
Pressure Drop: With tube banks, pressure drop is a significant factor, as it determines the fan power
required to maintain the fluid flow. Zukauskas (1987) recommends that th
The second geometry considered is a very long cylinder of diameter 2R. The temperature response
for this situation is
(4.1.29)
Now the n are the roots of nR J1(nR) + Bi Jo (nR) = 0, and
The common definition of Bessels functions applies here.
For the simi
(4.4.16)
where D is the diameter in millimeters. A good generalized empirical correlation for predicting dryout
or CHF conditions in vertical uniformly heated tubes is that recently proposed by Katto and Ohno (1984).
In many cases, post-dryout mist flow e
Correlations of nucleate pool boiling heat transfer data have typically been used as tools to predict
nucleate boiling heat transfer in engineering systems and heat exchangers. Many investigators have
proposed methods of correlating data of this type; so
1
2
4
1
, q q T T G Go o 1
TxT
TT
x
L
o
o
1
11
cos
cos
TrT
TT
Jr
Jr
o
o
o
o
1
1 11
Heat and Mass Transfer
4
-7
1999 by CRC Press LLC
In Equation (4.1.18), the Jo is the typical notation for the Bessel function. Variations of this function are
tabulated
of condensation is most likely when the liquid poorly wets the solid surface. When the condensation
rate is high or the liquid readily wets the surface, a film of liquid condensate covers the solid surface,
and the process is referred to as film condensat
CH
Nu Nu Nu
WH T
L
k t
q
*
.
.l
10 10 0 1
76 5
qH
W Tk
L
Nu
Wm-length * 3950 /
4-24 Section 4
1999 by CRC Press LLC
Properties: At = T1 + T2/2 = 0C = 273K
Solution: The appropriate correlations are given in Case 18 and by Equation (4.2.24).
Comments: Fo
P
vT
0
4-84 Section 4
1999 by CRC Press LLC
imperfections, heterogeneous nucleation is more common than homogeneous nucleation in systems
where boiling occurs.
Vapor entrapment in crevices of the heated walls of evaporator heat exchangers usually makes
.
sin . .
Nu= 0.603
Ra1 4
max
C
DD
LDLD
oi
io
l
ln
,
3535541
Nu =
Ra
14
14
max
qL
DD k T
C
L
i o Di D D D D
iooi
1 16 1
354554.
,l
4-22 Section 4
1999 by CRC Press LLC
Example Calculations
Problem 1: Heat Transfer from Vertical Plate, Figure 4.2.6A. Fo
FIGURE 4.1.4. Three types of bodies that can be analyzed with results given in this section. (a) Large plane wall
of 2L thickness; (b) long cylinder with 2R diameter; (c) composite intersection.
FIGURE 4.1.5. A one-dimensional finite differencing of a sla
layer thickness T depends both on ReX and Pr
Rex < Recr:
(4.2.30)
Recr < Rex:
(4.2.31)
Viscous dissipation and high-speed effects can be neglected if Pr 1/2 Ec/2 ! 1. For heat transfer with
significant viscous dissipation see the section on flow over flat
max 0
14
131 2
.
qmin
q hv fg
glv
lv
min 0
14
09 2
.
qmin
h
kgh
TTx
v v l v fg
vw
314
4
sat
Heat and Mass Transfer 4-89
1999 by CRC Press LLC
tube wall. At low quality the vaporization process is dominated by nucleate boiling, with convective
effects bei
max
qL
WH T T k 1 2
1 2 , 1.01
q WH
NTTk
L
/
.
.
.
1 2 1 01 20 0 24
0 01
48 5 W/m2
C,
Ct
V
Ct
H
Ct
T
Heat and Mass Transfer 4-25
1999 by CRC Press LLC
Edwards, J.A. and Chaddock, J.B. 1963. An experimental investigation of the radiation and freeconvecti
It is clear that (1) values of spectral surface emissivity are subject to great uncertainty and (2) only
a relatively small range of infrared wavelengths are of importance. Therefore, it is often assumed that
the surfaces are gray, i.e., the emissivity is
k
k
ln k
xx k k
,
.
.
0 exp .
1 44
1 0 018 0 00136
75 1 5 1 2 2
12
max Pr
Pr
Pr
Heat and Mass Transfer 4-21
1999 by CRC Press LLC
18. Vertical Layers, Figure 4.2.5(A), with = 90. W/L > 5. For a vertical, gas-filled (Pr 0.7) cavity
with H/L 5, the follow
. 1413ll
Ct
Ct
Nup
T
Nu
Nu
l
09
1 09
.2
ln .
p
p
T
LD
Nu
4-18 Section 4
1999 by CRC Press LLC
10. Spheres, Figure 4.2.3C. For spheres use Equation (4.2.6), with m = 6, and with
(4.2.14)
The table above contains values.
11. Combined Shapes, Figure 4.2.3D.
Nu Ra Nu
Nu
T Nu Ra
Ttt
C
G
V
ll
*. *
ln .
1 5 1 83 3 4 1 4
1 1 83
Gl
6
5 4 9 10
1 5 Pr
+ Pr Pr
Ct
V
Gl
Nu Ra Nu
Nu
T Nu Ra
Ttt
C CH
0 835
20
1 14
. 1413
.
ln . l l
T.
Nu Ra H
Pr
Nu =
2.45
Nu
T
T H
ll
15
9 10 2 9
0 527
1 19 1 2 45
.
. ln .
Heat and Mass
For given thermal boundary conditions (e.g., isothermal wall and uniform T), and for a given geometry
(e.g., a cube), Equation (4.2.2) states that Nu depends only on the Rayleigh number, Ra, and Prandtl
number, Pr. The length scales that appear in Nu and
.
.
Nu Re Pr x x 0 0296 . 4 5 1 3
Nu Re Re Pr x x x 1 596 . ln 2 584 1 3 .
Heat and Mass Transfer 4-29
1999 by CRC Press LLC
Equation (4.2.38) is obtained by applying Colburns j factor in conjunction with the friction factor
suggested by Schlicting (1979
(4.2.62)
where i is the specific enthalpy of the fluid evaluated at the temperature corresponding to the subscript.
Equation (4.2.62) gives the same values as Equation (4.2.55) if Cp is constant or varies linearly with
temperature.
At very high speeds the
Insulations
Insulations are used to decrease heat flow and to decrease surface temperatures. These materials are
found in a variety of forms, typically loose fill, batt, and rigid. Even a gas, like air, can be a good
insulator if it can be kept from movin
Magnesium oxide 275825 0.550.20
9001705 0.20
Magnesium, polished 35260 0.070.13
Mercury 0100 0.090.12
Molybdenum, polished 35260 0.050.08
5401370 0.100.18
Heat and Mass Transfer 4-63
1999 by CRC Press LLC
where i and j are the angles between the surface
d
sL
d
1 86
1 3 0 14
.
.
L
d
d
ss
Re Pr
Pr <
8
0 48 16 700 0 0044 9 75
0 42
.
.,.
q h dL T
TT
s
bi be
2
h
Uniform Surface Temperature Nud 3.66 (4.2.95)
Uniform Surface Heat Flux Nud 4.36 (4.2.96)
0.6 Pr 2000 2300 Re 106 0 1 d d L
Nu
Re Pr
1+12.7 Pr d
df
f
natural and forced convection in vertical and horizontal tubes. The maps are applicable for 10 2 < Pr(d/L)
< 1 where d and L are the diameter and the axial length of the tube. The maps show the limits of forced
and natural convection regimes. The limits a
1 01 6
1
200
0 55
12
. 0 42
.
.
.
2000 Re 400 0 00 2 5 7 5 2 12 d , . r d . H d
Nu Re Pr d d
rd
rd
r
d
1 29
0 88
1 69 1 2 0 4
8 5 1 07 17 1 17
.
tanh .
.
.
Re mass rate of flow per unit length of jet w
jw m
m
v22
Nuw
hw
k
2
Nu
Pr Re
w
w
m
x
w
H
w
1 53
22
. Wm K
m
K
W
mK
24
q 0 1 136
2000 1000
1
136 2 2 .
W
m
kW
mK
q L E L E m bw m bg 1
Heat and Mass Transfer 4-79
1999 by CRC Press LLC
surface may be calculated very accurately from Equation (4.3.43), provided the emissivity and absorptivity
of the mediu