Heal Transfer Lab 4 2

Department of Mechanical & Industrial Engineering

MEC701 Heat Transfer - Lab Report No. 4

FREE CONVECTION

Program: Mechanical Engineering

Lab Section 3

Lab Date: March 12, 2008

Due Date: March 26, 2008

Prepared for:

Instructor: Dr. D. Naylor

Teaching Assistance: Mr. Ebrahim Poulad

Names Student ID Signature*Aman, Aditya xxx025078

Kalashnikov, Andrey xxx098084Lin, Xu Zhong xxx558915

Matharoo, Raj (Manager) xxx551613Shanmugasundram, Sujeethan xxx726181

1

Summary

In this experiment, the free convective heat transfer coefficients for a horizontal

aluminum cylinder and an aluminum plate were calculated and compared. A hot air gun

was used to heat both the specimens for a specified time interval. Corresponding

calculations were made and then tabulated as displayed in the results section. A graph of

the log of Nusselt number vs the log of Prandtl Number was also plotted. A certain

degree of errors were seen in performing the experiment which could be attributed to

poor ventilation and also uneven heating of the aluminum bar. Here the percent errors in

the range of 42 – 47% were seen for the measured and theoretical values of h in the

horizontal cylinder, whereas errors in the range of 22%-35% were seen for the vertical

plate. Also the Biot number was calculated to be lower than 0.1, which subsequently

proved that lumped capacitance could also be used for corresponding calculations.

Generally the experiment was considered to be a success despite the percentage errors

seen and the objectives were met as well.

2

Table of contents:

1. Introduction and Theory …………………………………………………….Pg.4

2. Apparatus…………………………………………………………………….Pg.6

3. Procedure…………………………………………………………………….Pg.7

4. Results………………………………………………………………………. Pg.8

5. Discussion……………………………………………………………………Pg.10

6. Conclusion…………………………………………………………………...Pg.11

7. References……………………………………………………………………Pg.12

8. Appendices…………………………………………………………………...Pg.13

3

1.0 Introduction

A heated fluid tends to rise in the presence of the Earth’s gravitational field and density

differences within the fluid produces buoyant forces that drive the flow. This buoyancy-

induced flow is called free convection or natural convection.

A horizontal cylinder of diameter D and a vertical flat plate of height L, is shown in

Figure1. Both objects have surface temperature TS and are immersed in a large body of

quiescent fluid at temperature . Most fluids expand when heated. So, the heated fluid

near the surface of the object will be less dense than the surrounding fluid. This fluid will

rise, producing a thermal boundary layer on the surface, and thermal plume above the

object.

Figure 1: Free Convection from an isothermal horizontal cylinder and an isothermal

vertical plate.

The following relationship predicts the Free Convective Heat Transfer

4

--------------------(1)

Where is the average Nusselt Number and Ra is the Rayleigh

number. In Equation (1), C and n are empirical constants which are

determined from experiments or analysis. The fluid properties in

equation (1) are evaluated at the film temperature, (TS+ )/2.

The characteristic dimension used in the Nusselt number and Rayleigh

number depends on the geometry of the problem. For free convective

heat transfer the dimension it has the biggest effect on the convective

heat transfer rate is the overall height of the object.

So, for a horizontal cylinder, the characteristic length is the diameter

D. Similarly, for a vertical plate, the characteristic length is the height,

L. Using these characteristic dimensions, the equation (1) is modified

to the following equation (2) valid for:

Horizontal Isothermal Cylinder

----------------(2)

Vertical Isothermal Cylinder

5

-----------------(3)

The values of both C and n depend on the Rayleigh number and are

different for different geometries.

2.0 Apparatus

The following apparatus was used for the experiment:

1. A long aluminum cylinder

2. A square aluminum plate

3. Plastic threaded rods

4. Thermocouple

6

3.0 Procedure

1. The air disturbance nearby the apparatus was kept at a minimum level.

2. The ambient temperature and atmospheric pressure were recorded.

3. The experiment was started with the vertical plate first to avoid any interaction

with the plume from the horizontal cylinder. The vertical plate was heated to

160-170 by using a hot air gun.

4. The plate’s internal temperature was kept uniform by leaving it for 2 minutes after

the heating was completed.

5. The plate’s temperature was taken every 120 seconds for 16 minutes.

6. The above steps were repeated for the horizontal cylinder.

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4.0 Results

Table 1 – Summary of Results for horizontal cylinder

Time step

I

Measured Average

Heat Transfer Coeff,

(W/m K)

Predicted Average

Heat Transfer

Coeff,

(W/m K)

Difference

Between

Measured &

Predicted (%)

Experimental

Rayleigh

Number, Ra

Measured

Average Nusselt

Number

1 4.215682 8.024959 47.46787 48048.75 7.1065982 4.51839 7.880066 42.66051 45541.35 7.0120133 4.441648 7.733628 42.56708 43063.17 6.9146114 3.850448 7.599315 49.33165 40852.11 6.8240925 4.069024 7.47179 45.5415 38721.53 6.7333226 3.891717 7.34539 47.01824 36672.54 6.6424227 3.873411 7.223405 46.37694 34724.8 6.5524128 4.069629 7.100402 42.68453 32795.52 6.45944

Table 2 – Summary of Results for vertical plate

Time step

I

Measured Average

Heat Transfer Coeff,

(W/m K)

Predicted Average

Heat Transfer

Coeff.,

(W/m K)

Difference

Between

Measured &

Predicted (%)

Experimental

Rayleigh

Number, Ra

Measured

Average Nusselt

Number

1 6.480549 9.7299 33.39552 11462784 53.395632 6.663447 9.553776 30.25327 10977932 52.63953 6.999992 9.372095 25.31027 10479686 51.8388

8

4 5.955623 9.202665 35.28371 10031267 51.096065 6.010026 9.045493 33.55778 9610191 50.378086 6.403375 8.88379 27.92068 9180241 49.622877 5.721765 8.728303 34.44585 8779885 48.898038 6.67398 8.569534 22.11968 8367875 48.12858

log Nusselt number vs. log Rayleigh number

1

10

100

1 10 100 1000 10000 100000 1000000 10000000 1E+08

log Rayleigh number

log

Nuss

elt n

umbe

r

Figure 1 – Graph Log of average Nusselt number vs. log Rayleigh number

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5.0 Discussion

For the horizontal cylinder, percent errors of 42%-47% were apparent for the

measured and theoretical heat transfer coefficient. While, for the vertical plate, percent

errors were calculated to be in the range of 22%-35% for the theoretical and measured

heat transfer coefficient. The reason for the percent errors can be explained by a couple of

factors during the experimentation. One of which is that the air in the room was not

perfectly quiescent and that it was disturbed because of the poor ventilation. Another

factor was the uneven heating of the aluminum bar as the temperature of the entire

surface had deviations. Also, inaccurate timing during the cooling stage may have

triggered some imprecise results. These errors might have accumulated to a point that it

drastically affected the results.

Lumped capacitance method is certainly valid for this type of experiment because

the Biot number was less than 0.1. As the conductive temperature resistance is much

lower than the convective temperature resistance, this signifies that the temperature

variation within the metal plate is much lower than the temperature variation between the

metal plate and the air.

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The total heat loss for the vertical plate is 18W, while the heat loss due to

radiation is 3W. Hence, heat loss due to radiation accounts for about

16% of the total heat loss. Polished surfaces have lower emissivity as compared to rough

surface, hence the cylinder and the plate was polished to prevent any major heat loss to

radiation.

6.0 Conclusion

The objective of the experiment was to compare the free convective heat transfer

coefficients of a horizontal cylinder and a vertical plate. For the calculation of the

average convective heat transfer coefficients of the cylinder, the Grashof, Prandtl,

Reyleigh and Nusselt numbers were evaluated. The predicted value for h was found to be

higher than the measured value, in both cases. Generally percent errors in the range of 42

– 47% were seen for the measured and theoretical values of h in the horizontal cylinder,

whereas errors in the range of 22%-35% were seen for the vertical plate. Generally, the

horizontal cylinder produced lower values for convective heat transfer coefficients when

compared to the vertical plate. In all the experiment was considered to be a success.

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7.0 References

[1] Naylor D., MEC 701 Heat Transfer Laboratory Manual, Toronto: Ryerson University,

2008.

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8.0 Appendix

Test conditions for cylinder experiment

Barometric pressure: 746.15 mmHg

Initial Room Temperature: 72.4 = 295.6 K

Table 2 – Collected data for horizontal cylinder

Index i Time t

(sec)

Instantaneous

Cylinder Temp.

Instantaneous

Cylinder Temp.

1 0 160.2 344.4

2 120 153.7 340.8

3 240 147.3 337.2

4 360 141.5 334.0

5 480 136.8 331.4

6 600 132.2 328.8

7 720 128.1 326.5

8 840 124.3 324.4

9 960 120.6 322.4

Sample calculations for horizontal cylinder

m = 0.4505 kg D = 2.46 cm L = 35.6 cm

For aluminum alloy 2024-T6

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and

= 0.0559762

4.212 (W/m K)

Interpolating the air properties at T=319.98K and using Table A.4 we get:

Plugging in all this variables into equation for Rayleigh number we get

Now we can find Nusselt number Nu = C Ra , where C = 0.480 and n = 0.250 because Ra

Nu = 7.106598From Nusselt number we can calculate the predicted value of :

(W/m K)

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Test conditions for plate experiment

Barometric pressure: 746.15 mmHg

Initial Room Temperature: 71.3 = 294.98 K

Table 2 – Collected data for vertical plate

Index i Time t

(sec)

Instantaneous

Plate Temp.

Instantaneous

Cylinder Temp.

1 0 159.8 344.15

2 120 154.4 341.15

3 240 149.2 338.2611

4 360 144.1 335.4278

5 480 140 333.15

6 600 136.1 330.9833

7 720 132.2 328.8167

8 840 128.9 326.9833

9 960 125.3 324.9833

Sample calculations for vertical plate

m = 0.8002 kg H = 0.1524 m

W =0.1524 m D = 0.0127 m

For aluminum alloy 2024-T6

and

A = 2 (HW+HD+WD) = 0.05419344 m

15

6.480 (W/m K)

K

Interpolating the air properties at T=319.875K and using Table A.4 we get:

Plugging in all this variables into equation for Rayleigh number we get

Now we can find Nusselt number Nu = C Ra , where C = 0.125 and n = 0.333 because Ra

Nu = 53.39563From Nusselt number we can calculate the predicted value of :

(W/m K)

16