456 Chapter 7 I External Flow
f1. niel, C2. 0., and
in Impinging 5
TABLE 7.9 (Continued)
Correlation Geometry Conditions _‘. .ped Nozzle ant
- . . . I 1. .P. Carey, and J.
S1ng1e round nozzle (7.75) Im

860 Chapter 13 I Radiation Exchange Between Surfaces
determine the power generation in watts per unit of
outer surface area.
13.52 Liquid oxygen is stored in a thin-walled, spherical
container 0.8 m in diameter, which is enclosed within
a second thin-wall

326
5.31
mass of the iron and copper in the transformer is 0.28 kg,
and its weighted—average speciﬁc heat is 400 J/kg ' K.
The transformer dissipates 4.0W and is operating in
ambient air at T0, = 20°C, with a convection coefﬁcient
of 10 W/m2 - K. List and

166
3.8
Summary
Chapter 3 I One-Dimensional, Steady-State Conduction
2. Measuring the true thermal conductivity of living tissue is very challenging,
ﬁrst because of the necessity of making invasive measurements in a living
being, and second because i

398
below and forcing air across it. Laboratory measure—
ments for this surface have provided the following heat
transfer correlation:
ML = 0.43ReQ-58 Pr“
The air flowing over the surface has a temperature
of 290 K, a velocity of 10 m/s, and is completely

I Problems
ooled by passing . .
'1 ocouple embedd
- e surface records :.
'I ing cooling.
surfaces must not exceed 325°C and 25°C, respectively,
after 30 min of heating, will the requirements be met?
3 It is well known that, although two material

Shape Factor
.785 In (W/w)
27'rL
a 1n (W/w)
— 0.050 ‘
4.3 I The Conduction Shape Factor 21 1
heated object and the far ﬁeld temperature of the surrounding medium, (Tmax —
T2). For the uniformly heated geometry of case 10 (a disk of diameter D in conta

Jane 7}, and the 4-.1'
exterior cases, Le.
70m. For the sph-
' [51
(-
1y mimics that r."
tion, regardless r;
' , q* initially foil-:-
cases, (1* even
:3 able 4.1. Note th
2 'es that have no
se to that of the 3:.-
1y 10‘}. This rem '-
o

106 Chapter 3 I One-Dimensional, Steady-State Conduction
The skin temperature can be calculated by considering conduction through the
skin/fat layer:
- ksz(Ti * T.)
q Lsf
or solving for T“
L —3
6] sf_350C lOOWXBXlO m
Ts — Ti
km 0.3 W/m - K x 1.8 m2
— 34

(2.1621)
(2.16b)
(2.16c)
by the appro—
te. Substituting
of the control
the heat diffu-
, provides the
btain the tem-
complexity of
ortant physical
understanding
. For example,
6 control vol-
(2.18)
ons. In words,
he

l Problems
-' Consider the sy
n (inset a), assu
across the web is . ._
_. -) Calculate the heat ﬂux through the composite wall
by assuming material A to have a uniform thermal
conductivity evaluated at the average temperature
of the section.

m
0.40
0.40
a single
inder
0.63
0.60
0.60
0.84
0.84
' has proposed a
I.
an of the ﬂuid i.
Table 7.7. The neat
(T,- = T0,) and on
' re will decrease ,._
If the ﬂuid temper
.-m evaluation of a.
tor may be appli.-
(7.65
10 13
L97 0.

356
Chapter 6 I Introduction to Convection
Analysis:
1. From Equation 6.14 the average value of the convection heat transfer coe
cient over the region from 0 to x is
E3. = EU) = % f /11(x) (ix
0
Substituting the expression for the local heat tra

86
FUNDAMENTALS OF HEAT AND MASS TRANSFER
LM
O
260 154.38 P
F
2 0.07 G 1 + 15 10
Q= M
0.13 P
H
MN ln 0.1 PQ
check
4
260 154.38
2
IJ
K
= 232.08 W, checks
dT
Q
=
dx
kA
k = 0.07 (1 + 15 104 260) = 0.0973 W/mK
slopes
Inside surface
A = 2r1 = 2 0.1
dT
232.08

365
CONVECTIVE HEAT TRANSFER-PRACTICAL CORRELATIONS-FLOW OVER SURFACES
Solution:
h =
=
FG IJ
H K
k
V
.C
x
hx =
1
L
z
0.5
x (m / 2) + 0.5 = k.C
hx dx = k. C
FG IJ
H K
k. C V
.
L
0.5
FG V IJ
H K
0.5
.
1
.
L
FG V IJ
H K
z
L
0
0.5
x (0.5 m 0.5)
x 0.5( m 1) dx

440
FUNDAMENTALS OF HEAT AND MASS TRANSFER
kA
From (10.2 (b),
dT
dy
= hA (Tw T)
y=0
dT
dy
=
y=0
2
(Tw T)
h
hx 2 x
2
=
=
or Nux =
k
k
Substituting in (10.13), we get (10.14).
and
(x3/4
Nux =
0.508 Pr 0.5 Grx 0.25
.(10.14)
(0.952 + Pr) 0.25
The average val

155
HEAT TRANSFER WITH EXTENDED SURFACES (FINS)
letting (hPk) (Tb T) = C, and substituting the values for the remaining
=C
t . tanh
t tanh
FH
(100 2 / 200) 5 10 4 (1 / t 3 / 2 )
IK
5 10 4 / t 3 / 2
differentiating Q with respect to t
(dQ)/(dt) = constant

.: convection
Q
_ and T3,”, as
cient.
l-fer from the
-'-ation domi—
i-t W/mz- K,
6 W/m2). In
-: of the sur-
may be ac-
r, check the
.at test your
r effects and
ratures that
-u what prob—
breadth of
'on and pro—
- reases with
gases inside
manufacture
. ee

med energy
of a control
imply stated
- ' amount of
' the control
.u ists of ki—
-;-: d internal
(which will
as chemical
.-= tention on
i the sum of
conversion
mical reac-
twill result
nergy con—
ﬁve or neg-
alysis is:
01 volume

-pherical abs”?
0.40. Under -,
.de with a '
: :dicate a re
ell as reflection
'le the plate is '
d the total hvivik.
Is the plate greyh-
furnace operating
5 having 7 = 0.8
'_u om the furnace.
rt dis opaque to u.
perature. The ouco‘
to surroundings : ' '
.v

' g-shaped disk.
., right-circular cone;
.1 OforOSGSn-Fl,
_'l ular cylinder of rite
positioned coaxially'
. disk (A,) shoWn_
-d lateral surfaces of
'ngle surface, A2. The
-. o the opening of the
ght-circular cylinder
uents, F2, = (A,/A;,)F,3
e F13 is

Appendix A I Thermophysical Properties of Matter 95 1
TABLE A.7 Thermophysical Properties of Liquid Metals“
Melting
Point T p C” v ' 107 k a- 105
Composition (K) (K) (kg/m3) (kJ/ kg - K) (m2/s) (W/m - K) (ml/s) Pr
Bismuth 544 589 10.011 0.1444 1.617 1

I Problems
-ual energy is gene .-.—. TOP View
thickness t and length Chip’ T”
: square sleeve of win-11". Air —> Side View
conditions, the rate . 1 I. T h
'- ponds to the rate:
sleeve.
T T If a convection heat transfer coefﬁcient of h =
5 100 W/m2-K

308
Chapter 5 I Transient Conduction
Hence, with
_ h Ax _ 1100 W/m2 ' K(0.002 m) _
Bl k 30 W/m . K 0.0733
it follows that
F0 S 0.466
or
F 2 0.4 2 X 10“3 2
A: — am) < 66( m) s 0373 s
a _ 5 X10'6m2/s
To be well within the stability limit, we select At

380 Chapter 6 I Introduction to Convection
2. Boundary layer approximations are valid.
3. Negligible viscous dissipation.
4. Mole fraction of water vapor in concentration boundary layer is much less
unity.
Properties.- Table A4, air (50°C): v = 18.2 X

278 Chapter 5 I Transient Conduction
Values of the center temperature 0;" are determined from Equation 5.49c or 5. t.
using the coefﬁcients of Table 5.1 for the appropriate system.
5.6.4 Additional Considerations
As for the plane wall, the f

426
Chapter 7 I External Flow
0 3O 6O 90 120 150 180
Angular coordinate, 9
FIGURE 7.9 Local Nusselt number for airﬂow normal to a circular cylinder. Adapted with
permission from Zukauskas, A., “Convective Heat Transfer in Cross Flow,” in S. Kaka

of 200°C. The ﬁns .
.system is in ambien
‘ surface convection
f:- d effectiveness?
.-r meter of tube 1e
.' iders of a combus. ,ii'
_a m casing with a «I
e cylinder wall (I: -
Aluminum casing
though heating at the
reasonable to assume“
an cylinder of

I Problems
Consider the packed bed of aluminum spheres
described in Problem 5.12 under conditions for which
the bed is charged by hot air with an inlet velocity of
= 1 m/s and temperature of T8, = 300°C, but for
which the convection coefﬁcient is not pres