1-21
1-55 The thermal conductivity of a material is to be determined by ensuring one-dimensional heat conduction, and by
measuring temperatures when steady operating conditions are reached.
W66)A 6.0)(V 110(=== IWeV
The rate of heat flow through each sample is
W66
W
Q
1-22
1-23
1-58 Heat loss by conduction through a concrete wall as a function of ambient air temperatures ranging from -15 to 38°C is
to be determined.
Assumptions 1 One-dimensional conduction. 2 Steady-state conditions exist. 3 Constant thermal conductivity. 4 Outside wall
temperature is that of the ambient air.
1-24
1-25
1-59 A hollow spherical iron container is filled with iced water at 0°C. The rate of heat gain by the iced water and the rate at
which ice melts in the container are to be determined.
Assumptions 1 Steady operating conditions exist since the surface temperatures of the wall remain constant at the specified
values. 2 Heat transfer through the shell is one-dimensional. 3 Thermal properties of the iron shell are constant. 4 The inner
1-26
1-60 Prob. 1-59 is reconsidered. The rate at which ice melts as a function of the container thickness is to be plotted.
L=0.2 [cm]
T_1=0 [C]
T_2=5 [C]
L
[cm]
mice
[kg/s]
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1515
0.07574
0.0505
0.03787
0.0303
0.02525
0.02164
0.01894
0.01683
0.01515
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.04
0.06
0.08
0.1
0.12
0.14
0.16
L [cm]
mice [kg/s]
1-27
1-28
1-29
1-64 A series of ASME SA-193 carbon steel bolts are bolted to the upper surface of a metal plate. The upper surface is
exposed to convection with the ambient air. The bottom surface is subjected to a uniform heat flux. Determine whether the
use of the bolts complies with the ASME Boiler and Pressure Vessel Code, where 260°C is the maximum allowable use
temperature.
Assumptions1 Heat transfer is steady. 2 One dimensional heat conduction through the metal plate. 3 Uniform heat flux on the
convcond0 W/m5000
From the Newton’s law of cooling, we have
)(
conv
−= TThq s
Assuming the temperature of the bolts is equal to the upper surface temperature of the plate,
C260C30
K W/m10
W/m5000
2
2
conv
bolt =+
=+== C530T
h
q
TT s
or lower, the convection heat transfer coefficient should be higher than 21.7 W/m2·K.
K W/m7.21
K )30260(
W/m5000 2
2
conv
−
−
TT
q
h
s
1-30
1-31
1-66 A boiler supplies hot water to a dishwasher through a pipe at 60 g/s. The pipe dimensions are given. The water exits
the boiler at 95°C. The pipe section between the boiler and the dishwasher is exposed to convection. The water temperature
entering the dishwasher is to be determined whether it meets the ANSI/NSF 3 standard.
Assumptions1Constant properties are used for the water.2Steady operating conditions. 3 Surface temperature of the pipe is
uniform.
1-67 Hot liquid flows in a pipe with PVDF lining on the inner surface. The pipe outer surface is subjected to uniform
heat flux. The liquid mean temperature and convection heat transfer coefficient are given. Determine whether the surface
temperature of the lining complies with the ASME Code for Process Piping.
Assumptions1 Steady operating conditions. 2 Heat transfer is one-dimensional through the pipe wall. 3 Surface temperature
is uniform. 4 Thermal properties are constant.
1-32
1-33
1-34
1-72E A 200-ft long section of a steam pipe passes through an open space at a specified temperature. The rate of heat loss
from the steam pipe and the annual cost of this energy lost are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer by radiation
is disregarded. 3 The convection heat transfer coefficient is constant and
uniform over the surface.
280F
1-35
1-36
0.5, we recognize that n = 0.6 is a reasonable choice. Hence, the best values of the constants are: C = 22.12 and n = 0.6. The
details of these trials are given in the following table and plot.
V (m/s)
LW /
(W/m)
h (W/m2K)
n
Vh 12.22=
(W/m2K)
n = 0.5
n = 0.6
n = 0.8
1
450
22.0
22.12
22.12
22.12
2
658
32.2
31.28
33.53
38.51
4
983
48.1
44.24
50.82
67.06
8
1507
73.8
62.56
77.03
116.75
12
1963
96.1
76.63
98.24
161.48
1-37
1-75 The convection heat transfer coefficient for heat transfer from an electrically heated wire to air is to be determined by
measuring temperatures when steady operating conditions are reached and the electric power consumed.
Assumptions 1 Steady operating conditions exist since the temperature readings do not change with time. 2 Radiation heat
The Newton’s law of cooling for convection heat transfer is expressed as
L = 1.4 m
Q
Air, 20C
1-38
1-39
1-78 A spacecraft in space absorbs solar radiation while losing heat to deep space by thermal radiation. The surface
temperature of the spacecraft is to be determined when steady conditions are reached.
Assumptions 1 Steady operating conditions exist since the surface temperatures of the wall remain constant at the specified
1-79 A person with a specified surface temperature is subjected to radiation heat transfer in a room at specified wall
temperatures. The rate of radiation heat loss from the person is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer by convection is disregarded. 3 The emissivity of the person
is constant and uniform over the exposed surface.
W26.7=
(b) Tsurr = 280 K
)(
4442428
4
surr
4
rad
−=
−
TTAQ ss
Qrad
32C
1-40
1-80 A sealed electronic box dissipating a total of 100 W of power is placed in a vacuum chamber. If this box is to be cooled
by radiation alone and the outer surface temperature of the box is not to exceed 55C, the temperature the surrounding
surfaces must be kept is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer by convection is disregarded. 3 The emissivity of the box is
1-81 One highly polished surface at 1070°C and one heavily oxidized surface are emitting the same amount of energy per
unit area. The temperature of the heavily oxidized surface is to be determined.
Assumptions The emissivity of each surface is constant and uniform.
Properties The emissivity of the highly polished surface is ε1 = 0.1, and the emissivity of heavily oxidized surface is
ε2 = 0.78.