17–21
17–35E A thin copper plate is sandwiched between two layers of epoxy boards. The effective thermal conductivity of the
board along its 9 in long side and the fraction of the heat conducted through copper along that side are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer is one-
dimensional since heat transfer from the side surfaces are disregarded 3
Thermal conductivities are constant.
L
T
wktkt
L
T
kA
L
T
kA
QQQ
epoxycopper
epoxycopper
epoxycopper
)()(
epoxycopper
epoxycopper
epoxycopperepoxycopper
)()(
)()()( tt
ktkt
kktktttk effeff
Note that heat conduction is proportional to kt. Substituting, the fraction of heat conducted along the copper layer and the
effective thermal conductivity of the plate are determined to be
FBtu/h. 56125.000375.05575.0)()()(
FBtu/h. 00375.0ft) F)(0.15/12Btu/h.ft. 15.0(2)(
FBtu/h. 5575.0ft) F)(0.03/12Btu/h.ft. 223()(
epoxycopp ertotal
epoxy
copper
ktktkt
kt
kt
and
FBtu/h.ft. 20.41
ft )]12/15.0(2)12/03.0[(
FBtu/h. 56125.0
t
)()(
epoxycopper
epoxycopper
t
ktkt
keff
99.3% 993.0
56125.0
5575.0
)(
)(
total
copper
copper kt
kt
f
Copper
Ts
½ tepoxy
tcopper
½ tepoxy
17–22
17–36E Two of the walls of a house have no windows while the other two walls have 4 windows each. The ratio of heat
transfer through the walls with and without windows is to be determined.
Assumptions 1 Heat transfer through the walls and the windows is steady and one-dimensional. 2 Thermal conductivity of
each wall is constant. 3 Any direct radiation gain or loss through the windows is negligible. 4 Heat transfer coefficients are
constant and uniform over the entire surface.
17–23
Thermal Contact Resistance
17–37C The resistance that an interface offers to heat transfer per unit interface area is called thermal contact resistance,
c
R
.
17–39C Thermal contact resistance can be minimized by (1) applying a thermally conducting liquid on the surfaces before
17-40C An interface acts like a very thin layer of insulation, and thus the thermal contact resistance has significance only for
17-41C An interface acts like a very thin layer of insulation, and thus the thermal contact resistance is significant for highly
17-42C Heat transfer through the voids at an interface is by conduction and radiation. Evacuating the interface eliminates
17-43 The thickness of copper plate whose thermal resistance is equal to the thermal contact resistance is to be determined.
Properties The thermal conductivity of copper is k = 386 W/m°C.
Analysis Noting that thermal contact resistance is the inverse of thermal contact conductance, the thermal contact resistance
is determined to be
11 25
17–26
17–46 Two identical aluminum plates are pressed against each other, where the interface is filled with glycerin. The thermal
contact conductance of the glycerin is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer is one-dimensional. 3 Thermal conductivity is constant.
Properties The thermal conductivity of the aluminum plates is given to be k = 237 W/mK.
K W/m30,810
2
1
2
1
K W/m237
)m 30.0(2
W/m7800
K )3050(2
k
L
q
T
h
c
17–29
17–49 A thin electronic component is cooled by dissipating heat through a heat sink attached on its top surface. There is
contact resistance at the interface of the electronic component and the heat sink, and the temperature of the electronic
component is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer is one-dimensional. 3 The electronic component maintains a
)m/cm 100/1)(cm 950)(K W/m000,25(
222
c
K/W 3.1
sinkheat R
The total thermal resistance is
C88.5 C30)K/W 300421.1)( W45(
total TRQTs
17–31
17-51 An Inconel® plate covered with a layer of thermal barrier coating (TBC). The plate is exposed to hot combustion gases
1.5 W/mK, respectively. The thermal contact conductance at the interface is given as hc = 10,500 W/m2K.
Analysis The thermal resistances of different layers are
Ak
L
R
1
1
1
(Inconel layer resistance)
1
PROPRIETARY MATERIAL. © 2017 McGraw-Hill Education. Limited distribution permitted only to teachers and educators for course preparation. If
you are a student using this Manual, you are using it without permission.
17-52C Two approaches used in development of the thermal resistance network in the x-direction for multi-dimensional
17-53C The thermal resistance network approach will give adequate results for multi-dimensional heat transfer problems if
heat transfer occurs predominantly in one direction.
17–33
17–55 A wall is to be constructed of 10-cm thick wood studs or with pairs of 5-cm thick wood studs nailed to each other.
The rate of heat transfer through the solid stud and through a stud pair nailed to each other, as well as the effective
conductivity of the nailed stud pair are to be determined.
17–36
17–58 A typical section of a building wall is considered. The average heat flux through the wall is to be determined.
Assumptions 1 Steady operating conditions exist.
17–37
17–59 A wall consists of horizontal bricks separated by plaster layers. There are also plaster layers on each side of the wall,
and a rigid foam on the inner side of the wall. The rate of heat transfer through the wall is to be determined.
0.026 W/m°C for the rigid foam.
Analysis We consider 1 m deep and 0.33 m high portion of wall which is representative of the entire wall. The thermal
resistance network and individual resistances are
R5
Ri
R2
R3
R4
R6
Ro
R1
17–38
17–60 Prob. 17–59 is reconsidered. The rate of heat transfer through the wall as a function of the thickness of the rigid
foam is to be plotted.
Analysis The problem is solved using EES, and the solution is given below.
“GIVEN”
A=4*6 [m^2]
h_2=20 [W/m^2-C]
A_1=0.33*1 [m^2]
A_2=0.30*1 [m^2]
A_3=0.015*1 [m^2]
“ANALYSIS”
17–39
17-61 A wall is constructed of two layers of sheetrock spaced by 5 cm 16 cm wood studs. The space between the studs is
filled with fiberglass insulation. The thermal resistance of the wall and the rate of heat transfer through the wall are to be
Analysis (a) The representative surface area is
2
m 65.065.01 A
. The thermal resistance network and the individual
thermal resistances are
11
C/W 843.7
)m 60.0(C) W/m034.0(
m 16.0
C/W 091.29
)m 05.0(C) W/m11.0(
m 16.0
C/W 090.0
)m 65.0(C) W/m17.0(
m 01.0
C/W 185.0
)m 65.0(C) W/m3.8(
11
2
3
2
2
2
41
22
fiberglass
stud
sheetrock
i
i
kA
L
RR
kA
L
RR
kA
L
RRR
Ah
R
Ri
R1
R2
R4
R5
