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8-62
ṁ [kg/s] V∞ [m/s]
0.5 1.393
0.6 2.087
0.7 2.961
0.8 4.034
0.9 5.331
1.0 6.876
1.1 8.696
1.2 10.82
1.3 13.29
1.4 16.13
1.5 19.39
1.6 23.11
1.7 27.33
1.8 32.13
1.9 37.54
2.0 43.65
2.1 50.53
2.2 58.26
2.3 66.92
2.4 76.64
Discussion As the mass flow rate of the glycerin increases, the free-stream velocity of the H2 gas needs to increase as well in
order to keep Te = 40°C
0 0.5 1 1.5 2 2.5 3
0
10
20
30
40
50
60
70
80
90
m [kg/s]
V¥ [m/s]
8-65
8-81 Air is being heated by constant wall temperature over the first 2 m of the pipe and then the heating takes place by
constant heat flux. The air temperature at the 2 m length, the air temperature at the exit, the total heat transfer to the air, and
the wall temperature at the exit of the tube are to be determined.
Assumptions 1 The flow issteady. 2 The flow is fully developed. 3 The air in first half of the pipe is being heat at constant
wall temperature. 4 The air in second half of the pipe is being heated by constant heat flux. 5 The pipe wall is smooth.
Properties The properties of air at80C are (Table A-15):
= 0.9994 kg/m3, k = 0.02953 W/mK,
= 2.097 10-5 m2/s, cp =
1008 J/kgK, and Pr=0.7154
Analysis (a) First the cross sectional and surface areas will be determined.
8-71
8-86 Air flows in a pipe whose inner surface is not smooth. The rate of heat transfer is to be determined using two different
Nusselt number relations.
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The pressure of air is 1 atm.
Properties Assuming a bulk mean fluid temperature of 20C based on the problem statement, the properties of air are (Table
A-15)
7309.0Pr
CJ/kg. 1007
/sm 10516.1
C W/m.02514.0
kg/m 204.1
25-
3
=
=
=
=
=
p
c
k
Analysis The mean velocity of air and the Reynolds number are
kg/s 065.0
m
Air
10ºC
0.065 kg/s
L = 5 m
D = 12 cm
8-78
8-93 Air (1 atm) enters into a 5-cm diameter circular tube at 20°C with an average velocity of 5 m/s. The length of the tube is
to be determined.
Assumptions 1 Steady operating conditions exist. 2 Properties are constant. 3 Constant tube surface temperature.
Properties The properties of air at Tb = (Ti + Te)/2 = 50°C: cp = 1007 J/kg∙K, k = 0.02735 W/m∙K,
= 1.092 kg/m3,
= 1.963
10−5 kg/m∙s,
= 1.798 10−5 m2/s, and Pr = 0.7228 (Table A-15).
Analysis The Reynolds number is
)m 05.0)(m/s 5(
avg =
DV
