7-136
7-136 A cylindrical rod is placed in a cross flow of air, (a) the average drag coefficient, (b) the convection heat transfer
coefficient using the Churchill and Bernstein relation, and (c) the convection heat transfer coefficient using Table 7-1 are to
be determined.
Assumptions 1 Steady operating conditions exist. 2 Properties are constant. 3 The surface temperature is constant.
Properties The properties of air (1 atm) at Tf = (120°C + 20°C)/2 =70°C are given in Table A-15: k = 0.02881 W/m∙K,
=
1.995 10−5 m2/s, and Pr = 0.7177.
Analysis (a) The Reynolds number for the air flowing across the rod is
)m 005.0)(m/s 10(
VD
K W/m148.3 2=
(c) Using Table 7-1, the relation for Nusselt number with Re = 2506 is
3/1466.0
hD
7-137
7-137 A spherical tank used to store iced water is subjected to winds. The rate of heat transfer to the iced water and the
amount of ice that melts during a 24-h period are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Thermal resistance of the tank is negligible. 3 Radiation effects are
negligible. 4 Air is an ideal gas with constant properties. 5 The pressure of air is 1 atm.
Properties The properties of air at 1 atm pressure and the free stream temperature of 30C are (Table A-15)
7282.0Pr
kg/m.s 10729.1
kg/m.s 10872.1
/sm 10608.1
C W/m.02588.0
5
C0@
,
5
25–
=
=
=
=
=
−
−
s
k
Analysis (a) The Reynolds number is
52
(8 1000/3600) m /s (0.57 m )
Re 78,773
1.608 10 m /s
VD
n–
éù
´
ëû
= = =
´
The Nusselt number corresponding to this Reynolds number is determined from
1/4
0.5 2/3 0.4
1/4
5
0.5 2/3 0.4
5
2 0.4Re 0.06Re Pr
1.872 10
2 0.4(78,773) 0.06(78,773) (0.7282)
1.729 10
201.9
s
hD
Nu k
m
m
¥
–
–
æö
÷
ç
éù
÷
= = + + ç ÷
êú
ç÷
ëû
÷
ç
èø
æö
´÷
ç
éù
÷
ç
= + + ÷
ç
êú
÷
ëû
ç÷
´
èø
=
and
2
0.02588 W /m .C (201.9) 9.167 W /m .C
0.57 m
k
h Nu
D
°
= = = °
The rate of heat transfer to the iced water is
2 2 2
( ) ( )( ) (9.167 W /m .C)[ (0.57 m ) ](30 0)C
s s s
Q hA T T h D T Tpp
¥¥
= – = – = ° – ° = 280.7 W
(b) The amount of heat transfer during a 24-hour period is
333.7 kJ/kg
if
if
1 cm
Di = 0.55 m
Iced water
0C
Q
Ts = 0C
V = 8 km/h
T = 30C
7-139
7-139 Air is heated by an array of electrical heating elements. The rate of heat transfer to air and the exit temperature of air
are to be determined.
Assumptions 1 Steady operating conditions exist.
Properties The exit temperature of air, and thus the mean temperature, is not known. We evaluate the air properties at the
assumed mean temperature of 35C (will be checked later) and 1 atm (Table A-15):
k = 0.02625 W/m-K = 1.145 kg/m3
cp =1.007 kJ/kg-K Pr = 0.7268
= 1.89510-5 kg/m-s Prs = Pr@ Ts = 0.6937
Also, the density of air at the inlet temperature of 25C (for use in the mass flow rate calculation at the inlet) is
i = 1.184
kg/m3.
Analysis It is given that D = 0.012 m, SL = ST = 0.024 m, and V = 8 m/s. Then the maximum velocity and the Reynolds
number based on the maximum velocity become
m/s 16m/s) 8(
1224
24
max =
−
=
−
=V
DS
S
V
T
T
600,11
skg/m 10895.1
m) m/s)(0.012 16)(kg/m 145.1(
Re 5
3
max =
== −
DV
D
The average Nusselt number is determined using the proper relation from Table 7-2 to be
55.88)6937.0/7268.0()7268.0()600,11(27.0
)Pr(Pr/PrRe27.0Nu
25.036.063.0
25.036.063.0
==
=sDD
This Nusselt number is applicable to tube banks with NL > 16. In our case the number of rows is NL = 3, and the
corresponding correction factor from Table 7-3 is F = 0.86. Then the average Nusselt number and heat transfer coefficient
for all the tubes in the tube bank become
15.76)55.88)(86.0(NuNu ,=== DND F
L
C W/m6.166
m 0.012
C) W/m02625.0(15.76 2
,=
== D
kNu
hL
ND
The total number of tubes is N = NL NT = 34 = 12. The heat transfer surface area and the mass flow rate of air (evaluated at
the inlet) are
2
m 09048.0 m) m)(0.200 012.0(12 ===
DLNAs
kg/s 1819.0m) m)(0.200 024m/s)(4)(0. 8)(kg/m 184.1()( 3==== LSNVmm TTii
Then the fluid exit temperature, the log mean temperature difference, and the rate of heat transfer become
C67.50
C)J/kg kg/s)(1007 (0.1819
C) W/m6.166)(m 09048.0(
exp)25350(350exp)(
22
=
−−−=
−−−=
p
s
isse cm
hA
TTTT
C0.312
)]67.50350/()25350ln[(
)67.50350()25350(
)]/()ln[(
)()( =
−−
−−−
=
−−
−−−
=
esis
esis
lm TTTT
TTTT
T
W4703=== )C0.312)(m C)(0.09048 W/m6.166(22
lmsThAQ
Air
Ti = 25C
V = 8 m/s
D = 12 mm
(L = 200 mm)
24 mm
24 mm
Ts = 350C
To
7-140
Fundamentals of Engineering (FE) Exam Problems
7-140 For laminar flow of a fluid along a flat plate, one would expect the largest local convection heat transfer coefficient for
the same Reynolds and Prandtl numbers when
(a) The same temperature is maintained on the surface
(b) The same heat flux is maintained on the surface
(c) The plate has an unheated section
(d) The plate surface is polished
(e) None of the above
7-141 Air at 20ºC flows over a 4-m long and 3-m wide surface of a plate whose temperature is 80ºC with a velocity of 7 m/s.
The length of the surface for which the flow remains laminar is
(a) 0.9 m (b) 1.3 m (c) 1.8 m (d) 2.2 m (e) 3.7 m
(For air, use k = 0.02735 W/m°C, Pr = 0.7228, =1.79810-5 m2/s.)
7-142
7-143 Engine oil at 105ºC flows over the surface of a flat plate whose temperature is 15ºC with a velocity of 1.5 m/s. The
local drag force per unit surface area 0.8 m from the leading edge of the plate is
(a) 21.8 N/m2 (b) 14.3 N/m2 (c) 10.9 N/m2 (d) 8.5 N/m2 (e) 5.5 N/m2
(For oil, use =8.56510-5 m2/s,
= 864 kg/m3.)
7-144 Air (k = 0.028 W/mK, Pr = 0.7) at 50oC flows along a 1 m long flat plate whose temperature is maintained at 20oC
with a velocity such that the Reynolds number at the end of the plate is 10,000. The heat transfer per unit width between the
plate and air is
(a) 20 W/m (b) 30 W/m (c) 40 W/m (d) 50 W/m (e) 60 W/m
7-143
7-145 Air at 15ºC flows over a flat plate subjected to a uniform heat flux of 240 W/m2 with a velocity of 3.5 m/s. The surface
temperature of the plate 6 m from the leading edge is
(a) 40.5ºC (b) 41.5ºC (c) 58.2 ºC (d) 95.4ºC (e) 134ºC
(For air, use k=0.02551 W/m°C, Pr = 0.7296, =1.56210-5 m2/s.)
7-145
7-147 Water at 75ºC flows over a 2-m-long, 2-m-wide surface of a plate whose temperature is 5ºC with a velocity of 1.5 m/s.
The total drag force acting on the plate is
(a) 2.8 N (b) 12.3 N (c) 13.7 N (d) 15.4 N (e) 20.0 N
(For air, use = 0.65810-6 m2/s,
= 992 kg/m3.)
7-146
7-148 Air at 25ºC flows over a 5–cm-diameter, 1.7-m-long smooth pipe with a velocity of 4 m/s. A refrigerant at -15ºC flows
inside the pipe and the surface temperature of the pipe is essentially the same as the refrigerant temperature inside. The drag
force exerted on the pipe by the air is
(a) 0.4 N (b) 1.1 N (c) 8.5 N (d) 13 N (e) 18 N
(For air, use =1.38210-5 m2/s,
= 1.269 kg/m3.)
7-149 Air at 25ºC flows over a 4–cm-diameter, 1.7-m-long pipe with a velocity of 4 m/s. A refrigerant at −15ºC flows inside
the pipe and the surface temperature of the pipe is essentially the same as the refrigerant temperature inside. Air properties at
the average temperature are k=0.0240 W/m°C, Pr = 0.735, = 1.38210-5 m2/s. The rate of heat transfer to the pipe is
(a) 126 W (b) 245 W (c) 302 W (d) 415 W (e) 556 W
7-147
7-150 Kitchen water at 10ºC flows over a 10-cm-diameter pipe with a velocity of 1.1 m/s. Geothermal water enters the pipe
at 90ºC at a rate of 1.25 kg/s. For calculation purposes, the surface temperature of the pipe may be assumed to be 70ºC. If the
geothermal water is to leave the pipe at 50ºC, the required length of the pipe is
(a) 1.1 m (b) 1.8 m (c) 2.9 m (d) 4.3 m (e) 7.6 m
(For both water streams, use k = 0.631 W/m°C, Pr = 4.32, =0.65810-6 m2/s, cp= 4179 J/kg°C.)
7-148
7-151 Wind at 30ºC flows over a 0.5-m-diameter spherical tank containing iced water at 0ºC with a velocity of 25 km/h. If
the tank is thin-shelled with a high thermal conductivity material, the rate at which ice melts is
(a) 4.78 kg/h (b) 6.15 kg/h (c) 7.45 kg/h (d) 11.8 kg/h (e) 16.0 kg/h
(Take hif= 333.7 kJ/kg and use the following for air: k=0.02588 W/m°C, Pr = 0.7282, =1.60810-5 m2/s,
=1.87210-5
kg/ms,
s = 1.72910-5 kg/ms)
