1-41
1-82 A spherical probe in space absorbs solar radiation while losing heat to deep space by thermal radiation. The incident
radiation rate on the probe surface is to be determined.
Assumptions 1 Steady operating conditions exist and surface temperature remains constant. 2 Heat generation is uniform.
Properties The outer surface the probe has an emissivity of 0.9 and an absorptivity of 0.1.
Analysis The rate of heat transfer at the surface of the probe can be expressed as
1-42
1-83 Spherical shaped instrumentation package with prescribed surface emissivity within a large laboratory room having
walls at 77 K.
Assumptions 1 Uniform surface temperature. 2 Laboratory room walls are large compared to the spherical package. 3 Steady
state conditions.
W
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1-43
Surface temperature, °C
40 50 60 70 80 90
Power dissipation, W
2
4
6
8
10
= 0.20
= 0.25
= 0.30
Family of curves for power dissipation (
W
) versus surface temperature (Ts) for different values of emissivity ()
Discussion:
(1) As expected, the internal power dissipation increases with increasing emissivity and surface temperature. Because the
radiation rate equation is non-linear with respect to temperature, the power dissipation will likewise not be linear with surface
W
W
W
W
W
1-44
Simultaneous Heat Transfer Mechanisms
1-84C All three modes of heat transfer cannot occur simultaneously in a medium. A medium may involve two of them
simultaneously.
1-86C The human body loses heat by convection, radiation, and evaporation in both summer and winter. In summer, we can
1-45
1-88 The right surface of a granite wall is subjected to convection heat transfer while the left surface is maintained as a
constant temperature. The right wall surface temperature and the heat flux through the wall are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer through the granite wall is one dimensional. 3 Thermal
conductivity of the granite wall is constant. 4 Radiation hest transfer is negligible.
Analysis The heat transfer through the wall by conduction is equal to heat transfer to the outer wall surface by convection:
+
−=
−
=
1
2
21
convcond
)/(
)(
hTLkT
TTh
L
TT
k
qq
Granite
20 cm
1-46
1-89 The upper surface of a solid plate is being cooled by air. The air convection heat transfer coefficient at the upper plate
surface is to be determined.
1-90 Air is blown over a hot horizontal plate which is maintained at a constant temperature. The surface also loses heat by
radiation. The inside plate temperature is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer through the steel plate is one dimensional. 3 Thermal
conductivity of the steel plate is constant.
Analysis The heat transfer by conduction through the plate is equal to the sum of convection and radiation heat loses:
radconvcond QQQ +=
where
W300
W2185K)20250()m38.0()KW/m25()( 22
=
=−=−=
rad
sconv
Q
TThAQ
Then,
W2485W300W2185 =+=
−
=L
TT
kAQsi
cond
Solving for the inside plate temperature
C253=
+=+= )m38.0()KW/m43(
)m02.0()W2485(
C250 2
kA
LQ
TT cond
si
Discussion Heat loss by convection is much more dominant than heat loss by radiation. If we had not accounted for the heat
loss by radiation in our calculation, the inside plate temperature would be 252.7ºC, which is only 0.3ºC less than the actual
value. In this case we could have neglected the heat loss by radiation.
Ts =250C
Air, 20C
Steel Plate
Ti =?
1-47
1-91 For an electronic package with given surface area, power dissipation, surface emissivity and absorptivity to solar
radiation and the solar flux, the surface temperature with and without incident solar radiation is to be determined.
Assumptions 1 Steady operating conditions exist.
Analysis Apply conservation of energy (heat balance) to a control volume about the electronic package in rate form
in
Q
–
out
Q
+
gen
E
=
stored
E
= 0
With the solar input, we have
Surface, As= 1 m2,
= 1.0, s= 0.25
.
qs= 750 W/m2
.
1-48
1-92 Two large plates at specified temperatures are held parallel to each other. The rate of heat transfer between the plates is
to be determined for the cases of still air, evacuation, regular insulation, and super insulation between the plates.
Assumptions 1 Steady operating conditions exist since the plate temperatures remain constant. 2 Heat transfer is one-
dimensional since the plates are large. 3 The surfaces are black and thus = 1. 4 There are no convection currents in the air
space between the plates.
Properties The thermal conductivities are k = 0.00015 W/mC for super insulation, k = 0.01979 W/mC at –50C (Table A-
15) for air, and k = 0.036 W/mC for fiberglass insulation (Table A-6).
Analysis (a) Disregarding any natural convection currents, the rates of conduction and
radiation heat transfer
W511=+=+=
=−=
−=
=
−
=
−
=
−
372139
W372)K 150()K 290()m1)(K W/m1067.5(1
)(
W139
m 0.02
K )150290(
)m C)(1 W/m01979.0(
radcondtotal
442428
4
2
4
1rad
22
21
cond
QQQ
TTAQ
L
TT
kAQ
s
(b) When the air space between the plates is evacuated, there will be radiation heat
transfer only. Therefore,
W372== radtotal QQ
(c) In this case there will be conduction heat transfer through the fiberglass insulation
only,
W252=
−
=
−
== m 0.02
K )150290(
)m C)(1 W/m036.0( 2o
21
condtotal L
TT
kAQQ
(d) In the case of superinsulation, the rate of heat transfer will be
W1.05=
−
=
−
== m 0.02
K )150290(
)m C)(1 W/m00015.0( 2
21
condtotal L
TT
kAQQ
Discussion Note that superinsulators are very effective in reducing heat transfer between to surfaces.
Q
·
T1
T2
2 cm
1-49
1-93 The upper surface temperature of a silicon wafer undergoing heat treatment in a vacuum chamber by infrared heater is
to be determined.
Assumptions 1 Steady operating conditions exist. 2 Radiation heat transfer between upper wafer surface and surroundings is
between a small object and a large enclosure. 3 One-dimensional conduction in wafer. 4 The silicon wafer has constant
properties. 5 No hot spot exists on the wafer.
Properties The thermal conductivity of silicon at 1000 K is 31.2 W/m ∙ K (Table A-3).
Analysis The heat transfer through the thickness of the wafer by conduction is equal to net heat transfer at the upper wafer
1-94 The total rate of heat transfer from a person by both convection and radiation to the surrounding air and surfaces at
specified temperatures is to be determined.
Assumptions 1 Steady operating conditions exist. 2 The person is
completely surrounded by the interior surfaces of the room. 3 The
surrounding surfaces are at the same temperature as the air in the
room. 4 Heat conduction to the floor through the feet is negligible. 5
The convection coefficient is constant and uniform over the entire
surface of the person.
Tsurr
Qrad
23C
1-50
1-95E A spherical ball whose surface is maintained at a temperature of 170°F is suspended in the middle of a room at 70°F.
The total rate of heat transfer from the ball is to be determined.
Assumptions 1 Steady operating conditions exist since the ball surface and
the surrounding air and surfaces remain at constant temperatures. 2 The
thermal properties of the ball and the convection heat transfer coefficient are
constant and uniform.
Properties The emissivity of the ball surface is given to be = 0.8.
1-96 A 1000-W iron is left on the iron board with its base exposed to the air at 20°C. The temperature of the base of the iron
is to be determined in steady operation.
Assumptions 1 Steady operating conditions exist. 2 The thermal
properties of the iron base and the convection heat transfer coefficient are
constant and uniform. 3 The temperature of the surrounding surfaces is
the same as the temperature of the surrounding air.
Air
70F
170F
Iron
1000 W
1-51
1-97 A series of ASTM B21 naval brass bolts are bolted on the upper surface of a plate. The upper surface is exposed to
convection with air and radiation with the surrounding surface. Determine whether the use of the bolts complies with the
ASME Code for Process Piping, where 149°C is the maximum use temperature for ASTM B21 bolts.
Assumptions1 Heat transfer is steady. 2 Kirchhoff’s law is applicable. 3 Surrounding surface is treated as blackbody. 4
Uniform surface temperature at the upper plate surface. 5 The temperature of the bolts is equal to the upper plate surface
temperature.
Properties The emissivity of the plate and bolts is given as 0.3.
Well-insulated surface
Air, T∞, h
Bolt
Surface, Ts,
Surrounding, Tsurr
1-52
1-98 A spherical tank located outdoors is used to store iced water at 0C. The rate of heat transfer to the iced water in the
tank and the amount of ice at
0C
that melts during a 24-h period are to be determined.
Assumptions 1 Steady operating conditions exist since the surface temperatures of the wall remain constant at the specified
values. 2 Thermal properties of the tank and the convection heat transfer coefficient is constant and uniform. 3 The average
surrounding surface temperature for radiation exchange is 15C. 4 The thermal resistance of the tank is negligible, and the
entire steel tank is at 0C.
Properties The heat of fusion of water at atmospheric pressure is
kJ/kg 7.333=
if
h
. The emissivity of the outer surface of the tank is 0.75.
1 cm
0C
Iced
Air
25C
1-53
1-99 A draw batch furnace front is subjected to uniform heat flux on the inside surface, while the outside surface is subjected
to convection and radiation heat transfer. The outside surface temperature is to be determined.
Assumptions 1 Heat conduction is steady. 2 One dimensional heat conduction across the furnace front thickness. 3 Uniform
heat flux on inside surface.
Properties Emissivity and convective heat transfer coefficient are given to be 0.23 and 12 W/m2∙K, respectively.
Analysis The uniform heat flux subjected on the inside surface is equal to the sum of heat fluxes transferred by convection
and radiation on the outside surface
4
1-54
1-100 A flat-plate solar absorber is exposed to an incident solar radiation. The efficiency of the solar absorber (the ratio of
the usable heat collected by the absorber to the incident solar radiation on the absorber) is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Temperature at the surface remained constant.
Properties The absorber surface has an absorptivity of 0.93 and an emissivity of 0.9.
Analysis The rate of usable heat at the absorber plate can be expressed as
1-55
1-101 A flat-plate solar collector is used to heat water. The temperature rise of the water heated by the net heat rate from the
solar collector is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Specific heat of water is constant. 3 Temperature at the surface remained
constant. 4 Conduction through the solar absorber is negligible. 5 Heat loss through the sides and back of the absorber is
negligible.
Properties The absorber surface has
an absorptivity of 0.9 and an
emissivity of 0.9. The specific heat
of water is given as 4.2 kJ/kg∙K.
Analysis The net heat rate absorbed
by the solar collector is
1-56
1-102 A draw batch furnace front is subjected to uniform heat flux on the inside surface, while the outside surface is
subjected to convection and radiation heat transfer. The outside surface temperature is to be determined whether it is below
50°C or not.
Assumptions 1 Heat conduction is steady. 2 One dimensional heat conduction across the furnace front thickness. 3 Uniform
heat flux on inside surface.
Properties Emissivity and convective heat transfer coefficient are given to be 0.7 and 15 W/m2∙K, respectively.
Analysis The uniform heat flux subjected on the inside surface is equal to the sum of heat fluxes transferred by convection
and radiation on the outside surface
4
1-103E A flat plate solar collector is placed horizontally on the roof of a house. The rate of heat loss from the collector by
convection and radiation during a calm day are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The emissivity and convection heat transfer coefficient are constant and
uniform. 3 The exposed surface, ambient, and sky temperatures remain constant.
Properties The emissivity of the outer surface of the collector is given to be 0.9.
Analysis The exposed surface area of the collector is
2
ft 75ft) ft)(15 5( ==
s
A
Noting that the exposed surface temperature of the collector is 100F,
the total rate of heat loss from the collector to the environment by
convection and radiation becomes
Btu/h 5625F)70100)(ft F)(75Btu/h.ft 5.2()(
44428–244
22
conv
=−=−=
ss
TThAQ
radconvtotal QQQ
Q
Solar
collector
Tsky = 50F
Air, 70F
1-57
1-104 Temperature of the stainless steel sheet going through an annealing process inside an electrically heated oven is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Temperature of the stainless steel sheet is uniform. 3 Radiation heat
transfer between stainless steel sheet and surrounding oven surfaces is between a small object and a large enclosure.
Properties The emissivity of the stainless steel sheet is given to be 0.40.
1-58
1-105 The roof of a house with a gas furnace consists of a 15-cm thick concrete that is losing heat to the outdoors by
radiation and convection. The rate of heat transfer through the roof and the money lost through the roof that night during a
14 hour period are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The emissivity and thermal conductivity of the roof are constant.
Properties The thermal conductivity of the concrete is given to be k = 2 W/mC. The emissivity of the outer surface of the
roof is given to be 0.9.
Analysis In steady operation, heat transfer from the outer surface of the roof to the surroundings by convection and radiation
must be equal to the heat transfer through the roof by conduction. That is,
1-59
1-106 A nonmetal plate and an ASME SA-240 stainless steel plate are bolted together by ASTM B21 naval brass bolts.
The bottom surface is subjected to uniform heat flux. The top surface is exposed to convection and radiation heat transfer.
Determine whether the ASME Boiler and Pressure Vessel Code and the ASME Code for Process Piping are being complied.
Assumptions1 Heat transfer is steady. 2 One dimensional heat conduction through the plates. 3 Uniform heat flux on bottom
surface. 4 Uniform surface temperatures. 5 No contact resistance at the interface.
Properties The thermal conductivities for the steel plate is given as k1 = 15 W/m·K and for the nonmetal plate as k2 = 0.05
W/m·K.
Uniform heat flux
Air, T∞, h
Bolt
Surrounding, Tsurr
Steel plate
Nonmetal plate
Surface 2, T2,
Surface 1, T1
Interface, Ti
1-60
1-107 The outer surface of a wall is exposed to solar radiation. The effective thermal conductivity of the wall is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 The heat transfer
coefficient is constant and uniform over the surface.
Properties Both the solar absorptivity and emissivity of the wall
surface are given to be 0.8.
44ºC
150 W/m2
27ºC