EML 4906L Exp 1
EML 4906L Exp 1
EML 4906L Exp 1
Table of Contents
Nomenclature.................................................................................................................. i
Apparatus...................................................................................................................... ii
Abstract........................................................................................................................ 1
Introduction.................................................................................................................... 2
Theory of the Experiment................................................................................................... 2
Experimental Procedure..................................................................................................... 4
Experiment Part I.......................................................................................................... 4
Table 1: Constants............................................................................................................ 7
Table 2: Temperature and Current data for 10 V.......................................................................7
Table 3: Temperature and Current data for 15 V.......................................................................8
Table 4 : Temperature and Current data for 20 V......................................................................8
Table 5: Constants............................................................................................................ 9
Table 6 : Temperature and Current data for velocity 1 m/s.........................................................10
Table 7: Temperature and Current data for velocity 3 m/s..........................................................10
Table 8 : Temperature and Current data for velocity 5 m/s.........................................................10
Table 9 : Error analysis for 10.0 V readings.........................................................................13
Table 10: Error analysis for 15.0 V readings........................................................................13
Table 11 : Error analysis for 20.0 V readings.......................................................................13
Table 12 : Error analysis for velocity 1.0 m/s readings...........................................................14
Table 13: Error analysis for velocity 3.0 m/s readings............................................................14
Table 14: Error analysis for velocity 5.0 m/s readings............................................................14
Y
Figure 1......................................................................................................................... 2
Figure 2: Heat Transfer Coefficient vs. Temperature Difference....................................................9
Figure 3: Heat Transfer Percentage vs. Temperature Difference....................................................9
Figure 4: Heat Transferred % vs. Temperature Difference.........................................................11
Figure 5: Surface Temperature vs. Corrected Air Velocity.........................................................12
Figure 6: Nusselt Number Vs Reynolds Number....................................................................12
Nomenclature
DESCRIPTION
SYMBOL
UNITS
Area
m2
Diameter of cylinder
Current
kf
Thermal conductivity
Length of cylinder
Num
W/(m2.K)
A
W/(m.K)
m
Pr
Prandtl number
Heat rate
Re
Reynolds number
Temperature
Velocity
m/s
Voltage
Emissivity of surface
Kinematic viscosity
Ambient
Force convection
nc/c
W/(m2.K4)
m2/s
Natural convection
Radiation
Surface
Apparatus
Abstract
This lab report presents heat transfer modes through a heated cylinder. The experiment
focuses on convection and radiation. There was two parts to the experiment: natural convection
combined with radiation and forced convection combined with radiation. The temperature
difference between a hot surface and the surrounding varies with the heat loss from the cylinder
for natural convection.
coefficient will be greater than the radiation heat transfer coefficient and vice versa at high
surface temperature. For the second part of the experiment, the forced convection heat transfer
coefficient surface temperature is less compared to natural convection. Based on theoretical
information the heat rate of forced convection is greater compared to natural convection resulting
in improved heat transfer.
Introduction
In this experiment, there was two parts consisting of Combined Natural Convection and
Radiation and Combined Forced Convection and Radiation.
experiment, we established the heat loss due to radiation and natural convection. This was
conducted by measuring the surface temperature of a cylinder at various voltages. For the
second part of our experiment, we found the heat loss caused by both radiation and natural
convection. The forced convection was performed measuring the surface temperature of the
cylinder at different air velocities.
Figure 1
There are three modes of heat transfer: conduction, radiation, and convection. Also, there
are two types of convection: natural convection and forced convection. Natural convection is
when the motion of fluid is caused by the density gradient. The fluid motion of a forced
convection is generated by mechanical power or gravitational effects. The following is the
formula to calculate the heat transfer coefficient of natural convection.
T T a
hnc =1.32 s
D
0.25
(1)
The natural convection heat transfer coefficient is used in calculating the natural
convection heat transfer rate.
q c =hc A s ( T sT a )
A s =DL
(2)
(3)
The above equation is dependent on the surface area of the cylinder, the heat transfer
coefficient and both the ambient and surface temperature of the cylinder. The purpose of this
equation is to determine the heat loss due to the surface temperature of the cylinder. When the
cylinder is heated, the temperature of the cylinder rises causing the surrounding air of the
cylinder to become less dense resulting in natural convection heat loss.
When the cylinder heats up, thermal radiation occurs through electromagnetic waves.
The heat transfer rate due to radiation is:
q r=h r A s (T sT a )
(4)
hr =
T s T a
T sT a
(5)
Both , emissivity, and , Stefan Boltzmann, are constants in the above equation.
The second part of our experiment was based on forced convection combined with
radiation. Compared to natural convection, forced convection results in improved heat transfer
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rate due to the increase of air velocity. It is usually used in fans and blow-dryers. For the same
power input as the natural convection, the surface temperature of the cylinder will be less
compared to the natural convection surface temperature. The forced heat transfer coefficient is:
hf=
kf
Nu
D m
(6)
Nu m=0.3+
( ( ) )
0.4
1+
Pr
[ (
1+
282000
0.5
(7)
The Prandtl number, Pr, can be found using the table from the book at room temperature
and the Reynolds number, Re, is calculated by using the following formula:
UcD
(8)
(9)
During this experiment, the effects of conduction on the cylinder have been neglected due
to the design of the equipment.
Experimental Procedure
Experiment Part I
Beginning with HT10X heat transfer service unit prior to switch it on it is useful to check
the corresponding temperature reading outlets T9 for ambient and T10 for surface, in order to read
the correct values accordingly. Following with the cylinder to which outlets T9 and T10 are
connected to.
After all equipment is connected as shown in figure 1,The next step is to start the heat
transfer unit and set the voltage to 10 volts wait for the surface temperature T10 readings to
stabilize, and then proceed to record both surface and ambient T9 as well as the current I
readings.
Repetitively follow the same process at voltages of 15 and 20 volts and record for each
voltage current I, ambient T9 and surface T10 temperatures five times, these trials will help
with the error analysis section.
Experiment Part II
Beginning with HT10X heat transfer service unit prior to switch it on it is useful to check
the corresponding temperature reading outlets T9 for ambient and T10 for surface, in order to read
the correct values accordingly. Next start the centrifugal fan controller and the fan itself.
Following with the cylinder to which outlets T9 and T10 are connected to.
After all equipment is connected as shown in figure 1, The next step is to start the heat
transfer unit and set the voltage to 20 volts and then switch to position Ua set air velocity to 1.0
m/s wait for the surface temperature T10 readings to stabilize, and then proceed to record surface
T10, ambient T9, current I as well as air velocity Ua readings.
Repetitively follow the same process at air speeds of 3.0 and 5.0 m/s and record for each
voltage current I, ambient T9, surface T10 and air velocity Ua five times, these trials will help
with the error analysis section.
Qtot =Qf + Qr
(10)
Q =I V
(11)
For the second part of the experiment only few details defer now we compute the heat
loss by force convection using equation 6 and the same heat transfer area, thus, we can then
compute the heat loss by forced convection accordingly using equation 9.
Heat loss coefficient by forced convection has temperature dependent variables such as
the Average Nusselt Number which we obtain using equation 7
The Reynolds number depends on the velocity of the moving fluid and it can be
determined using equation 8.
Lastly the Corrected Air velocity computed using equation 12.
U c =1.22 U a
(12)
Experiment Part I
Table 1:
D(m)
= 0.010
L(m)
= 0.070
Table 2:
Constants
= 0.950
(W/m2*K4)
= 5.67010^-8
V(V)= 10.000
I(A)= 1.640
Trial #
T9(C)
25.400
25.300
25.200
25.300
25.000
T10(C)
262.000
260.000
259.00
0
258.000 257.000
T9,average(C)= 25.240
Qc(W)= 8.399
T10,average(C)= 259.200
Qr(W)= 0.535
As (m2)= 0.002
hnc(W/m2*K)= 16.325
Qtot(W)= 8.934
Qin(W)= 16.400
hr(W/m2*K)= 1.039
Table 3:
V(V)= 15.000
I(A)= 2.430
Trial #
T9(C)
26.500
26.500
26.400
26.400
26.500
404.000
404.00
0
403.000 402.000
T10(C)
406.000
T9,average(C)= 26.460
Qc(W)= 15.266
T10,average(C)= 403.800
Qr(W)= 3.149
As (m2)= 0.002
hnc(W/m2*K)= 18.397
Qtot(W)= 18.416
Qin(W)= 36.450
hr(W/m2*K)= 3.795
Table 4
V(V)= 20.000
I(A)= 3.220
Trial #
T9(C)
26.700
26.800
26.900
27.000
27.100
T10(C)
525.000
526.000
527.00
0
527.000 527.000
T9,average(C)= 26.900
Qc(W)= 21.677
T10,average(C)= 526.400
Qr(W)= 9.095
As (m2)= 0.002
hnc(W/m2*K)= 19.734
Qtot(W)= 30.772
Qin(W)= 64.400
hr(W/m2*K)= 8.280
Plotting the heat transfer coefficient vs. the temperature of both Radiation and natural
Convection side to side as seen in figure 2 gives us a clear picture of the correlation between
them, although not so evident to the naked eye as temperature increases radiation picks up at a
mild rate. This however can be easily observed on figure 3 not the case of tables 2-4.
10
20.000
18.000
16.000
14.000
Natural Convection
Linear
(Natural Convection)
12.000
10.000
Heat Transfer Coefficient (W/m2K)
8.000
6.000
4.000
2.000
Linear (Radiation)
0.000
200.000 300.000
Radiation
400.000
500.000
Temperature (C)
Figure 2:
100.000%
90.000%
80.000%
70.000%
60.000%
50.000%
40.000%
30.000%
20.000%
10.000%
0.000%
300.000
200.000 400.000
Temperature (C)
Figure 3: Heat
Experiment Part II
Table 5:
D(m) 0.01
= 0
0.07
L(m)= 0
0.95
= 0
Constants
5.67010^(W/m2*K4)= 8
11
Correction= 1.220
Table 6
V(V)= 20.000
I(A)= 3.210
Ua(m/s)= 1.000
Trial #
T9(C)
27.200
27.200
27.300
27.300
27.300
T10(C)
430.00
0
431.000
431.000
432.000
432.000
T9,average(C)= 27.260
431.20
T10,average(C)= 0
As (m2)= 0.002
Uc(m/s)= 1.220
Pr= 0.707
Qf(W)= 29.904
hf(W/m2*K)= 33.664
Qr(W)= 4.095
hr(W/m2*K)= 4.610
Qtot(W)= 33.999
kf(Wm-1*K1
)= 0.0263
Table 7:
Qin(W)= 64.200
V(V)= 20.000
I(A)= 3.230
Ua(m/s)= 3.000
Trial #
T9(C)
25.300
25.200
25.200
25.200
25.200
T10(C)
332.00
0
332.000
332.000
332.000
332.000
T9,average(C)= 25.220
332.00
T10,average(C)= 0
As (m2)= 0.002
Uc(m/s)= 3.660
Qf(W)= 40.277
hf(W/m2*K)= 59.701
Qr(W)= 1.439
hr(W/m2*K)= 2.133
Qtot(W)= 41.716
kf(Wm-1*K1
)= 0.0263
Table 8
Qin(W)= 64.600
V(V)= 20.000
I(A)= 3.250
Ua(m/s)= 5.000
Trial #
T9(C)
24.000
24.200
24.200
24.200
24.200
T10(C)
279.00
0
278.000
278.000
278.000
278.000
T9,average(C)= 24.160
278.20
T10,average(C)= 0
As (m2)= 0.002
Uc(m/s)= 6.100
hf(W/m2*K)= 78.637
Qr(W)= 0.710
hr(W/m2*K)= 1.270
Qtot(W)= 44.641
kf(Wm-1*K1
)= 0.0263
Qin(W)= 65.000
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Figure 4:
350.000
300.000
250.000
1.000 2.000 3.000 4.000 5.000 6.000 7.000
Corrected Air Velocity (m/s)
Figure 5:
40.000
30.000
Nu
20.000
10.000
0.000
0.000
1,000.000
2,000.000
Re
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3,000.000
4,000.000
Figure 6:
Error Analysis
Error is present on all measured data, it accumulated by a series of factors which are
uncontrollable within the time frame of the experiment. By inspection it is noticeable form
tables 2-4 and tables 6-8 that between Qin and Qtot there is around a 2:1 ratio and this ratio
decreases as surface temperature goes up.
The uncertainty ux is calculated using a 95% confidence interval using equation 13,
which to calculate the Standard Deviation of each set, equation 14 and 15 were used
consequently.
u x =t n , p S x
1
Sx =
( x jx )2
N 1 j=1
x =
1
N
(13)
1
2
(14)
xi
(15)
i=0
Experiment Part I
Table 9
V(V)= 10.000
I(A)= 1.640
Trial #
T9(C)
25.400
25.300
25.200
25.300
25.000
T10(C)
262.000
260.000
259.000
258.000
257.000
15
T9,average(C)= 25.240
T9 ux(C)= 0.390
T10,average(C)= 259.200
T9(C)= 25.2400.390
Thus:
259.2004.94
T10(C)= 5
V(V)= 15.000
I(A)= 2.430
Trial #
T9(C)
26.500
26.500
26.400
26.400
26.500
T10(C)
406.000
404.000
404.000
403.000
402.000
T9,average(C)= 26.460
T9 ux(C)= 0.141
T10,average(C)= 403.800
T9(C)= 26.4600.141
Thus:
403.8003.8
T10(C)= 13
Table 11
V(V)= 20.000
I(A)= 3.220
Trial #
T9(C)
26.700
26.800
26.900
27.000
27.100
T10(C)
525.000
526.000
527.000
527.000
527.000
T9,average(C)= 26.900
T9 ux(C)= 0.407
T10,average(C)= 526.400
T9(C)= 26.9000.407
Thus:
526.4002.30
T10(C)= 0
V(V)= 20.000
I(A)= 3.210
Ua(m/s)= 1.000
Trial #
T9(C)
27.200
27.200
27.300
27.300
27.300
T10(C)
430.00
0
431.000
431.000
432.000
432.000
T9,average(C)= 27.260
T9 ux(C)= 0.141
431.20
T10,average(C)= 0
T9(C)= 27.2600.141
Thus:
431.2002.15
T10(C)= 1
Table 13:
V(V)= 20.000
I(A)= 3.230
Ua(m/s)= 3.000
Trial #
T9(C)
25.300
25.200
25.200
25.200
25.200
T10(C)
332.00
0
332.000
332.000
332.000
332.000
T9,average(C)= 25.220
T9 ux(C)= 0.115
T10,average(C)= 332.00
0
T9 Std.Dev Sx(C)= 0.045
332.0000.0
T10(C)= 00
Table 14:
T9(C)= 25.2200.115
Thus:
V(V)= 20.000
I(A)= 3.250
Ua(m/s)= 5.000
Trial #
T9(C)
24.000
24.200
24.200
24.200
24.200
T10(C)
279.00
0
278.000
278.000
278.000
278.000
T9,average(C)= 24.160
T9 ux(C)= 0.230
278.20
T10,average(C)= 0
Thus:
T9(C)= 24.1600.230
278.2001.1
T10(C)= 50
Conclusions
During this experiment, we were able to determine the effects of both natural convection
and radiation in a heated cylinder. We concluded that heat loss varies with the temperature
difference between the surface temperature and the ambient temperature. In the first part of our
experiment, the results obtained varied compared to the theoretical background. As we increased
voltage, both the ambient and surface temperature increased. The natural convection heat
18
transfer coefficient was greater compared to the radiation heat transfer coefficient. In theory,
natural convection is more when there is small temperature difference and radiation is dominant
when the temperature difference is large. From our results, we did not have a great value of
radiation heat transfer coefficient during high surface temperature. This error could have been
reduced if there was more time for the surface temperature to stabilize and if there was longer
period of time intervals during our trials.
For the second part of the experiment, we illustrated the effects of forced convection
combined with radiation. The heat transfer rate due to forced convection value is greater than the
value for natural convection.
temperature than the natural convection when the power input is the same. Also, the value of the
heat transfer rate for forced convection is greater than the natural convection. In part two of the
experiment, we found very minimal error compared to part one. The results obtained in this part
match the theoretical background.
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