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13-134
13-155 Combustion gases flow inside a tube in a boiler. The rates of heat transfer by convection and radiation and the rate of
evaporation of water are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The inner surfaces of the duct are smooth. 3 Combustion gases are
/sm 10395.0/s)/3m 10185.1(
24-24-
===
7107.0Pr
CJ/kg. 1140
=
=
p
c
Analysis (a) The Reynolds number is
m) m/s)(0.15 (3
avg =
DV
m 5.1m) 15.0(1010 == DLL th
52.36)7107.0()392,11(023.0PrRe023.0 3.08.03.08.0 ==== k
hD
Nu h
Ts = 105C
D = 15 cm
Combustion
gases, 3 atm
Ti = 1000 K
3 m/s
13-135
Then the effective emissivity of the combustion gases becomes
0.2020.0068.08.1053.05.1
atm 1 ,atm 1 , =−+=−+=
wwccg CC
1568.0)065.0(
K 378
K 725
)8.1(
0916.0)040.0(
K 378
K 725
)5.1(
45.0
atm 1 ,
45.0
65.0
atm 1 ,
65.0
=
=
=
=
=
=
w
s
g
ww
c
s
g
cc
T
T
C
T
T
C
13-136
Fundamentals of Engineering (FE) Exam Problems
13-156 Consider an infinitely long three-sided triangular enclosure with side lengths 5 cm, 3, cm, and 4 cm. The view factor
from the 5 cm side to the 4 cm side is
(a) 0.3 (b) 0.4 (c) 0.5 (d) 0.6 (e) 0.7
13-157 Consider a 15-cm-diameter sphere placed within a cubical enclosure with a side length of 15 cm. The view factor
from any of the square cube surface to the sphere is
s=0.15 [m]
A1=pi*D^2
13-137
13-158 A 90-cm-diameter flat black disk is placed in the center of the top surface of a 1 m 1 m 1 m black box. The view
factor from the entire interior surface of the box to the interior surface of the disk is
d=0.9 [m]
A1=pi*d^2/4 [m^2]
13-159 Consider two concentric spheres with diameters 12 cm and 18 cm, forming an enclosure. The view factor from the
inner surface of the outer sphere to the inner sphere is
D2=0.18 [m]
A1=pi*D1^2
A2=pi*D2^2
13-160 The number of view factors that need to be evaluated directly for a 10-surface enclosure is
(a) 1 (b) 10 (c) 22 (d) 34 (e) 45
13-138
13-161 Consider two concentric spheres forming an enclosure with diameters 12 and 18 cm and surface temperatures 300 and
500 K, respectively. Assuming that the surfaces are black, the net radiation exchange between the two spheres is
D2=0.18 [m]
T1=300 [K]
T2=500 [K]
13-162 Consider a vertical 2-m-diameter cylindrical furnace whose surfaces closely approximate black surfaces. The base,
top, and side surfaces of the furnace are maintained at 400 K, 600 K, and 1200 K, respectively. If the view factor from the
base surface to the top surface is 0.2, the net radiation heat transfer between the base and the side surfaces is
(a) 73 kW (b) 126 kW (c) 215 kW (d) 292 kW (e) 344 kW
13-139
13-163 Consider a vertical 2-m-diameter cylindrical furnace whose surfaces closely approximate black surfaces. The base,
top, and side surfaces of the furnace are maintained at 400 K, 600 K, and 900 K, respectively. If the view factor from the base
surface to the top surface is 0.2, the net radiation heat transfer from the bottom surface is
(a) -93.6 kW (b) -86.1 kW (c) 0 kW (d) 86.1 kW (e) 93.6 kW
Answer (a) -93.6 kW
13-164 A solar flux of 1400 W/m2 directly strikes a space vehicle surface which has a solar absortivity of 0.4 and thermal
emissivity of 0.6. The equilibrium temperature of this surface in space at 0 K is
e=0.6
13-140
13-165 A 70-cm-diameter flat black disk is placed at the center of the ceiling a 1 m 1 m 1 m black box. If the
temperature of the box is 620oC and the temperature of the disk is 27oC, the rate of heat transfer by radiation between the
d=0.7 [m]
A1=pi*d^2/4 [m^2]
13-166 Consider two infinitely long concentric cylinders with diameters 20 and 25 cm. The inner surface is maintained at 700
K and has an emissivity of 0.40 while the outer surface is black. If the rate of radiation heat transfer from the inner surface to
D2=0.25 [m]
T1=700 [K]
epsilon_1=0.40
13-141
13-167 Consider a surface at 0ºC that may be assumed to be a blackbody in an environment at 25ºC. If 300 W/m2 radiation is
incident on the surface, the radiosity of this black surface is
(a) 0 W/m2 (b) 15 W/m2 (c) 132 W/m2 (d) 300 W/m2 (e) 315 W/m2
Answer (e) 315 W/m2
13-168 Consider a gray and opaque surface at 0ºC in an environment at 25ºC. The surface has an emissivity of 0.8. If the
radiation incident on the surface is 240 W/m2, the radiosity of the surface is
(a) 38 W/m2 (b) 132 W/m2 (c) 240 W/m2 (d) 300 W/m2 (e) 315 W/m2
Answer (d) 300 W/m2
