866 Chapter 13 I Radiation Exchange Between Surfaces
(a) If the two surfaces have the same radiative proper- 13.87 Work Problem [323, part (b), except with wall and experie
ties, show that the required surface emissivity is cylinder emissivities
(a) Sketch the temperature distribution on T—x coor-
dinates and identify its key features. Assume that
T1 > T3 > T3,.
(b) Derive an expression for the midpoint tempera—
ture T2 in terms of the thermal and geometric pa-
rameters of the system.
minum alloy and
500 K and is ex-
W/m2 - K. Annu—
to the surround—
gth L = 20 mm,
of the ﬁns?
3.6 l Heat Transfer from Extended Surfaces 157
With the ﬁns, the total heat transfer rate is then
_ 0.0527 m2
0 0716 2 (0.05)] 200 K = 690
130 Chapter 3 I One-Dimensional, Steady-State Conduction
4. Inner surface of A adiabatic.
5. Constant properties for materials A and B.
1. From the prescribed physical conditions, the temperature distribution in the
composite is known to have th
100 Chapter 3 I One-Dimensional, Steady-State Conduction
X Toot Tm T2 Ta 71:4 T 4
FIGITRE 3.2 Equivalent thermal circuit for a series composite wall.
resistances due to layers of different materials. Consider the series com
76 Chapter 2 I Introduction to Conduction
1. One—dimensional conduction in the x direction.
2. Isotropic medium with constant properties.
3. Uniform internal heat generation, 6'] (W/m3).
1. Recall that once the temperature distribut
Plaster board, kpj
Chapter 3 I One-Dimensional, Steady-State Conduction
A house has a composite wall of wood, ﬁberglass insula-
tion, and plaster board, as indicated in the sketch. On a
cold winter day the convection heat transfer coefﬁ
I2 Shape factors for
geometries may also
be estimated with the
that is described in
Chapter 4 I Two-Dimensional, Steady-State Conduction
where AT1_2 is the te
.= 86.7, and h -'
7.64 therefore :.¢._
'on 7.68, the he.
' 105°C, evalu
.~-i ation. Howe.
.peated with u -' .
'nn pertains to .
s it appears '
ity to provide a, '
nearing the tube '-
sed by increas'
ey may be van
: s, parametric c
Chapter 7 l External Flow
2024 aluminum pin ﬁn through the wall separating the
two ﬂuids. The pin is inserted to a depth of a’ into
ﬂuid 1. Fluid 1 is air with a mean temperature of 10°C
and nearly uniform velocity of 10 m/s. Fluid 2 is air
with a mea
: _/s and 300 K.
. ’xed with an o . -.
400 W/mZ'K. ' .
: mass flow rate :2}
ator if the vehicle?! if
rating at 50% '
_; temperature is '
. the inlet and o _.
'ater with respect;
' and Tm, = 330
. perature is as in
air is proportional '-
Chapter 1 I Introduction
(a) For an initial condition corresponding to a wafer
temperature of TM. = 300 K and the position of the
wafer shown schematically, determine the corre-
sponding time rate of change of the wafer tempera-
Chapter 4 I Two-Dimensional, Steady-Slate Conduction
while nodes 16 and 17 are situated on a plane surface with convection (case 3):
Node 16: 2T,0 + Tl5 + T17 — 2 T + 2 T16 =
In each case heat transfer to nodal re
ite solid is physi
*' t except at extreru
ﬂux may be ob :m'.
d case 3 surface
l — erf w.
'- e 5.7, and distin-
T, with increasing
hence the surface
: x (case 2), Equa-
. For surface con-
thin the medium
roaches Tm, there
Chapter 3 I Internal Flow
Having acquired the means to compute convection transfer rates for ex
ﬂow, we now consider the convection transfer problem for internal ﬂow. Rec._ .I:
706 Chapter 11 I Heat Exchangers
- What effect do ﬁnned surfaces have on the overall heat transfer coefﬁw.
and hence the performance of a heat exchanger? When is the use of ﬁns 1-3-
' When can the
Sphere A Sphere B
Diameter (mm) 300 30
Density (kg/m3) 1600 400
Speciﬁc heat (kl/kg - K) 0.400 1.60
Thermal conductivity (W/m - K) 170 1.70
Convection coefﬁcient (W/mZ ' K) 5 50
(a) Show in a qualitative manner, on Tversus I coordi—
nates, the t
I a gas—liquid
n 6.61 may then
ted conditions at
' from the ideal
and Le should
6.7 l Boundary Layer Analogies 383
T“m 2 (TA. + Tog/2. A representative value of n = :i; has been assumed for the Pr and
(' ".1 P 'I' I37 If 6
' perature of 275°C-
art table, where r- _
-ical properties of
: g/m3, c = 800 J/kg
e vs. Time cOmm:I-,a.-
Ir selected locatio
- the rib? If s
7.2 I The Flat Plate in Parallel Flow 405
Flat Plate in Parallel F low
Despite its simplicity, parallel ﬂow over a ﬂat plate (Figure 7.3) occurs in numerous
engineering applications. As discussed in Section 6.3, laminar boundary layer
4.48 The steady—state temperatures (°C) associated with sel—
ected nodal points of a two-dimensional system having
a thermal conductivity of 1.5 W/m - K are shown on the
l 129 4 45.8
0.1 m w = 30°C
L T3 I1: 50 W/mZ-K
0612 = 2 X 107 W
' menu, the Con i
. e transient solu:
ich accompani t.
. node att+ At .7
r- neighboring n
rature at some
.tations on the s '3
-_ be compatible v_~'
uely small valu -.
process in which
d its surround—
5.3 I General Lumped Capacitance Analysis 269
Using TC = 150°C with T5.“ = 25°C for the cooling process, we also obtain hm. =
8.8 W/m2 - K. Since the values of hm and hm are comparabl
Chapter 8 I Internal Flow
Known: Flow rate and inlet and outlet temperatures of water ﬂowing thro_ mar Flow
tube of prescribed dimensions and surface temperature. lySls and (
Find: Average convection heat transfer coefﬁcient.
D = 5
748 Chapter 12 I Radiation: Processes and Properties
0 0,2 0.4 0.6 0.8 1.0
Total, normal emissivity, 8,
FIGURE 12.19 Representative values ofthe total, normal
Representative values of the total, normal emissivity 3, are plotted in Figur
Properties of M atter1
A.1 Thermophysical Properties of Selected Metallic Solids 929
A.2 Thermophysical Properties of Selected Nonmetallic Solids 933
A.3 Thermophysical Properties of Common Materials 935
568 Chapter 9 I Free Convection
Using Fourier’s law to obtain qi.’ and expressing the surface temperature gradi-i -
terms of 7), Equation 9.13, and T*, Equation 9.16, it follows that
, (9T k Ga) ”4 dT*
V k 2 T5 Too
4. ay F0 x( )< 4 dn
Chapter 9 I Free Convection
A solar collector design consists of an inner tube
enclosed concentrically in an outer tube that is trans—
parent to solar radiation. The tubes are thin walled
with inner and outer diameters of 0.10
Chapter I I Introduction
The units required to specify other physical quantities may then be inferred from
this group. For example, the dimension of force is related to mass through Newton’s
second law of motion,
F = i Ma (1.14)
where the accelerati