(91481689) [Senior]Free and Forced Convection (Repaired)

7/27/2019 (91481689) [Senior]Free and Forced Convection (Repaired)

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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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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

4


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5. Appendices....................................................................................................................... 39

5


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Appendix 1....................................................................................................................... 39

6. References ........................................................................................................................ 40

7. Nomenclature list ............................................................................................................. 41

6


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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

7


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VI. Summary

8


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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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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

10


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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


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


Graph 4: Forced Convection - Surface temperature vs. Time (v = 0.6 m/s)


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.


= 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


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


Graph 6: Forced convection - Surface temperature vs. Time (v = 0.9 m/s)


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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.


= 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


From Table A.4, of Appendix 1



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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 :


=

= 147.65 %


=

= 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


34

33.5

Steady State

Time (min)

33

32.5

32

31.50 50 100 150 200 250 300 350 400 450


Graph 8: Forced Convection - Surface temperature vs. Time (v = 1.2 m/s)


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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.


= 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:


From Table A.4, of Appendix 1



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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



=

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,

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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

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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)

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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_number


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7. Nomenclaturelist

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