21–41
21–73 Two view factors associated with three very long ducts with different geometries are to be determined.
21–42
Radiation Heat Transfer between Surfaces
rate of radiation heat transfer between two surfaces in this case is expressed as
)( 4
2
4
1121TTFAQ
where A1 is the
surface area, F12 is the view factor, and T1 and T2 are the temperatures of two surfaces.
radiation energy as well as reflected energy. Radiosity and emitted energy are equal for blackbodies since a blackbody does
not reflect any radiation.
ii
i
radiation. It is zero for black surfaces. The space resistance is the radiation resistance between two surfaces and is expressed
as
iji
ij FA
R1
back sides of these surfaces are well insulated and net heat transfer through these surfaces is zero. When the convection
effects on the front (heat transfer) side of such a surface is negligible and steady-state conditions are reached, the surface
must lose as much radiation energy as it receives. Such a surface is called reradiating surface. In radiation analysis, the
surface resistance of a reradiating surface is taken to be zero since there is no heat transfer through it.
and 21-35 give N linear algebraic equations for the determination of the N unknown radiosities for an N -surface enclosure.
Once the radiosities are available, the unknown surface temperatures and heat transfer rates can be determined from these
equations respectively. This method involves the use of matrices especially when there are a large number of surfaces.
Therefore this method requires some knowledge of linear algebra.
The network method involves drawing a surface resistance associated with each surface of an enclosure and
connecting them with space resistances. Then the radiation problem is solved by treating it as an electrical network problem
where the radiation heat transfer replaces the current and the radiosity replaces the potential. The network method is not
practical for enclosures with more than three or four surfaces due to the increased complexity of the network.
21–43
21–79 The rate of heat loss from a person by radiation in a large room whose walls are maintained at a uniform temperature is
to be determined for two cases.
Assumptions 1 Steady operating conditions exist. 2 The surfaces are opaque,
W30.1
])K 300()K 303)[(K W/m1067.5)(m 9.1)(1)(85.0(
)(
444282
4
2
4
1112112 TTAFQ
(b) When the walls are at a temperature of 280 K,
W209
])K 280()K 303)[(K W/m1067.5)(m 9.1)(1)(85.0(
)(
444282
4
2
4
1112112 TTAFQ
Qrad
21–46
21–82 Two coaxial parallel disks of equal diameter 1 m are originally placed at a distance of 1 m apart. The new distance
between the disks such that there is a 75% reduction in radiation heat transfer rate from the original distance of 1 m is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 The surfaces are black. 3 Convection heat transfer is not considered.
2
2
1
D
2
22
1
2
2)/(42
1
2
1
1DL
RR
R
S
(2)
D
21–48
21–84E For a square room with specified dimensions and floor, wall and ceiling temperatures, determine the net radiation
heat transfer (a) from floor to walls and (b) from floor to ceiling.
Assumptions 1 All surfaces are assumed black.
Analysis
4
4
21–50
21–86 The base and the dome of a long semi-cylindrical dryer are maintained at uniform temperatures. The drying rate per
unit length experienced by the base surface is to be determined.
Assumptions 1 Steady operating conditions exist. 2 The surfaces are black. 3 Convection heat transfer is not considered. 4
The dryer is well insulated from heat loss to the surrounding.
2
or
mkg/s 0.0370
444428
3
4
1
4
2
4
1
4
2
4
1
4
221
K )3701000)(K W/m1067.5(
)J/kg 102257(
m) 5.1(
)(
)(
2
2
)(
2
TT
h
D
TT
h
D
TTF
h
D
L
m
fg
fgfg
21–52
21–88 Two parallel disks whose back sides are insulated are black, and are maintained at a uniform temperature. The net rate
of radiation heat transfer from the disks to the environment is to be determined.
Assumptions 1 Steady operating conditions exist 2 The surfaces are opaque, diffuse, and gray. 3 Convection heat transfer is
21-7, we read
)rulesummation ( 74.026.01
26.0
13
2112
F
FF
The net rate of radiation heat transfer from the disks into the environment
W781
]K 300K 450)[K W/m1067.5]()m 3.0()[74.0(2
44
4282
21–89 The base and the dome of a hemispherical furnace are maintained at uniform temperatures. The net rate of radiation
heat transfer from the dome to the base surface is to be determined.
Assumptions 1 Steady operating conditions exist 2 The surfaces are
opaque, diffuse, and gray. 3 Convection heat transfer is not
considered.
T1 = 400 K
Environment
1 = 1
D = 0.6 m
T2 = 1000 K
21–53
21–90 The base and the dome of a long semi-cylindrical dryer are maintained at uniform temperatures. The length of the
dryer necessary to dry the materials at 0.1 kg/s is to be determined.
Assumptions 1 Steady operating conditions exist. 2 The surfaces are black. 3 Convection heat transfer is not considered. 4
The dryer is well insulated from heat loss to the surrounding.
Properties The latent heat of vaporization for water is hfg = 2257 kJ/kg (Table A-3)
m 5.73
444428
3
K )313773)(K W/m1067.5)(m 2(
)J/kg 102257)(kg/s 1.0(
Discussion The view factor from the dome to the base is constant F21 = 2/π, which implies that the view factor is independent
of the dryer dimensions.
21–55
21–92E A radiation shield is placed between two parallel disks which are maintained at uniform temperatures. The net rate of
radiation heat transfer through the shields is to be determined.
Assumptions 1 Steady operating conditions exist 2 The
surfaces are black. 3 Convection heat transfer is not
1 = 2 = 1 and 3 = 0.15.
black surfaces on both sides. Therefore, heat transfer between
T1 = 1200 R, 1 = 1
1 ft
1 ft
3 = 1
21–56
21–93 The radiation heat flux between two infinitely long parallel plates of specified surface temperatures is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 The surfaces are black. 3 Convection heat transfer is not considered. 4
204.0
2
w
The radiation heat flux between the two surfaces is
444428
4
2
4
11212
)( TTFq
21–59
21–96 Two perpendicular rectangular surfaces with a common edge are maintained at specified temperatures. The net rate of
radiation heat transfers between the two surfaces and between the horizontal surface and the surroundings are to be
determined.
21–60
21–97 A furnace shaped like a long equilateral-triangular duct is considered. The temperature of the base surface is to be
determined.
Assumptions 1 Steady operating conditions exist 2 The surfaces are opaque, diffuse, and gray. 3 Convection heat transfer is
not considered. 4 End effects are neglected.
Properties The emissivities of surfaces are given to be 1 = 0.8 and 2 = 0.4.