The experiment was carried out to verify the relationship between Nusselt number , Reynolds number and Prandtl Number using the different concepts of convection. Relative discussions and conclusions
were drawn including the various factors affecting the accuracy of the calculated results.
The main objective of this experiment was to verify the following heat transfer relationship:
Therefore, the experiment is conducted by an apparatus where hot ait from heater is generated and flow through copper tube. Different values of temperatures and pressure were taken and recorded in order to calculate. Besides, graphs plotted and analysed to have a better understanding of convection heat transfer.
Thus a Laboratory experiment was conducted where hot air from a heater was introduced through a copper tube with the help of a blower. Thermocouples were fixed in placed at various locations along the length of the copper tube. The different values of temperature and pressure were measured along with the various sections of the tube and other required values were recorded and calculated. Graphs were also plotted with the data obtained and then analysed.
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INTRODUCTION
Heat transfer science deals with the time rate of energy transfer and the temperature distribution through the thermal system. It may be take place in three modes which is conduction, convection and radiation. Theory of convection is presented since this experiment is concerned about convective heat transfer. Convective is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion due to a temperature difference. It involves the combined effects of conduction and fluid motion.
There are two major type of convective
Forced convection is known as fluid motion generated by blowing air over the solid by using external devices such as fans and pumps.
The other type is natural convection which meant by a phenomenon that occurs in fluid segments and facilitated by the buoyancy effect. It is less efficient than forced convection, due to the absence of fluid motion. Hence, it depends entirely on the strength of the buoyancy effect and the fluid viscosity. Besides, there is no control on the rate of heat transfer.
Forced Convection
Force convection is a mechanism of heat transfer in which fluid motion is generated by an external source like a pump, fan, suction device, etc. Forced convection is often encountered by engineers designing or analyzing pipe flow, flow over a plate, heat exchanger and so on.
Convection heat transfer depends on fluids properties such as:
Dynamic viscosity (µ)
Thermal conductivity (k)
Density (Ï)
Specific heat (Cp)
Velocity (V)
Type of fluid flow (Laminar/Turbulent)
Newton’s law of cooling
Where
h = Convection heat transfer (W/(m2.°C)
A = Heat transfer area
= Temperature of solid surface (°C)
= Temperature of the fluid (°C)
The convective heat transfer coefficient (h) is dependent upon the physical properties of the fluid and the physical situation.
Applications of Forced Convection
In a heat transfer analysis, engineers get the velocity result by performing a fluid flow analysis. The heat transfer results specify temperature distribution for both the fluid and solid components in systems such as fan or heat exchanger. Other applications for forced convection include systems that operate at extremely high temperatures for functions for example transporting molten metal or liquefied plastic. Thus, engineers can determine what fluid flow velocity is necessary to produce the desired temperature distribution and prevent parts of the system from failing. Engineers performing heat transfer analysis can simply click an option to include fluid convection effects and specify the location of the fluid velocity results during setup to yield forced convection heat transfer results.
TYPICAL APPLICATIONS
Computer case cooling
Cooling/heating system design
Electric fan simulation
Fan- or water-cooled central processing unit (CPU) design
Heat exchanger simulation
Heat removal
Heat sensitivity studies
Heat sink simulation
Printed Circuit Board (PCB) simulation
Thermal optimization
Forced Convection through Pipe/Tubes
In a flow in tupe, the growth of the boundary layer is limited by the boundary of the tube. The velocity profile in the tube is characterized by a maximum value at the centerline and zero at the boundary.
For a condition where the tube surface temperature is constant, the heat transfer rate can be calculated from Newton’s cooling law.
Reynolds Number
Reynolds number can be used to determine type of flow in fluid such as laminar or turbulent flow. Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant. The condition of flow is smooth and constant fluid motion. Meanwhile, turbulent flow occurs at high Reynolds number and is dominated by inertial forces and it produce random eddies, vortices and other flow fluctuations.
Reynolds number is a dimensionless number. It is the ratio of the inertia forces to the viscous forces in the fluids. Equation for Reynolds Number in pipe or tube is as below:
Where
Ï = Fluid density (kg/m3)
V = Fluid velocity (m/s)
D = Diameter of pipe
μ = The dynamic viscosity of the fluid (Pa·s or N·s/m²)
ν = Kinematic viscosity (ν = μ / Ï) (m²/s)
Q = Volumetric flow rate (m³/s)
A = Pipe cross-sectional area (m2)
EXPERIMENT OVERVIEW
Apparatus
Figure 1 : Apparatus being used
The experimental apparatus comprises of a copper pipe, which is supplied with air by a centrifugal blower and heater as figure 1. The test section of the pipe is wound with a heating tape, which is covered with lagging. Six copper constantan thermocouples are brazed into the wall of the test section. Another six thermocouples extend into the pipe to measure the flowing air temperature. In addition five static pressure tapping are positioned in the tube wall. A BS 1042 standard orifice and differential manometer measure the air mass flow rate though the pipe.
Experimental Procedure
Fully close the valve which controlling the air flow rate.
Measure the everage intermal diameter (D) of the test section pipe by using a vernier calliper.
Adjust the inclination angle of the manometer bundle α to 30°.
Start the blower and turn the valve to the fully open position gradually,
Adjust the power input to the heating tape to its maximum valve and allow the apparatus to attain thermal equilibrium.
Take down the data and record
Pressure drop through the metering orifice
Pressure and temperature downstream of the orifice
Ammeter and voltmeter readings
Tube wall temperature along the testing section
Air temperature along the test section
Air pressure along the test section
Ambient temperature and pressure.
Repeat the foregoing procedure for another four different flow rate and adjust the heater input to give approximately the same wall temperature at each flow rate.
DATA AND MEASUREMENT TABLE
Property
Symbol
Units
Value
Barometric Pressure
Pb
mm Hg
741.60
Diameter of the test section pipe
Dp
m
0.038
Density of water (Manometer’s fluid)
Ï
Kg/m3
1000
Angle of the manometers bundle
α
degree
30
Property
Symbol
Units
Test
1
2
3
4
5
Pressure drop across orifice
ΔH
mm H2O
685
565
460
360
260
Pressure drop d/s orifice to atmosphere
ΔP
mm H2O
178
152
120
93
68
Air temperature downstream orifice
t
°C
35
38
38
38
39
EMF (Voltage) across tape
V
Volts
230
200
165
142
129
Current through tape heater
I
Amps
7.3
6.3
5.5
5.0
4.0
Flowing air temperature
t1
°C
35.0
36.9
38.2
40.0
41.4
Flowing air temperature
t2
°C
36.1
37.7
38.9
40.6
41.9
Flowing air temperature
t3
°C
43.1
43.6
43.4
44.4
45.6
Flowing air temperature
t4
°C
42.2
42.4
42.4
43.5
44.6
Flowing air temperature
t5
°C
49.6
48.6
47.0
47.3
48.1
Flowing air temperature
t6
°C
63.2
59.6
55.7
54.3
54.6
Tube wall temperature
t7
°C
38.9
40.0
40.6
41.9
43.0
Tube wall temperature
t8
°C
81.20
73.6
65.9
62.2
61.2
Tube wall temperature
t9
°C
99.8
89.1
77.5
71.5
69.5
Tube wall temperature
t10
°C
105.9
93.9
81.3
74.6
72.4
Tube wall temperature
t11
°C
106.5
94.5
81.8
75.1
73.1
Tube wall temperature
t12
°C
108.1
95.5
82.3
75.0
72.5
Air static gauge pressure (Δl.sin α)
P1
mm H2O
385
324
255
195
145
Air static gauge pressure (Δl.sin α)
P2
mm H2O
264
223
175
132
99
Air static gauge pressure (Δl.sin α)
P3
mm H2O
210
181
141
108
79
Air static gauge pressure (Δl.sin α)
P4
mm H2O
108
97
81
57
42
Air static gauge pressure (Δl.sin α)
P5
mm H2O
23
31
20
16
14
Air static gauge pressure (Δl.sin α)
P6
mm H2O
≈0
≈0
≈0
≈0
≈0
Sample Calculations
Based on 1st set data,
Power Input to the tape heater:
Power = = (230 x 7.3)/1000 = 1.679
Absolute Pressure downstream of the orifice:
741.60 + (178/13.6)=754.69 mmHg
Absolute Temperature downstream of the orifice:
T = t + 273 = 365+ 273 = 308 K
The Air Mass Flow Rate:
air =5.66x = = 231.88
231.88 Kg/hr = 0.06441 Kg/sec,
Since 1 Kg/hr = Kg/sec
Average Wall Temperature:
= (38.9+81.2+99.8+105.9+106.5+108.1)/6 =90.07
Average Air Temperature:
= (35+36.1+43.1+42.2+49.6+63.2)/6 = 44.87
The Bulk Mean Air (arithmetic average of mean air) Temperature:
= (35+63.2)/6 =49.1
The Absolute Bulk Mean Air (arithmetic average of mean air) Temperature:
49.1+273 =322.10 K
The Properties of Air at Tb:
Using the tables provided in “Fundamentals of Thermal-Fluid Sciences by Yunus A.Cengel”
From the table A-18 (Page958), Properties of Air at 1atm pressure at K
Density, Ï = 1.1029 kg/m3
Specific Heat Capacity, Cp = 1.006 kJ/(kg.K)
Thermal Conductivity, k = 0.0277 kW/(m.K)
Dynamic Viscosity, µ = 1.95 x 10-5 kg/(m.s)
Prandtl Number, Pr = 0.7096
The Increase in Air Temperature:
63.2-35 = 28.2
The Heat Transfer to Air:
(231.88/3600) x 1.006 x 28.2 =1.827
Where: = Heat Transfer to air
= Mass flow rate
= Specific heat capacity
= Increase in air temperature
The Heat Losses:
1.679-1.827 = -0.148
Where: = Heat losses
= Heat Transfer to air
The Wall/Air Temperature Difference:
90.07-44.87 = 45.2
Where: = Wall/Air temperature difference
= Average air temperature
The Heat Transfer Coefficient:
= ((231.88/3600) x 1.006 x 28.2) / (3.14 x .0382 x 1.69 x 45.2) = 0.199 kW/ (m^2 .k)
Where:
= Mass flow rate
= Specific heat capacity
= Increase in air temperature
= Average Diameter of the Copper pipe.
= Length of the tube
= Wall/Air temperature difference
The Mean Air Velocity:
= (4 x (231.88/3600))/ (1.1029 x 3.14 x (0.0382 ^2) = 50.9575 m/s
Where:
= Mean air velocity
= Mass flow rate
= Density
= Average Diameter of the Copper pipe.
The Reynolds Number:
The Nusselt Number:
= Nusselt Number
= Average Diameter of the Copper pipe.
= Thermal conductivity
The Stanton Number:
Where:
St = Stanton Number
= Nusselt Number
= Prandtl number
Re = Reynolds number
The Pressure Drop across the testing section:
at Tb = 320.1 K
= Pressure drop across the testing section
= Absolute pressure downstream of orifice.
= Barometric Pressure
The Friction Factor:
RESULT
Power
Power
kW
1.679
1.260
0.908
0.710
0.516
Absolute Pressure downstream of the orifice
P
mm Hg
754.69
752.78
750.42
748.44
746.60
Absolute temperature downstream of the orifice
T
K
308
311
311
311
312
Pressure drop across the orifice
∆H
mm H20
685
565
460
360
260
Air mass flow Rate
air
231.88
209.31
188.57
166.60
141.18
Average wall Temperature
tw
90.07
81.1
71.57
66.72
65.28
Average air temperature
tair av
44.87
44.80
44.27
45.02
46.03
Bulk Mean air temperature
tb
49.1
48.25
46.95
47.15
48.0
Absolute bulk mean air temperature
Tb
K
322.1
321.25
319.95
320.15
321.0
Density at Tb
Ï
1.1029
1.1058
1.1102
1.1095
1.1066
Specific Heat Capacity at Tb
Cp
1.0060
1.0060
1.0060
1.0060
1.0060
Thermal Conductivity at Tb
K
2.77
2.76
2.75
2.75
2.76
Dynamic Viscosity at Tb
μ
1.95
1.95
1.94
1.94
1.95
Prandtl Number at Tb
Pr
0.7096
0.7096
0.7100
0.7100
0.7098
Increase in air temperature from t1 to t6
∆t a
28.2
22.7
17.5
14.3
13.2
Heat transfer to air
air
W
1.827
1.328
0.922
0.666
0.521
Heat losses
losses
W
-0.148
-0.068
-0.015
-0.044
-0.005
Wall/Air temperature difference
∆t m
45.2
36.3
27.3
21.7
19.25
Heat transfer Coefficient
h
0.199
0.180
0.167
0.151
0.133
Mean air velocity
Cm
50.9575
45.877
41.167
36.394
30.922
Reynolds’s Number
Re
110096.353
99380.
144
89994.
330
79509.
225
67204.
418
Nusselt Number
Nu
274.4
249
232
209.8
184.1
Stanton Number
St
0.00351
0.00353
0.00363
0.0037
0.0039
Pressure Drop across the testing section
∆P
1746.42
1491.59
1176.73
912.57
667.08
Friction Factor
f
0.01378
0.0145
0.0141
0.0141
0.0143
Results
Plot A
Experiment
1
2
3
4
5
Y=ln(Nu x Pr-0.4)
5.75
5.65
5.58
5.48
5.35
X=ln(Re0.8)
9.29
9.21
9.13
9.03
8.89
Y-X
-3.54
-3.56
-3.55
-3.55
-3.54
Plot B
Experiment
1
2
3
4
5
Y=Nu
274.4
249
232
209.8
184.1
X=Re x Pr
78124.37
70520.15
63895.97
56451.55
47701.69
Stanton number:
Reynolds Analogy:
Experiment
1
2
3
4
5
Friction factor
0.01378
0.0145
0.0141
0.014
0.0143
Reynolds Analogy
0.00689
0.00725
0.00705
0.007
0.00715
Stanton number
0.00351
0.00353
0.00363
0.0372
0.0386
DISCUSSION
In order to get more accurate results, there are some suggestions like cleaning the manometer, checking the insulation on the pipe and making sure the valve is closed tightly.
An additional way to prove the heat transfer equation is by re-arranging it.
Nu = 0.023 x (Re0.8 x Pr 0.4)
Substituting in the experimental values into the above equation from section 5.0 returns the following results below:
Experiment
1
2
3
4
5
Y=Nu
274.4
249
232
209.8
184.1
X=Re0.8 x Pr0.4
9415.08
8674.51
8014.48
7258.34
6344.14
Y/X
0.029
0.0287
0.0289
0.0289
0.029
Comparing this to the heat transfer constant, it shows that there is a little difference only which can be negligible.
It can also be done by taking the gradient of the line from the plot Nu against (Re0.8 x Pr0.4)
as shown below:
CONCLUSION
A better understanding of the heat transfer was achieved through conducting the experiment. Theoretical sums and experimental values were found to be approximately similar and the different sources of error have been identified.
The main objective of this experiment was to verify the following heat transfer relationship:
Nu = 0.023 x (Re0.8 x Pr 0.4)
Therefore, relation of forced convective heat transfer in pipe is cleared and the objectives were completed.
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