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SCHOOL OF CHEMICAL AND BIOMEDICAL
ENGINEERING (Division of Chemical & Biomolecular Engineering)
Nanyang Technological
University
Yr 2 / SEMESTER 2
N1.2-B4-16
CH2702
Experiment C5
Forced Convection
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Name: Le Vu Anh Phuong Student ID: U1320848B Group: 14 Date: 3/2/15
Experiment description
The experiments aim to calculate the heat transfer coefficients h of forced convection for a
heated cylinder under cross air flow, and compare with that obtained from theoretical formula
with empirical corrections. Experimental h can be computed based on power delivered to the
heater, area of heat transfer and the temperature difference. To compare that with the
theoretical model, Nusselt numbers using experimental data and theoretical model are
calculated and plotted as a function of Reynolds numbers. From here h from both models can be
obtained and compared at each Re number.
Pre-laboratory problems:
1).
Forced convection: fluid movement caused by external forces such as a fan, pump, wind, ect.
Natural convection: fluid movement caused by its own density differences within the fluid body,
leading to buoyancy forces acting on fluid elements.
2).
๐๐ข =โ๐ฟ
๐
๐ ๐ =๐๐ ๐
๐
๐๐ =๐ถ๐๐
๐
All are dimentionless
3).
Nusselt number: the measure of convection heat transfer
Reynolds number: the ratio of inertial force to viscous force in fluid
Prandtl number: ratio of momentum diffusivity to thermal diffusivity.
4).
a.
๐๐ =๐ถ๐๐
๐=
1007 ร 184.6 ร 10โ7
26.3 ร 10โ3= 0.7068
b.
๐๐ =๐ถ๐๐
๐=
1004 ร 230.1 ร 10โ7
33.8 ร 10โ3= 0.6903
c.
๐ ๐ =๐๐ท๐
๐=
5 ร 0.02 ร 1.1614
184.6 ร 10โ7= 6291
d.
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๏ฟฝฬ ๏ฟฝ๐ข๐ท = ๐ถ๐ ๐๐ท๐๐๐๐ (
๐๐
๐๐๐)
14
= 0.26 ร 62910.6 ร 0.70680.37 ร (0.7068
0.6903)
14
= 43.75
โฬ =๐๏ฟฝฬ ๏ฟฝ๐ข๐ท
๐ท=
0.0263 ร 43.75
0.0158= 72.8
5).
From equation 15 we have
1
2๐๐2 = โ๐๐ป2๐ => ๐ = โ
2โ๐๐ป2๐
๐
With the correction constant we have:
๐ = ๐ถ๐ทโ2โ๐๐ป2๐
๐= ๐ถ๐ทโ
2โ๐๐ป2๐๐ ๐โ
๐๐๐๐๐๐๐๐
Since 1mmH2O = 9.81 Pa we have
๐ = 0.98โ2 ร 9.81 ร 8.314 ร โ๐๐ป2๐๐โ
0.029 ร ๐๐๐๐= 73.48โ
โ๐๐ป2๐๐โ
๐๐๐๐
LOG SHEET Forced Convection Experiment
Atmospheric pressure pair = 101000 Pa
25V Speed (Hz) 20 25 30 35 40
Power P (W) 8.93 8.93 8.93 8.93 8.93
Air temperature Tโ (oC) 22.3 22.6 22.8 22.9 23.1
Surface temperature TS (oC) 48.4 46 44.1 42.6 41.6
ฮpH2O (mmH2O) 18 27 41 51 65
U 16.86 20.66 25.47 28.41 32.08
h 137.83 153.73 168.89 182.61 194.45
35V Speed (Hz) 20 25 30 35 40
Power P (W) 17.50 17.50 17.50 17.50 17.50
Air temperature Tโ (oC) 22.9 23.1 23.2 23.4 23.6
Surface temperature TS (oC) 74.4 66.8 64.4 60.3 58.2
ฮpH2O (mmH2O) 17 28 40 50 64
U 16.40 21.05 25.17 28.15 31.85
h 136.91 161.34 171.14 191.08 203.78
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Sample calculation: 20 Hz, 25 V
Air temperature Tโ(oC): 22.3
Surface temperature TS (oC): 48.4
Duct air velocity U (m/s): 16.86
Mass density of air ฯ at Tโ (kg/m3): 1.18
ยต viscosity of air at Tโ (kg/s.m): 182.5x10-7
ยต viscosity of air at TS (kg/s.m): 195x10-7
Reynolds number
๐ ๐๐ท =๐๐ท๐
๐=
16.86 ร 15.8 ร 10โ3 ร 1.18
182.5 ร 10โ7= 17192.8
Air thermal conductivity k in flow Tโ (W/m.K): 25.9x10-3
Air thermal conductivity k at surface TS (W/m.K): 27.875x10-3
Specific heat CP of air in flow Tโ (J/kg.K): 1006.875
Specific heat CP of air at surface TS (J/kg.K): 1007.625
Prandtl number in fluid:
๐๐ =๐ถ๐๐
๐=
1006.875 ร 182.5 ร 10โ7
25.9 ร 10โ3= 0.709
Prandtl number at surface:
๐๐ =๐ถ๐๐
๐=
1007.625 ร 195 ร 10โ7
27.875 ร 10โ3= 0.701
Calculated Nusselt number:
๐๐ข๐ทฬ ฬ ฬ ฬ ฬ ฬ = ๐ถ๐ ๐๐ท
๐๐๐๐ (๐๐
๐๐๐)
14
= 0.26 ร 17192.80.6 ร 0.7090.37 ร (0.709
0.701)
14
= 79.816
Experimental Nusselt number at Tโ:
๐๐ข๐ทฬ ฬ ฬ ฬ ฬ ฬ =
โฬ ๐ท
๐=
137.83 ร 0.0158
25.936 ร 10โ3= 83.96
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Discussion and conclusion
From both sets of experiments, both experimental and theoretical Nusselt number follow a
linear relation with the Reynolds number. The experimental Nu graph is consistently higher but
closed to the theoretical values. The discrepancy between them could have been due to
experimental errors. For instance the power delivered by the electrical source to the cylindrical
heater may be less than what indicated from the voltmeter, possibly due to internal resistance
of the instrument causing heat loss. This makes the calculated heat transfer coefficient
1.880
1.900
1.920
1.940
1.960
1.980
2.000
2.020
2.040
2.060
2.080
2.100
4.200 4.250 4.300 4.350 4.400 4.450 4.500 4.550
log1
0(N
u)
log10(Re)
25V
Theoretical Nu
Experimental Nu
1.880
1.900
1.920
1.940
1.960
1.980
2.000
2.020
2.040
2.060
2.080
2.100
2.120
4.200 4.250 4.300 4.350 4.400 4.450 4.500 4.550
log1
0(N
u)
log10(Re)
35V
Experimental Nu
Theoretical Nu
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consistently higher than its actual value and hence higher experimental ๏ฟฝฬ ๏ฟฝ๐ข. However the
experimental model to calculate average Nusselt number is still within good range of agreement
with the theoretical model.