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MONASH UNIVERSITY S UNWAY CAMPUS
Free andFo rced
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Convectio
n
CHE2163 LaboratoryReport
9/17/2010
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Free and Forced Convection 2010
I. Title Page
ii
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Free and Forced Convection 2010
II. Table of Contents
I. Title Page ........................................................................................................................ii
II. Table of Contents ...................................................................................................... iii
III. Table of figures ...........................................................................................................
v IV. List of Graphs..............................................................................................................
v V. List of Tables...............................................................................................................
v VI. Summary
....................................................................................................................vi
1. Introduction........................................................................................................................ 1
1.1. Background information .......................................................................................... 1
1.2. Relevant theories and Key equations....................................................................... 2
1.3. Motivation for study ................................................................................................ 4
1.4. Intended Scope ........................................................................................................ 4
2. Aims ................................................................................................................................... 5
3. Experimental Work ............................................................................................................ 6
3.1. Safety issues ............................................................................................................ 6
3.2. Description of apparatus .......................................................................................... 7
3.3. Diagram of apparatus............................................................................................... 9
3.4. Experimental Procedure ........................................................................................ 12
4. Results and Discussion .................................................................................................... 14
4.1. Calculated Data...................................................................................................... 14
4.2 Discussion of trends and interpretation of graphs ................................................. 32
4.3 Comparison of Results........................................................................................... 34
4.4 Comparison with expectations............................................................................... 34
4.5 Errors ..................................................................................................................... 37
4.6 Difficulties/Limitations ......................................................................................... 38
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Free and Forced Convection 2010
5. Appendices....................................................................................................................... 39
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Free and Forced Convection 2010
Appendix 1....................................................................................................................... 39
6. References ........................................................................................................................ 40
7. Nomenclature list ............................................................................................................. 41
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Free and Forced Convection 2010
III. Table of figures
Figure 1: Heat Convection example: Transfer of heat from a fire to the body.......................... 1
Figure 2: Heat Convection example: boiling of water ............................................................... 1
Figure 3: Free convection example: Water cycle ...................................................................... 2
Figure 4: Forced Convection example: Blowing a hot cup of coffee ........................................ 2
Figure 5: Free and forced convection apparatus (LS-17004) .................................................... 9
Figure 6: Finned Plate .............................................................................................................. 10
Figure 7: Digital Handheld Anemometer ................................................................................ 10
IV. List of Graphs
Graph 1: Free Convection - Temperature Profile versus Time................................................ 15
Graph 2: Free convection - Surface temperature vs. Time ...................................................... 16
Graph 3: Forced convection - Temperature Profile versus Time (v = 0.6m/s) ........................ 20
Graph 4: Forced Convection - Surface temperature vs. Time (v = 0.6 m/s) ........................... 21
Graph 5: Forced convection - Temperature Profile versus Time (v = 0.9 m/s) ....................... 25
Graph 6: Forced convection - Surface temperature vs. Time (v = 0.9 m/s) ............................ 25
Graph 7: Forced convection - Temperature Profile versus Time (v = 1.2 m/s) ....................... 29
Graph 8: Forced Convection - Surface temperature vs. Time (v = 1.2 m/s) ........................... 29
V. List ofTables
Table 1: Free convection: Temperature profile vs. Time ........................................................ 14
Table 2: Forced convection - Temperature profile vs. Time (v = 0.6 m/s) ............................. 20
Table 3: Forced Convection - Temperature Profile versus Time (v = 0.9 m/s) ....................... 24
Table 4: Forced Convection Temperature Profile vs. Time (v = 1.2 m/s) ............................ 29
Table 5: Forced Convection - Comparison of results .............................................................. 34
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Free and Forced Convection 2010
VI. Summary
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Free and Forced Convection 2010
1.Introduction
1.1. Backg rou n d in f orm ation
Heat transfer is the movement of heat from one place to another. When an object is at
a different temperature from its surrounding temperature, the heat will move from the
higher temperature to the lower temperature until the object and the surrounding have the
same temperature. There are many modes of heat transfers, but the one that will be
considered in the following experiment will be heat transfer through convection.
Heat convection is the transfer of heat between an object and its surrounding due to
fluid movement. An example of this phenomenon is the cooling of hot water; where hot
water vapour is released into the atmosphere until it reaches the surrounding temperature.
More examples include the heat obtained by a fireplace, the boiling of water, the transfer
of heat from a hot water radiator etc. A few heat convection methods are illustrated
below.
Figure 1: Heat Convection example:
Transfer of heat from a fire to the body
Invalid source specified.
Figure 2: Heat Convection example: boiling of
water
9
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Free and Forced Convection 2010
Heat convection can be divided into two categories. They are free convection and
forced convection. Free convection is the movement of fluid due to the density difference
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in the fluid and the surrounding. Forced convection is fluid motion which is generated by
an external source such as a pump or a fan. The figures below include a few examples of
free and forced convection.
Invalid source specified.Invalid source specified.
Figure 3: Free convection example:
Water cycle
Figure 4: Forced Convection
example: Blowing a hot cup of
coffee
1.2. Rele van t th eori es an d Ke y equ ation s
This experiment was divided into two parts; namely, free and forced convection.
Using the results obtained, the Nusselt number (Nu), Rayleigh number (Ra), and Prandtl
number (Pr) will first be calculated for free convection. This will be followed by the
calculation of the Reynolds number (Re), Nusselt and Prandtl number for forced
convection. The convection heat coefficient was calculated using Newtons law of
cooling. The equation is as follows:
- Equation (1)
Where ,
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The Prandtl Number (Pr) relates the kinematic viscosity and thermal diffusivity
with the specific heat , dynamic viscosity , and the thermal conductivity .
It is a dimensionless number and since it does not change with the fin or flat plate length,
it is not subscripted with the length scale. In heat transfer problems the Prandtl numbercontrols the relative thickness of momentum and the thermal boundary layers. I.e. when
the Pr is small, the heat diffuses quickly compared to the velocity (momentum). The
equation for the Prandtl number is as follows: (Prandtl Number, 2010)
- Equation (2)
The Nusselt number, relates the convective heat transfer coefficient, the
thermal conductivity of the fluid, and the characteristic length . Just as the
Prandtl number, the Nusselt number is also dimensionless. A which is close to
unity, i.e. convection and conduction of similar magnitude, is characteristic of a laminar
flow. The larger the Nusselt number, it corresponds to a more active convection with
turbulent flow. The equation of the Nusselt number is as follows: (Nusselt Number,
2010)
- Equation (3)
The Rayleigh Number, is a dimensionless number related to the buoyancy
driven flow which is also known as free convection. This number is the multiplication of
the Grashof number, and the Prandtl Number. The Grashof number is the
measure of the ratio of buoyancy forces to viscous forces and relates the acceleration due
to gravity, , The thermal expansion coefficient, , the surface temperature, , the
fluid temperature , the characteristic length and the kinematic viscosity, .
When the Rayleigh number is below the critical number of that fluid, heat transfer is
primarily in the form of conduction. When it exceeds the critical value, heat transfer is
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primarily in the form of convection. The equation of the Rayleigh number is as follows:
(Rayleigh Number, 2010)
- Equation (4)
The Reynolds number is a dimensionless number which gives the ratio of the
inertia and viscous forces. This number relates the density, dynamics viscosity, ,
velocity, and the characteristic length . It can also be related to the kinematic
viscosity . The equation of the Reynolds number is given below. (Reynolds Number,
2010)
- Equation (5)
1.3. Motivati on f or stu d y
The main motivation to conduct this experiment was the opportunity to apply our
theoretical knowledge on fins practically. By doing this we were able to analyse andstudy the phenomena of free and forced convection. Furthermore, we managed to
compare the coefficient of heat transfer using the equation of a flat plate to the expected
value for a fin. Also by calculating the numbers mentioned above we were able to get a
better idea of the type of flow of the system.
1.4. In ten de d S c
op e
The scope of this experiment is to calculate the heat transfer coefficients with
temperature profiles and a heat flux in a rectangular air duct fitted with a finned plate
surface. By calculating the experimental heat transfer coefficient and the theoretical heat
transfer coefficient we are able to analyse the comparison and errors of the experiment.
The rest of the report includes the objectives, experimental procedure, results and
discussion and the conclusion of our experiment.
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2.Aims
The aim of this experiment is to make a comparison between the theoretical and experimental
value obtained for the convection heat transfer coefficient
For free convection, we have compared the Nusselt number so as to determine the
percentage error of the experiment in comparison to the theory. In this case the rate of heat
transfer will be constant throughout the experiment. Therefore we will obtain one value for
each of the numbers.
For forced convection, we have found the convection heat transfer coefficient through the
Reynolds number as well as the Nusselt Number. Just as before the rate of heat
transfer will be constant but the velocities will change. Therefore, we will obtain more than
one value for each of the numbers. As a result, the values will be plotted in order to obtain a
pattern in the data.
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3. Experimental Work
2.
3.
3.1. S afe t y is su es
It is an undisputable fact that safety comes first in every aspect of our lives,
particularly when an experiment is being conducted. Professionalism must prevail in
every undertaking to elude any possible hazard. Therefore, a few precautions and golden
rules have to be adhered duly at all times. Firstly, only students with proper attires are
permitted into the lab. Laboratory dress code is strictly practiced; all students must don
up in lab coats and covered shoes as these attires are designed to protect students should
any accidents occur. Besides that, locations of safety aids are identified prior to the
conduction of the experiment. Usage of fire extinguishers, emergency bells, emergency
shower, emergency route and first aid kit must be integrated into ones mind.
Experiments as such require undivided attention and patience as it subjects to
cooling and heating of an element to steady state. Often, some individuals may perceive
it as dull and time consuming, causing them to lose concentration and further exposed to
underlying dangers. Therefore, air circulation in the lab must be kept at a comfortable
level with the help of fans and air conditioners. Besides that, ample space must be
provided in the workspace for students mobility. In accordance to that, the workspace
must be kept neat and number of students permitted into the lab must be limited at all
times. Moreover, students must master the theory of free and forced convection before
the commencement of the lab session.
Also, the setup of the experimental apparatus must be done appropriately. A good
setup of the experimental apparatus is arranged systematically so that nothing intertwines
or impedes the progress of the experiment. Therefore, all experimental apparatus, such as
the stopwatch was positioned at a strategic location. Besides that, the nuts and bolts (M)
securing the heat plate must be tightly secured to reduce any possible inaccuracies suchas heat loss, posed. Whilst conducting the experiment, students are prohibited
from
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touching the heat plate (P) or air duct (B) as it may inflict burns and blisters. Besides
that, the fan (A) of the apparatus (LS-17004) was kept out of reach to avoid potentially
harmful cuts. First aid are carried out immediately should any misfortune occurs. Any
injury must be reported instantaneously, so that any possible threats are under medicalattention.
Apart from that, the fan (A) is switched off when conducting the free convection
experiment. It is imperative to only remove heat plate from chamber after the heat plate
has been cooled down to avoid burns from occurring. Moreover, the handheld digital
anemometer (Q) should be handled dexterously, with extreme care as the probe (R) is
exceptionally fragile and tremendously costly to replace. The handheld digital
anemometer is positioned suitably once the temperature and air velocity is noted down.
Before the temperature readings are recorded, the temperature probe must be in contact
with the heat plate surface. Besides this, the electrical power source should be
disconnected when the heat socket is connected to the power source in order to prevent a
short circuit. Consequently, students should never attempt to change the setting of the
digital power meter.
3.2. Des cripti on o f ap par
atu s
In this experiment, the free and forced convection apparatus (LS-17004 Lotus) is
developed for the demonstration of free and forced convection phenomena. The
apparatus mainly consists of a vertical air duct and a control panel. Inside the
convection chamber, there is a compartment where different heated surfaces can be
fitted in to determine its heat convection coefficients. Under our case study, we are
given the task to scrutinize finned plate as shown in Figure 3. The finned plate is
attached to an electrical heating element which in this scenario functions as the heat
source.
In the free convection experiment, a handheld digital anemometer was used to
measure the initial temperature of the heater. Then, probes of the free and forced
convection apparatus (LS-17004 Lotus) were inserted into its respective hole to
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calculate its respective temperature point from time to time. The digital screen of
control panel displays the temperature points at that specific time.
For forced convection, air is fed into the duct by the fan which is placed at the top
of the air ducts. Air flow or rather air circulation is generated when the fan is switched
on as air is drawn out concurrently from the top of the air duct. Before the
commencement of forced convection, the handheld digital anemometer was used to
measure the initial temperature of the heater and the velocity of air flow which
functions as the manipulated variable. The air velocity is adjusted using the fan speed
regulator function found in the control panel.
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3.3. Diagram o f ap paratu s
A
B
N
M
C
L
K
J
I
H
D GE F
Figure 5: Free and forced convection apparatus (LS-17004)
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O
P
Figure 6: Finned Plate
Q
R
Figure 7: Digital Handheld Anemometer
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Legend
A
B
=
=
Fan
Air duct
C
D
=
=
Temperature probes
Timer
E
F
G
=
=
=
Fan speed regulator
Fan switch
Temperature switch (T1, T2, T3)
H
I
=
=
ON/OFF Switch
Power regulatorJ
K
=
=
Power meter
Temperature points (T1, T2, T3)
L
M
=
=
Temperature (Ts) indicator
Bolts and buts
N
O
=
=
Heater Placement
Fins
P = Heater Plate
Q = Digital handheld Anemometer
R = Digital handheld Anemometer probe
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3.4. Experim en tal Pro ce d u re
3.4.1. Free Convection Experiment
1. The LS-17004-FFC Free and forced convection apparatus was placed on a
level table. The adjustable levelling feet was adjusted if necessary.
2. Three pins plug to the 240VAC was plugged to the main power supply. The
power supply was activated
3. The power supply unit in front of the control panel was switched on.
4. The shape and the dimensions of the finned plate(O) was measured and
recorded.
5. The finned plate was fixed tightly to the heater placement(N) with the bolts
and nuts(M) provided.
6. The finned plate heater cable was connected to the heater socket which was
located at the back of the control panel.
7. The digital handheld temperature probe and meter(Q) was used to measure the
initial temperature of the heater by putting the temperature probe into
temperature point. It was ensured that the probe was touching the surface of
the heater and the fan was switched off before the readings were taken down.
8. The power supplied was regulated to 100W by turning the power regulator.
9. For every 5 minutes elapsed, the heater plate surface temperature and the
temperature points was recorded.
10. The experiment was continued until steady state was achieved.
11. A graph of time against temperature difference was plotted for the different
temperature point. T1, T2, T3 respectively.
12. The overall coefficient for the heater was calculated.
13. The Nusselt number, Nu, Rayleigh number, Ra and Prandtl number Pr was
calculated.
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3.4.2. Forced Convection Experiment
1. The same apparatus set up was assembled as the one in free convection
experiment.
2. The power supplied was regulated to 100W by turning the power regulator.
3. The digital handheld anemometer probe(R) was inserted into the side opening
of the air duct where the temperature points were. The initial temperature of
the heater was taken down with probe touching the heater surface. Then, the
desired wind speed was adjusted with the help of the handheld anemometer
probe(Q).
4. For every 30 seconds elapsed, the temperature at different points T1, T
2,T
3
was taken down.
5. The experiment was continued until steady state is achieved.
6. The experiment was repeated with wind speed regulated to 0.9m/s and 1.2 m/s
respectively, by repeating steps 4 and 5.
7. The overall coefficient for all the heaters was calculated.
8. The Nusselt number, Nu, Rayleigh number, Ra and Prandtl number Pr for all
the cases was determined and a graph of Nusselt number versus Rayleigh
number was plotted.
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4. Results and Discussion
4.
4.1. Calcu lat ed Data
Free Convection
Power = 100W
= 24.1C = 297.1 K
Time (min)
0 36 48 39 50
5 40 40 43 55
10 43 43 46 60
15 45 45 48 64
20 47 47 50 67
25 49 49 52 71
30 50 50 55 74
35 51. 51 55 76
40 51 51 56 77
45 51 52 57 77
Table 1: Free convection: Temperature profile vs. Time
90
80
70T1
60T2
50T3
40Tsurface
30Log.
(T2)
Log.
(T2)20
Linaire (T3)10
00 10 20 30 40 50
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Graph 1: Free Convection - Temperature Profile versus Time
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Surface temperature vs. Time
80
75
Stea
dy State
70
Time (min)
65
60
55
500 5 10 15 20 25 30 35 40 45
Surface Temperature (K)
Graph 2: Free convection - Surface temperature vs. Time
4.1.1. Assumptions
The following assumptions were assumed for this experiment:
A vertical flat plate was assumed to be used
Steady state condition
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Negligible radiation effect
Negligible heat conduction from the air duct and the plate
Ideal gas behaviour
4.1.2. Experimental Values
The experimental value of h can be calculated using the following formula:
UsingEquation (1);
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Total surface area of fins exposed is:
A = 6 [ 2(8.7 0.6 ) + 2 (10.8 8.7 ) + 2 (0.6 10.8) ]= 1267.97 = 0.127
Assuming the total surface area of the fins exposed is equal to a vertical plate area,since the assumption taken in these calculations is that a vertical flat plate was
used.
The average value of was calculated using Microsoft Excel,
= 67.4 C = 340.4 K
Thus, calculating for the value of h gives :
4.1.3. Calculation of the Nusselt Number, Rayleigh Number and Prandtl
Number
(Incropera, 2007)
Thermo physical properties of Air at Atmospheric Pressure
At = = 318.75 K
From Table A.4, using interpolation method at temperature of :
W/m.K
Density of air, = 1.099 kg/
Assuming that air is an ideal gas and is the absolute temperature, can be
calculated using the following formula:
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Substituting intoEquation (3) gives:
UsingEquation (2);
UsingEquation (4);
4.1.4. Theoretical calculations
The Rayleigh Number was found to be which was in the interval of
.
Thus, it is laminar flow.
For laminar flow, C = 0.59 and n = .
Thus, the following equation is used as Ra
Using equation (9.27)
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Where,
Thus,
Calculating percentage error of :
=
= 23.45 %
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Forced Convection
A) Velocity = 0.6 m/s
= 24.3C = 297.3 K
Power = 100W
Time
0 40.0 27.8 29.3 31.1
30 40.2 27.8 29.2 31.2
60 40.4 27.8 29.5 31.3
90 40.5 27.8 29.5 31.3
120 40.7 27.9 29.4 31.4
150 40.9 27.9 29.7 31.5
180 41.0 28.1 29.7 31.6
210 41.3 28.1 29.8 31.7
240 41.3 28.2 29.9 31.8
270 41.5 28.2 29.9 31.8
300 41.5 28.3 30.0 31.9
330 41.7 28.4 30.1 32.0
360 41.7 28.4 30.1 32.0
Table 2: Forced convection - Temperature profile vs. Time (v = 0.6 m/s)
45
40
35
30
25
20
15
10
5
0
0100200300400
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Tsurface
T1
T2
T3
Linaire
(Tsurface)
Linaire (T1)
Linaire (T2)
Linaire (T3)
Graph 3: Forced convection - Temperature Profile versus Time (v = 0.6m/s)
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41.8
Surface temperature vs. Time
41.6
41.4
41.2
Steady State
41
Time (min)
40.8
40.6
40.4
40.2
400 50 100 150 200 250 300 350 400
Surface Temperature (K)
Graph 4: Forced Convection - Surface temperature vs. Time (v = 0.6 m/s)
4.1.5. Experimental Values
UsingEquation (1);
Total surface area of fins exposed is,
A = 6 [ 2(8.7 0.6 ) + 2 (10.8 8.7 ) + 2 (0.6 10.8) ]= 1267.97 = 0.127
Assuming the total surface area of the fins exposed is equal to a vertical plate area, since the
assumption taken in these calculations is that a vertical flat plate was used.
The average value of was calculated using Microsoft Excel,
= 40.9 C = 313.98 K
Thus, calculating for the value of h gives
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4.1.6. Calculation of Prandtl Number, Nusselt Number and Reynolds Number
Thermo physical properties of Air at Atmospheric Pressure:
From Appendix .. Table A.4,
Using interpolation at a v = 0.6 m/s and
Pr number = 0.7062
Using the equation below taken from Chapter 7 section 7.4.1 of the prescribed
text book, Reynolds number is calculated:
UsingEquation (5);
UsingEquation (3);
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Theoretical Calculations
Using equation 7.52 below, Nusselt number is calculated:
Where from table 7.3 of Appendix 2, following the assumption of a vertical flat
plate, C = 0.228 and m = 0.731
To obtain ,
=
86.17 =
= 21.43
Calculati ng P er centa ge E rror :
Percentage error of Nusselt number =
=
= 121.61 %
Percentage error ofh =
=
= 120.30 %
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B) Velocity = 0.9 m/s
= 22.0C = 295 K
Power = 100W
Time
0 31.8 28.8 26.5 31.3
30 32.0 28.8 26.5 31.4
60 32.2 28.8 26.6 31.6
90 32.6 28.8 26.7 31.8
120 32.6 29.0 26.8 32.1
150 32.8 29.0 26.7 31.9
180 33.0 29.1 27.0 32.5
210 33.2 29.2 27.0 32.6
240 33.4 29.4 27.1 32.8
270 33.6 29.4 27.2 33.0
300 33.7 29.7 27.3 33.2
330 33.8 29.7 27.3 33.5
360 33.8 29.7 27.3 33.5
Table 3: Forced Convection - Temperature Profile versus Time (v = 0.9 m/s)
40
35
30
25
20
15
10
5
0
0100200300400
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Tsurface
T1
T2
T3
Linaire (T1) Linaire (T2) Linaire (T3) Linaire
(T3)
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Graph 5: Forced convection - Temperature Profile versus Time (v = 0.9 m/s)
33.8
Surface temperature vs. Time
33.6
33.4
33.2
tate
Time (min)
33
32.8
32.6
32.4
32.2
32
31.80 50 100 150 200 250 300 350 400
Surface Temperature (K)
Graph 6: Forced convection - Surface temperature vs. Time (v = 0.9 m/s)
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4.1.7. Experimental Values
The experimental value of h can be calculated using the following formula
UsingEquation (1);
Total surface area of fins exposed is,
A = 6 [ 2(8.7 0.6 ) + 2 (10.8 8.7 ) + 2 (0.6 10.8) ]= 1267.97 = 0.127
Assuming the total surface area of the fins exposed is equal to a vertical plate area,
since the assumption taken in these calculations is that a vertical flat plate was
used.
The average value of was calculated using Microsoft Excel,
= 32.9 C = 305.96 K
Thus, calculating for the value of h gives:
4.1.8. Calculation of Prandtl Number, Nusselt Number and Reynolds Number
Thermo physical properties of Air at Atmospheric Pressure:
From Table A.4, of Appendix 1
Using interpolation at a v = 0.9 m/s and
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Pr number = 0.7069
Using the equation below taken from Chapter 7 section 7.4.1 of the prescribed textbook, Reynolds number is calculated
UsingEquation (5);
UsingEquation (3);
4.1.9. Theoretical Calculations
Using equation 7.52 below, Nusselt number is calculated:
Where from table 7.3, following the assumption of a vertical flat plate, C = 0.228
and m = 0.731
To obtain the ,
=
119.12 =
= 29.00
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Calculati ng P er centa ge E rror :
Percentage error of Nusselt number =
=
= 147.65 %
Percentage error ofh =
=
= 147.72 %
C) Velocity = 1.2 m/s
= 22.2C = 295.2 K
Power = 100W
Time (s)
0 31.8 26.4 25.9 29.2
30 32.1 26.5 25.9 29.4
60 32.2 26.6 26.0 29.490 32.5 26.7 25.9 29.7
120 32.6 26.8 26.1 29.9
150 32.8 26.8 26.2 30.0
180 32.9 27.0 26.3 30.2
210 33.1 27.1 26.4 30.3
240 33.2 27.2 26.4 30.5
270 33.5 27.3 26.5 30.6
300 33.5 27.4 26.5 30.8
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330 33.7 27.5 26.6 30.9
360 33.9 27.5 26.6 31.1
390 34.2 27.8 26.6 31.6
420 34.3 27.9 27.0 31.8
Table 4: Forced Convection Temperature Profile vs. Time (v = 1.2 m/s)
40
35
30
25
20
15
10
5
0
0 100 200 300400 500
Tsurface
T1
T2
T3
Linaire
(Tsurface)
Linaire (T1)
Linaire (T2)
Linaire (T3)
Graph 7: Forced convection - Temperature Profile versus Time (v = 1.2 m/s)
34.5
Surface temperature vs. Time
34
33.5
Steady State
Time (min)
33
32.5
32
31.50 50 100 150 200 250 300 350 400 450
Surface Temperature (K)
Graph 8: Forced Convection - Surface temperature vs. Time (v = 1.2 m/s)
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4.1.10. Experimental Values
The experimental value of h can be calculated using the following formula:
UsingEquation (1)
Total surface area of fins exposed is :
A = 6 [ 2(8.7 0.6 ) + 2 (10.8 8.7 ) + 2 (0.6 10.8) ]= 1267.97 = 0.127
Assuming the total surface area of the fins exposed is equal to a vertical plate area,
since the assumption taken in these calculations is that a vertical flat plate was
used.
The average value of was calculated using Microsoft Excel,
= 33.11 C = 306.11 K
Thus, calculating for the value of h gives,
Calculati ng fo r Prandtl N umber, Nusselt Number and Re yn old s Number:
Thermo physical properties of Air at Atmospheric Pressure:
From Table A.4, of Appendix 1
Using interpolation at a v = 0.9 m/s and
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Pr number = 0.7069
Using the equation below taken from Chapter 7 section 7.4.1 of the prescribed text book,Reynolds number is calculated,
UsingEquation (5);
4.1.11. Theoretical Calculations
Using equation 7.52 below, Nusselt number is calculated,
Where from table 7.3, following the assumption of a vertical flat plate, C = 0.228
and m = 0.731
To obtain the ,
=
147.0 =
31
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= 35.80
31
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Calculati ng P er centa ge E rror
Percentage error of Nusselt number =
Percentage error ofh =
=
1
2
3
4
4.1
4.2 Dis cu s sion o f tr en ds an d in ter pret ation o f
graph s
For free convection, the rate of heat transfer was held constant while the temperature
of the surface of the fin was measured with time. The surface temperature of the fin increased
exponentially with time. Therefore we can say that the surface temperature is proportional to
time. Once the temperature reached its steady state, it was used to calculate all the
dimensionless groups which were dependent on the fin length, i.e. Nusselt Number, Rayleigh
Number and Reynolds Number.
Graph 1 is the increment of the temperature profiles, T1, T2, T3 and surface temperature with
time. This shows that temperature is directly proportional to time during free convection. The
surface temperature changes more rapidly with time whereas the temperatures T1, T2 and
T3 increase less rapidly with a similar pace. As the graph illustrates,
45
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This is because Tsurface is nearest to the vertical plate and T3, T2 and T1 follow
respectively. This is shown in the figure below.
This pattern of temperature increments are seen during force convection as well.
The progress of the surface temperature with time is seen more clearly in Graph 2. Here thesurface temperature increases exponentially until it reaches the steady state. The time taken
for the free convection experiment spans from 0 50 minutes and the temperatures range
from approximately 30 80 K.
Graph 3 shows the temperature patterns during forced convection at a velocity of 0.6 m/s.
Here the surface temperature starts at a higher level in comparison to T1, T2 and T3 even
though it increases in a similar pace. All the temperatures increase linearly but due to various
types of errors the experimental values do not produce a perfectly linear graph. This is seen in
Graph 4 where the surface temperature ultimately reaches steady state. The time taken for the
two forced convection graphs span from 0 400 seconds and the temperatures range from 25
45 K.
The surface temperature in Graph 5 increases linearly at a similar pace as the rest of the
temperature values. Here the temperatures are taken during forced convection at a velocity at
0.9 m/s. This shows that as velocity increases the values of the temperature tend to produce
similar patterns. Graph 6explains the increment of surface temperature and shows how it
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enters steady state clearly. The temperatures of these two graphs span from 25 35 K and the
time taken is between 0 and 400 seconds.
Graph 5 shows the same temperature patterns for a velocity of 1.2 m/s as seen previously for
the forced convection velocities at 0.6 and 0.9 m/s. Graph 6 shows a linear increment of
surface temperature until it reaches its steady state. The temperatures of these two graphs
span from 25 35 K and the time taken is between 0 and 400 seconds.
4.3 Com parison of Resu lts
Velocity
(m/s)
Re Pr
0.6 21.43 109.96.
0.9 29.00 295.00.
1.2 35.80 296.98.
Table 5: Forced Convection - Comparison of results
4.4 Com pari son with e xp ect ation s
Graph of heat transfercoefficient against
velocity ofair9047
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Heat Transfer coefficient, h
80
70
60
50
40
30
20
10
0
0 0,2 0,4 0,6 0,8 11,2 1,4
Velocity of air(m/s)
Graph 9: Heat transfer coefficient vs. velocity of air
48
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As the above graph shows, the experiment values of the heat transfer coefficient do no
coincide perfectly with the expect values. Theoretically, the graph of heat transfer coefficient
against the velocity of air should ne linear but due to certain unavoidable errors this is not so.
Graph of log (Nu/Pr) against log (Re)
3
2,5
log (Nu/Pr)
2
1,5
1
0,5
03,55 3,6 3,65 3,7 3,75 3,8 3,85
3,9 3,95
logRe
Graph 10: log (Nu/Pr) vs. log (Re)
Theoretically even though the log values of (nu/Pr vs. The log value of Re should be linear
the experimental results do not give a perfectly linear graph.
Graph of log (Nu exp) against log (Re)
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3
2,5
2
1,5
log (Nu)
1
0,5
0
3,55 3,6 3,65 3,7 3,75 3,83,85 3,9 3,95
log(Re)
50
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Graph 11: log (Nu exp) vs. log (Re)
The experimental results of the above graph are almost similar to the expected theoretical
results. But due to certain errors the obtained points do not contribute to a linear graph. But
since we use the best fit graph at instances such as these we could achieve the graph wereR = 0,99
expecting.
Graph of theoretical nusselt numberagainst
160
140
reynoldsnumber
y = 0,0144x + 30,049
92
120Nusselt number
100
80
60
4020
00 2000 4000 6000 800010000
Reynoldsnumber
Graph 12: Theoretical Nusselt number vs. Reynolds Number
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350
Graph of experiment nusseltnumber against
reynoldsnumber
300
Nusselt number
250
200
150
100
50
00 1000 2000 3000 4000 5000 6000
7000 8000 9000
ReynoldsNumber
Graph 13: Experimental Nusselt number vs. Reynolds number
Graph 12 and 13 show the comparison between the expected and the obtained graph using
the experimental results. Graph 12 was calculated using the theoretical value of
, whereas, the experimental value was calculated using
. This equation uses the experimental heat transfer coefficient. Therefore, the
experimental graph does not give perfectly linear points.
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4.5 Errors
Errors are inevitably prevalent in any experiment. Nevertheless, it is best to keep it as
minimal as possible. The discrepancies of data are due to a few assumptions made in the
calculation of theoretical forces. These assumptions made paradoxically do not happen in the
real world. One of the many assumptions made was the negligence of heat conduction
through the air duct. Contrary to that theory, heat loss to surrounding would hugely influence
the final result as huge amount of energy might have been lost to the surrounding before the
calculation was done. Consequently, affects the convection heat transfer coefficient. In
addition, heat loss may have happened at the back of the heat plate as the outer layer may not
be perfectly insulated. Not to forget, the opening present at the temperature points of the wall
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of air duct may disrupt the data accuracy. This is because; the openings may affect the
temperature and the properties of the air, especially when forced convection was carried out.
This error could be reduced by closing any opening present as tight as possible. Insulation of
the system could also be improved. Besides that, the system was assumed to reach steadystate when the slightest visible temperature could still be observed. The effect of such
assumptions cannot be totally ignored, as it might contribute to discrepancies of results.
Moreover, the experiment conducted may have been different from the standard
conditions where the table of coefficient was set up. The constantly changing humidity and
temperature in the air conditioned lab may affect the consistency of data yielded. Factors
stated above may clarify the discrepancies of experimental and theoretical data.
4.6 Dif ficu lti es/Lim itat io
n s
Contrasting from errors, limitations are mistakes present due to governing parameters
beyond our control which further explains the differences between the experimental values
and theoretical. One of the main reasons is human limitation. This problem surfaced due to
time lag. Time lags sets in as human do not have that most immediate and accurate response
to time the stop watch and record down the data, concurrently. Nevertheless, this error can be
reduced by repeating the experiments and conducting them with the same method,
consistently.
Another limitation present was the air humidity. The humidity of air might be different at
any time of the experiments especially the free and forced convection experiments. This
humidity although not taken into great importance, does affect the results because
temperature gradients exist. Consequently, defy the notion to set Tinfinity
as a constant as
temperature distribution was occurring rapidly from time to time. The key to tackle these
limitations is to perform the experiment several times consistently in a closed lab with
stagnant air of constant air humidity and air velocity.
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5.Appendices
Appen di x 1
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6.References
Incropera, F. D. (2007). In Fundamentals of Heat and Mass Transfer (6th Edition ed., pp.
371-377). New Jersy: John Wiley & Sons (Asia) Pte Ltd.
Nusselt Number. (17 08, 2010). Retrieved 13 09, 2010, from Wikipedia, the free
encyclopedia: h t tp : // e n.wikipedi a .or g /wik i /Nussel t _number
Prandtl Number. (04 09, 2010). Retrieved 13 09, 2010, from Wikipedia, the free
encyclopedia: h t tp : // e n.wikipedi a .or g /wik i /P r a ndt l _number
Rayleigh Number. (03 09, 2010). Retrieved 13 09, 2010, from Wikipedia, the freeencyclopedia: h t tp : // e n.wikipedi a .or g /wik i /R a y le i g h_numb e r
Reynolds Number. (10 09, 2010). Retrieved 13 09, 2010, from Wikipedia, the free
encyclopedia: h t tp : // e n.wikipedi a .or g /wik i /R e y no l ds_numb e r
http://en.wikipedia.org/wiki/Nusselt_numberhttp://en.wikipedia.org/wiki/Prandtl_numberhttp://en.wikipedia.org/wiki/Rayleigh_numberhttp://en.wikipedia.org/wiki/Reynolds_numberhttp://en.wikipedia.org/wiki/Prandtl_numberhttp://en.wikipedia.org/wiki/Rayleigh_numberhttp://en.wikipedia.org/wiki/Reynolds_numberhttp://en.wikipedia.org/wiki/Nusselt_number7/27/2019 (91481689) [Senior]Free and Forced Convection (Repaired)
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7. Nomenclaturelist