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Heat Transfer Experiment

HeatTransfer Experiment

HeatTransfer Experiment

Abstract

Inthis laboratory experiment, the various concepts of heat transferwithin a liquid and from a liquid to the environment have beencamptured. The rate of heat transfer by two types of cups, stryrofoamand paper cups, were studied. The report finds out that the rate ofheat transfer by a body depends on its overall heat transfercoefficient, U0.The report further finds out that the overall coefficient of amaterial is a function of the material’s properties, and variesfrom a one material to the other. After a thorough data analysis, thereport concludes that the rate of heat transfer by a stryrofoam cupis lower than that of a paper cup. .

Thereare three main modes of heat transfer. They include conduction,radiation, and convection (Bejan,2013).&nbspThislaboratory experiment focused on the heat transfer through convectionand conduction. Conduction is the transfer of heat by means ofvibration of particles of a material without the material moving(Nellis&amp Klein, 2011).On the other hand, convection is defined as the transfer of heatwithin a fluid as a result of movement of the fluid molecules due tochanges in temperature. In convection, the heat energy is transferredby the actual movement of fluid molecules. There are two forms ofconvection. They include natural convection and forced convection.

Innatural convection, the movement of fluid molecules is not caused byany external sources. Here, the motion of the fluid molecules takesplace only due to density differences, which is caused by temperaturegradients. In forced convection, the motion of fluid molecules iscaused by an external source, such as a pump, suction device, or fan(Kaufman,2012).

Inorder to obtain an expression for heat transfer from a surface of asolid to a fluid, scientists and engineers have used the empiricalformula shown below.

=—(1)

Theequation (1) can be expressed as,

UoA(TSurface– TAir)—(2)

Theconstant of proportionality, Uo,isalso referred to as an overall coefficient of heat transfer. It is afunction of a fluid’s thermal conductivity, velocity, and physicalproperties.

WaterCooling Experiment

Water-coolingexperiment has been used to study natural convection. In thislaboratory experiment, a stryrofoam and paper cups were filled withhot water and the temperatures of the water recorded as function oftime. As stated in the introduction part, the heat transfer of afluid is a function of many factors. It also varies from one fluid tothe other. With proper data analysis, the heat transfer of each cupwas determined accordingly. Again, as shown in Equation 1, the rateof heat transfer depends on the surface area of a cup. Therefore, thesurface area of each cup was determined as shown below.

—(3)

Theequation of the slanted line of a cup is given as,

(4)

Therefore,the total length of the slanted is given as,

—(5)

Thecurved surface area of the cup is given as,

—(6)

EngineeringObjectives

Themajor objectives of this laboratory experiment were:

  1. To understand the concept of heat transfer.

  2. To learn why and how the electric heaters are used in aquarium.

Methodsand Materials

Inthis laboratory experiment, the overall heat transfer coefficients ofstryrofoam and paper cups were determined through a water-coolingmethod. The materials used included, a stryrofoam cup, paper cup,water, electrical heater, thermometer, and stopwatch

ExperimentalProcedure

Thegeometry of the cups used was as shown below.

Firstly,the dimensions of each cup were taken and recorded. Secondly, thecurved and top surface areas of each cup were calculated and theresults recorded as shown in the results section. A hot plate wasthen used to boil 500ml-water. Thirdly, the weight of an emptystryrofoam cup and its lid was taken and recorded. The cup was thenfilled with the hot water. The weight of the cup filled with waterwas then taken and recorded. Fourthly, a thermometer was carefullyplaced through the hole in the plastic lid. The tip of thethermometer was placed half-way in the cup. The temperature of thewater was then recorded at the intervals of 30 seconds. The resultsare shown in the result section. The procedures were repeated for apaper cup and the results recorded accordingly.

Resultsand Discussion

Theresults for each cup are as shown

PaperCup

L= 9.5 cm

Topdiameter = 7.5 cm

Bottomdiameter = 5.0 cm

Emptymass = 9.1 g

Massof cup filled of water = 261.8 g

Time in Seconds

0

30

60

90

120

150

180

210

Temperature in ˚C

100

93

92.3

91.7

91

90.3

89.7

89

Time in Seconds

240

270

300

330

360

390

420

450

Temperature in ˚C

88.4

87.7

87

86.4

85.2

84.5

83.8

83.3

Time in Seconds

480

510

540

570

600

630

660

690

Temperature in ˚C

82.7

82.1

81.8

81.5

81

80.4

79.7

79.3

Time in Seconds

720

750

780

810

840

870

900

930

Temperature in ˚C

78.8

78.3

77.8

77.2

76.6

76.1

75.6

75.1

Time in Seconds

960

990

1020

1050

1110

1140

1170

1200

Temperature in ˚C

74.6

74.1

73.7

73.1

72.2

71.8

71.3

70.9

StryfoamCup

L= 9.5 cm

Topdiameter = 7.5 cm

Bottomdiameter = 4.4 cm

Emptymass = 3.5 g

Massof cup filled of water = 228.0 g

Time in Seconds

0

30

60

90

120

150

180

210

Temperature in ˚C

100

94.2

93.7

92.7

91.9

91.3

90.7

90.1

Time in Seconds

240

270

300

330

360

390

420

450

Temperature in ˚C

89.6

89

88.4

87.8

87.3

86.8

86.2

85.2

Time in Seconds

480

510

540

570

600

630

660

690

Temperature in ˚C

85.2

84.5

84.1

83.6

83.1

82.6

82.2

87.1

Time in Seconds

720

750

780

810

840

870

900

930

Temperature in ˚C

81.2

80.8

80.3

79.9

79.4

78.9

78.5

78.1

Time in Seconds

960

990

1020

1050

1110

1140

1170

1200

Temperature in ˚C

77.6

77

76.7

76.3

75.8

75.1

75

74.6

TheProcessed Data

Time(Seconds)

Time(Minutes)

Temperature for Paper Cup

Temperature for Styrofoam Cup

Ln for a Paper Cup

Ln for a Styrofoam Cup

0

0

100

100

0

0

30

0.5

93

94.2

-0.0981

-0.0806

60

1

92.3

93.7

-0.1085

-0.08786

90

1.5

91.7

92.7

-0.1174

-0.10255

120

2

91

91.9

-0.128

-0.11445

150

2.5

90.3

91.3

-0.1387

-0.12347

180

3

89.7

90.7

-0.1479

-0.13258

210

3.5

89

90.1

-0.1588

-0.14177

240

4

88.4

89.6

-0.1683

-0.14949

270

4.5

87.7

89

-0.1794

-0.15883

300

5

87

88.4

-0.1906

-0.16827

330

5.5

86.4

87.8

-0.2004

-0.17779

360

6

85.2

87.3

-0.2201

-0.1858

390

6.5

84.5

86.8

-0.2319

-0.19387

420

7

83.8

86.2

-0.2437

-0.20364

450

7.5

83.3

85.7

-0.2523

-0.21186

480

8

82.7

85.2

-0.2626

-0.22014

510

8.5

82.1

84.5

-0.2731

-0.23186

540

9

81.8

84.1

-0.2784

-0.23862

570

9.5

81.5

83.6

-0.2837

-0.24713

600

10

81

83.1

-0.2926

-0.25571

630

10.5

80.4

82.6

-0.3034

-0.26437

660

11

79.9

82.2

-0.3125

-0.27135

690

11.5

79.3

81.7

-0.3235

-0.28014

720

12

78.8

81.2

-0.3327

-0.28902

750

12.5

78.3

80.8

-0.3421

-0.29617

780

13

77.8

80.3

-0.3515

-0.30519

810

13.5

77.2

79.9

-0.363

-0.31246

840

14

76.6

79.4

-0.3746

-0.32163

870

14.5

76.1

78.8

-0.3843

-0.33274

900

15

75.6

78.5

-0.3942

-0.33834

930

15.5

75.1

78.1

-0.4041

-0.34586

960

16

74.6

77.6

-0.4142

-0.35534

990

16.5

74.1

77

-0.4243

-0.36684

1020

17

73.7

76.7

-0.4325

-0.37263

1050

17.5

73.1

76.3

-0.445

-0.38041

1110

18.5

72.2

75.8

-0.4639

-0.39023

1140

19

71.8

75.1

-0.4724

-0.40413

1170

19.5

71.3

75

-0.4832

-0.40613

1200

20

70.9

74.6

-0.4919

-0.41418

Thegraph of Lnverses time for stryrofoam and paper cup.

Calculationof Areas

Apaper Cup:

dtop= 7.5 cm

dbottom= 4.4 cm

L= 9.5 cm

CurvedSurface Area =

=9.5 x 10-2πx10-2

=0.01776 m2

TopArea =

=)x10-4

=4.41786 x 10-3m2

TotalArea, A, = 4.41786 x 10-3m2+0.01776 m2

=0.0222 m2

Astrofoam Cup:

dtop= 7.5 cm

dbottom= 5.0 cm

L= 9.5 cm

CurvedSurface Area =

=9.5 x 10-2πx10-2

=0.01865 m2

TopArea =

=)x10-4

=4.41786 x 10-3m2

TotalArea, A, = 4.41786 x 10-3m2+0.01865 m2

=0.0231 m2

Calculationsof Overall Heat Transfer Coefficients

Apaper Cup:

Emptymass = 9.1 g

Massof cup filled of water = 261.8 g

Massof water, m, = 261.8-9.1=252.7 g

=252.7 x 10-3 kg

=0.2527 kg

Fromthe Equation,

Itcan be deduced that the heat transfer coefficient, U0,for a paper cup is given as,

U0=

=

=-842.98 J/ ( 0Cm2minute)

AStrufoam Cup:

Emptymass = 3.5 g

Massof cup filled of water = 228.0 g

Massof water, m, = 228.0-3.5= 224.5g

=224.5 x 10-3 kg

=0.2245 kg

Fromthe Equation,

Itcan be deduced that the heat transfer coefficient, U0,for a strofoam cup is given as,

U0=

=

=-845.78 J/ ( 0Cm2minute)

Conclusion

Thevalue of an overall heat transfer coefficient of a body is a measureof how fast heat energy is dissipated from the body ( Kaufman,2012).&nbspFromthe experiment results, it can be seen the overall heat transfer fora stryrofoam cup is smaller than that of a paper cup. This indicatesthat the styrofoam has a lower rate of heat transfer than a papercup. The experiment was successful as all the objectives wereachieved.

References

Bejan,A. (2013).&nbspConvectionheat transfer&nbsp(1stEd.). 1st ed.). Hoboken, N.J.: Wiley.

Kaufman,M. (2012).&nbspPrinciplesof thermodynamics&nbsp(1st Ed.). New York: Marcel Dekker.

Nellis,G. &amp Klein, S. (2011).&nbspHeattransfer&nbsp(1stEd.). Cambridge: Cambridge University Press.