3-1
Solutions Manual for
Heat and Mass Transfer: Fundamentals & Applications
6th Edition
Yunus A. Çengel, Afshin J. Ghajar
McGraw-Hill Education, 2020
Chapter 3
STEADY HEAT CONDUCTION
PROPRIETARY AND CONFIDENTIAL
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3-2
Steady Heat Conduction in Plane Walls
3-1C The temperature distribution in a plane wall will be a straight line during steady and one dimensional heat transfer with
constant wall thermal conductivity.
3-2C In steady heat conduction, the rate of heat transfer into the wall is equal to the rate of heat transfer out of it. Also, the
3-3C The thermal resistance of a medium represents the resistance of that medium against heat transfer.
3-3
3-10C The blanket will introduce additional resistance to heat transfer and slow down the heat gain of the drink wrapped in a
blanket. Therefore, the drink left on a table will warm up faster.
3-12C For a surface of A at which the convection and radiation heat transfer coefficients are
h h
conv rad
and
, the single
3-15C The window glass which consists of two 4 mm thick glass sheets pressed tightly against each other will probably have
3-16 The two surfaces of a wall are maintained at specified temperatures. The rate of heat loss through the wall is to be
determined.
Assumptions 1 Heat transfer through the wall is steady since the surface temperatures
remain constant at the specified values. 2 Heat transfer is one-dimensional since any
significant temperature gradients will exist in the direction from the indoors to the
outdoors. 3 Thermal conductivity is constant.
Properties The thermal conductivity is given to be k = 0.8 W/m°C.
L= 0.25 m
Q
Wall
3-4
3-5
3-19 A circuit board houses 100 chips, each dissipating 0.06 W. The surface heat flux, the surface temperature of the chips,
and the thermal resistance between the surface of the board and the cooling medium are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer from the back surface of the board is negligible. 2 Heat is
transferred uniformly from the entire front surface.
Analysis (a) The heat flux on the surface of the circuit board is
2
m 0216.0m) m)(0.18 12.0( ==
s
A
2
W)06.0100(
Q
T
3-6
3-21 A cylindrical resistor on a circuit board dissipates 0.15 W of power steadily in a specified environment. The amount of
heat dissipated in 24 h, the surface heat flux, and the surface temperature of the resistor are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat is transferred uniformly from all surfaces of the resistor.
Analysis (a) The amount of heat this resistor dissipates during a 24-hour period is
Wh3.6=== h) W)(2415.0(tQQ
(b) The heat flux on the surface of the resistor is
2
2
2
m) 003.0(
D
Resistor
Q
3-7
3-8
3-9
3-26 A double-pane window consists of two layers of glass separated by an evacuated space. For specified indoors and
outdoors temperatures, the rate of heat loss through the window and the inner surface temperature of the window are to be
determined.
Assumptions 1 Heat transfer through the window is steady since the indoor and outdoor temperatures remain constant at the
specified values. 2 Heat transfer is one-dimensional since any significant temperature gradients will exist in the direction
from the indoors to the outdoors. 3 Thermal conductivity of the glass is constant. 4 Heat transfer by radiation is negligible.
Properties The thermal conductivity of the glass is given to be kglass = 0.78 W/m°C.
Analysis Heat cannot be conducted through an evacuated space since the
thermal conductivity of vacuum is zero (no medium to conduct heat) and thus
its thermal resistance is zero. Therefore, if radiation is disregarded, the heat
transfer through the window will be zero. Then the answer of this problem is
zero since the problem states to disregard radiation.
Discussion In reality, heat will be transferred between the glasses by
radiation. We do not know the inner surface temperatures of windows. In
order to determine radiation heat resistance we assume them to be 5°C and
15°C, respectively, and take the emissivity to be 1. Then individual
resistances are
2
Vacuum
3-10
3-27 Prob. 3-26 is reconsidered. The rate of heat transfer through the window as a function of the width of air space is
to be plotted.
Analysis The problem is solved using EES, and the solution is given below.
“GIVEN”
A=1.5*2.4 [m^2]
L_glass=3 [mm]
k_glass=0.78 [W/m-C]
L_air=12 [mm]
Lair [mm]
3-11
3-12
3-29 A very thin transparent heating element is attached to the inner surface of an automobile window for defogging
purposes, the inside surface temperature of the window is to be determined.
Assumptions1 Steady operating conditions exist. 2 Heat transfer through the window is one-dimensional. 3 Thermal
properties are constant. 4 Heat transfer by radiation is negligible. 5 Thermal resistance of the thin heating element is
negligible.
Properties Thermal conductivity of the window is given
to be k = 1.2 W/m ∙ °C.
Analysis The thermal resistances are
1
1
L
3-13
3-14
3-31 Warm air blowing over the inner surface of an automobile windshield is used for defrosting ice accumulated on the
outer surface. The convection heat transfer coefficient for the warm air blowing over the inner surface of the windshield
necessary to cause the accumulated ice to begin melting is to be determined.
Assumptions1 Steady operating conditions exist. 2 Heat transfer through the windshield is one-dimensional. 3 Thermal
properties are constant. 4 Heat transfer by radiation is negligible. 5 The automobile is operating at 1 atm.
Properties Thermal conductivity of the windshield is given to be k = 1.4 W/m ∙ °C.
Analysis The thermal resistances are
1
3-15
3-16
3-33 An exposed hot surface of an industrial natural gas furnace is to be insulated to reduce the heat loss through that section
of the wall by 90 percent. The thickness of the insulation that needs to be used is to be determined. Also, the length of time it
will take for the insulation to pay for itself from the energy it saves will be determined.
Assumptions 1 Heat transfer through the wall is steady and one-dimensional. 2 Thermal conductivities are constant. 3 The
furnace operates continuously. 4 The given heat transfer coefficient accounts for the radiation effects.
Properties The thermal conductivity of the glass wool insulation is given to be k = 0.038 W/m°C.
Analysis The rate of heat transfer without insulation is
2
3-17
3-18
3-19
kmetal
[W/m.C]
Lins
[cm]
10
30.53
51.05
71.58
92.11
112.6
133.2
153.7
174.2
194.7
215.3
235.8
256.3
276.8
297.4
317.9
338.4
358.9
379.5
400
0.8743
0.8748
0.8749
0.8749
0.8749
0.8749
0.8749
0.875
0.875
0.875
0.875
0.875
0.875
0.875
0.875
0.875
0.875
0.875
0.875
0.875
050 100 150 200 250 300 350 400
0.8743
0.8744
0.8745
0.8746
0.8747
0.8748
0.8749
0.875
kmetal [W/m-C]
Lins [cm]
3-20
3-36 Heat is to be conducted along a circuit board with a copper layer on one side. The percentages of heat conduction along
the copper and epoxy layers as well as the effective thermal conductivity of the board are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer is one-dimensional
since heat transfer from the side surfaces is disregarded 3 Thermal conductivities are
constant.
Properties The thermal conductivities are given to be k = 386 W/m°C for copper and
0.26 W/m°C for epoxy layers.
Analysis We take the length in the direction of heat transfer to be L and the width of the
board to be w. Then heat conduction along this two-layer board can be expressed as
L
T
kA
L
T
kAQQQ
+
=+=
epoxycopper
epoxycopper
+
Epoxy
Copper