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ME3122-2 FORCED CONVECTION HEAT TRANSFER

BENJAMIN ANG ZI WEI

A0072215R

GROUP: 3L2 DATE: 7/9/2012

Department of Mechanical Engineering

National University of Singapore

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180 1.21E+01 9.35E+01 2.22E+01 3.66E+02 7.13E+01 1.34E+02 -0.63307 11.23574

210 1.22E+01 8.62E+01 2.21E+01 3.59E+02 6.41E+01 1.34E+02 -0.73979 13.10837

240 1.32E+01 8.00E+01 2.23E+01 3.53E+02 5.78E+01 1.34E+02 -0.84295 14.98099

270 1.26E+01 7.43E+01 2.21E+01 3.47E+02 5.21E+01 1.34E+02 -0.94644 16.85362

300 1.24E+01 6.66E+01 2.23E+01 3.40E+02 4.43E+01 1.34E+02 -1.10771 18.72624

330 1.26E+01 6.20E+01 2.24E+01 3.35E+02 3.96E+01 1.34E+02 -1.21968 20.59886360 1.24E+01 5.79E+01 2.24E+01 3.31E+02 3.55E+01 1.34E+02 -1.32935 22.47149

390 1.24E+01 5.42E+01 2.23E+01 3.27E+02 3.19E+01 1.34E+02 -1.43581 24.34411

420 1.27E+01 5.10E+01 2.25E+01 3.24E+02 2.85E+01 1.34E+02 -1.54842 26.21674

450 1.26E+01 4.79E+01 2.24E+01 3.21E+02 2.55E+01 1.34E+02 -1.65834 28.08936

480 1.24E+01 4.53E+01 2.24E+01 3.18E+02 2.29E+01 1.34E+02 -1.76799 29.96198

510 1.19E+01 4.29E+01 2.24E+01 3.16E+02 2.05E+01 1.34E+02 -1.87907 31.83461

540 1.14E+01 4.09E+01 2.26E+01 3.14E+02 1.83E+01 1.34E+02 -1.98814 33.70723

570 1.21E+01 3.91E+01 2.25E+01 3.12E+02 1.67E+01 1.34E+02 -2.0842 35.57986

600 1.22E+01 3.72E+01 2.22E+01 3.10E+02 1.50E+01 1.34E+02 -2.19273 37.45248

630 1.22E+01 3.57E+01 2.24E+01 3.09E+02 1.34E+01 1.34E+02 -2.30444 39.3251

660 1.21E+01 3.41E+01 2.23E+01 3.07E+02 1.19E+01 1.34E+02 -2.42527 41.19773690 1.20E+01 3.30E+01 2.23E+01 3.06E+02 1.07E+01 1.34E+02 -2.52878 43.07035

720 1.26E+01 3.17E+01 2.22E+01 3.05E+02 9.50E+00 1.34E+02 -2.64842 44.94298

750 1.21E+01 3.07E+01 2.23E+01 3.04E+02 8.46E+00 1.34E+02 -2.76348 46.8156

780 1.27E+01 2.99E+01 2.22E+01 3.03E+02 7.66E+00 1.34E+02 -2.86338 48.68822

810 1.28E+01 2.90E+01 2.21E+01 3.02E+02 6.97E+00 1.34E+02 -2.95942 50.56085

840 1.24E+01 2.85E+01 2.23E+01 3.01E+02 6.20E+00 1.34E+02 -3.07422 52.43347

870 1.23E+01 2.75E+01 2.21E+01 3.01E+02 5.45E+00 1.34E+02 -3.20546 54.3061

900 1.23E+01 2.69E+01 2.22E+01 3.00E+02 4.75E+00 1.34E+02 -3.34117 56.17872

Table 3: Teflon

tDiff

PressureTsphere Tair Tsphere T-Tair Tini-Tair

Ln[(T-Tair)/(

Tini-Tair)]at/(r^2)

sec mm water C C K

0 1.30E+01 1.19E+02 1.77E+01 392.1062 1.01E+02 1.01E+02 0 0

30 1.22E+01 1.15E+02 2.23E+01 388.3853 9.31E+01 9.68E+01 -0.03918 0.007301

60 1.20E+01 1.07E+02 2.22E+01 380.4773 8.53E+01 9.69E+01 -0.12781 0.014601

90 1.24E+01 1.03E+02 2.23E+01 376.0849 8.08E+01 9.69E+01 -0.18082 0.021902

120 1.23E+01 1.01E+02 2.23E+01 373.7415 7.84E+01 9.68E+01 -0.21043 0.029202

150 1.19E+01 9.86E+01 2.21E+01 371.6418 7.66E+01 9.70E+01 -0.2369 0.036503

180 1.25E+01 9.67E+01 2.24E+01 369.7353 7.43E+01 9.67E+01 -0.26316 0.043803

210 1.20E+01 9.52E+01 2.21E+01 368.2374 7.31E+01 9.70E+01 -0.28248 0.051104

240 1.23E+01 9.38E+01 2.21E+01 366.7908 7.16E+01 9.70E+01 -0.30258 0.058404

270 1.19E+01 9.22E+01 2.21E+01 365.1528 7.00E+01 9.70E+01 -0.32572 0.065705

300 1.19E+01 9.08E+01 2.20E+01 363.7608 6.88E+01 9.71E+01 -0.34505 0.073005

330 1.22E+01 8.92E+01 2.22E+01 362.1702 6.70E+01 9.70E+01 -0.36927 0.080306

360 1.24E+01 8.75E+01 2.21E+01 360.4656 6.54E+01 9.70E+01 -0.39473 0.087606

390 1.21E+01 8.60E+01 2.22E+01 358.9594 6.38E+01 9.69E+01 -0.41867 0.094907

420 1.20E+01 8.39E+01 2.22E+01 356.9286 6.18E+01 9.69E+01 -0.45075 0.102207

450 1.21E+01 8.22E+01 2.22E+01 355.1749 6.00E+01 9.69E+01 -0.4798 0.109508

480 1.21E+01 8.05E+01 2.20E+01 353.4882 5.85E+01 9.71E+01 -0.50724 0.116808

510 1.15E+01 7.88E+01 2.21E+01 351.8232 5.67E+01 9.70E+01 -0.53668 0.124109

540 1.19E+01 7.72E+01 2.22E+01 350.1521 5.50E+01 9.69E+01 -0.5673 0.131409

570 1.20E+01 7.51E+01 2.22E+01 348.126 5.30E+01 9.69E+01 -0.60464 0.13871

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600 1.24E+01 7.34E+01 2.21E+01 346.3952 5.13E+01 9.70E+01 -0.63757 0.14601

630 1.24E+01 7.06E+01 2.25E+01 343.6349 4.81E+01 9.66E+01 -0.69681 0.153311

660 1.22E+01 6.84E+01 2.20E+01 341.4237 4.64E+01 9.71E+01 -0.73813 0.160611

690 1.26E+01 6.51E+01 2.24E+01 338.1386 4.28E+01 9.67E+01 -0.81617 0.167912

720 1.24E+01 6.38E+01 2.20E+01 336.8212 4.18E+01 9.71E+01 -0.84223 0.175212

750 1.22E+01 6.23E+01 2.19E+01 335.2616 4.03E+01 9.72E+01 -0.87943 0.182513780 1.21E+01 6.03E+01 2.19E+01 333.3302 3.84E+01 9.72E+01 -0.92791 0.189813

810 1.20E+01 5.88E+01 2.16E+01 331.762 3.72E+01 9.75E+01 -0.96475 0.197114

840 1.19E+01 5.76E+01 2.19E+01 330.5574 3.57E+01 9.72E+01 -1.00224 0.204414

870 1.28E+01 5.62E+01 2.19E+01 329.1586 3.43E+01 9.72E+01 -1.04223 0.211715

900 1.19E+01 5.45E+01 2.17E+01 327.4553 3.27E+01 9.74E+01 -1.09067 0.219015

930 1.24E+01 5.34E+01 2.20E+01 326.426 3.14E+01 9.71E+01 -1.12904 0.226316

960 1.26E+01 5.19E+01 2.18E+01 324.8922 3.01E+01 9.73E+01 -1.1739 0.233616

990 1.24E+01 5.08E+01 2.23E+01 323.8453 2.86E+01 9.68E+01 -1.22021 0.240917

1020 1.29E+01 4.93E+01 2.19E+01 322.3028 2.74E+01 9.72E+01 -1.26701 0.248217

1050 1.20E+01 4.83E+01 2.22E+01 321.2921 2.61E+01 9.69E+01 -1.31162 0.255518

1080 1.26E+01 4.72E+01 2.23E+01 320.1827 2.49E+01 9.68E+01 -1.35872 0.2628181110 1.19E+01 4.61E+01 2.21E+01 319.1301 2.40E+01 9.70E+01 -1.39647 0.270119

1140 1.27E+01 4.51E+01 2.23E+01 318.1289 2.29E+01 9.69E+01 -1.44305 0.277419

1170 1.22E+01 4.41E+01 2.22E+01 317.0509 2.19E+01 9.69E+01 -1.48896 0.28472

1200 1.19E+01 4.33E+01 2.23E+01 316.3185 2.10E+01 9.68E+01 -1.52724 0.29202

1230 1.19E+01 4.24E+01 2.22E+01 315.3566 2.01E+01 9.69E+01 -1.57092 0.299321

1260 1.18E+01 4.13E+01 2.23E+01 314.2904 1.90E+01 9.69E+01 -1.62682 0.306622

1290 1.21E+01 4.06E+01 2.22E+01 313.5718 1.83E+01 9.69E+01 -1.66439 0.313922

1320 1.24E+01 3.96E+01 2.23E+01 312.5936 1.73E+01 9.68E+01 -1.7233 0.321223

1350 1.22E+01 3.88E+01 2.22E+01 311.7523 1.65E+01 9.69E+01 -1.76925 0.328523

1380 1.33E+01 3.84E+01 2.24E+01 311.3776 1.60E+01 9.67E+01 -1.79904 0.335824

1410 1.22E+01 3.74E+01 2.23E+01 310.3765 1.51E+01 9.68E+01 -1.85809 0.3431241440 1.23E+01 3.67E+01 2.21E+01 309.6899 1.46E+01 9.70E+01 -1.89421 0.350425

1470 1.22E+01 3.62E+01 2.22E+01 309.246 1.40E+01 9.69E+01 -1.93117 0.357725

1500 1.22E+01 3.57E+01 2.22E+01 308.7008 1.35E+01 9.69E+01 -1.97202 0.365026

1530 1.23E+01 3.48E+01 2.21E+01 307.771 1.26E+01 9.70E+01 -2.03741 0.372326

1560 1.26E+01 3.46E+01 2.23E+01 307.6372 1.23E+01 9.68E+01 -2.06308 0.379627

1590 1.16E+01 3.37E+01 2.20E+01 306.6661 1.16E+01 9.71E+01 -2.12034 0.386927

1620 1.21E+01 3.35E+01 2.24E+01 306.4594 1.11E+01 9.67E+01 -2.16648 0.394228

1650 1.18E+01 3.26E+01 2.23E+01 305.6443 1.04E+01 9.68E+01 -2.23425 0.401528

1680 1.20E+01 3.25E+01 2.23E+01 305.4535 1.01E+01 9.68E+01 -2.25566 0.408829

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Graph 1: Aluminium method 1

Graph 2: Aluminium method 2

y = -0.0403x + 0.1554

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 20 40 60 80 100

ln[(T-Ta

)/(Ti-

Ta

)]

(t)/r

ALUMINIUM - Graph of ln[(T-Ta)/(Ti-Ta)] against

(t)/r

METHOD 1

Linear (METHOD 1)

y = -0.172x + 384.822.90E+02

3.10E+02

3.30E+02

3.50E+02

3.70E+02

3.90E+02

4.10E+02

0 100 200 300 400 500 600

Tsphere

t

ALUMINIUM - Graph of Temperature of

Sphere(Tsphere)/K against time(t)/s

ALUMINIUM - METHOD 2

Linear (ALUMINIUM - METHOD

2)

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Graph 3: Brass method 1

Graph 4: Brass method 2

y = -0.0595x + 0.0247

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 10 20 30 40 50 60

ln[(T-Ta

)/(Ti-

Ta

)]

(t)/r

BRASS - Graph of ln[(T-Ta)/(Ti-Ta)] against (t)/r

METHOD 1

Linear (METHOD 1)

y = -0.1279x + 393.642.90E+02

3.10E+02

3.30E+02

3.50E+02

3.70E+02

3.90E+02

4.10E+02

4.30E+02

0 200 400 600 800

Tspher

e

t

BRASS - Graph of Temperature of Sphere(Tsphere)/K

against time(t)/s

BRASS - METHOD 2

Linear (BRASS - METHOD 2)

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Graph 5: Teflon method 1

Graph 6: Teflon method 2

y = -5.5035x + 0.0674

-2.5

-2

-1.5

-1

-0.5

0

0.5

0 0.1 0.2 0.3 0.4 0.5

ln[(T-Ta

)/(Ti-

Ta

)]

(t)/r

TEFLON - Graph of ln[(T-Ta)/(Ti-Ta)] against

(t)/r

Linear (METHOD 1)

y = -0.0487x + 377.313.00E+02

3.10E+02

3.20E+02

3.30E+02

3.40E+02

3.50E+02

3.60E+02

3.70E+02

3.80E+02

3.90E+02

4.00E+02

0 500 1000 1500

Tsph

ere

t

TEFLON - Graph of Temperature of Sphere(Tsphere)/K

against time(t)/s

METHOD 2

Linear (METHOD 2)

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CALCULATION

Validity of lumped-heat-capacity method

From equations (2) and (6),

)(3

20

k

rh

r

t

TT

TT

oai

aLn

Bi

h V A

k

hr

k

o

/ 1

3

Bi < 0.1

FOR ALUMINIUM:

Gradient ofGraph 1 = -3(hro/k) = -0.0403

Bi = gradient of graph / -9

= -0.0403 / -9

= 0.00448< 0.1 hence lumped heat capacity method is valid

COMPARING WITH HEISLER TEMPERATURE CHART,

At time = 240s,

(T-Tair)/(Ti-Tair) = 34.2/108 = 0.32

(t)/r = 32.6

From chart,

k/(hro) = 75 (approximately)

From Graph 1,

k/(hro) = 3/0.0403 = 74.4

The two values are close and hence it indicates a reasonable approximation using lumped-heat-capacity method.

FOR BRASS:


Bi = gradient of graph / -9= -0.0595 / -9

= 0.00661< 0.1 hence lumped heat capacity method is valid

COMPARING WITH HEISLER TEMPERATURE CHART,

At time = 240s,

(T-Tair)/(Ti-Tair) = 57.8/134 = 0.431

(t)/r = 14.98

From chart,


From Graph 3,

k/(hro) = 3/0.0595 = 50.4

The two values are close and hence it indicates a reasonable approximation using lumped-heat-capacity method.

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FOR TEFLON:


Bi = gradient of graph / -9

= -5.5035 / -9

= 0.6115

> 0.1 hence lumped heat capacity method is not valid

COMPARING WITH HEISLER TEMPERATURE CHART,At time = 840s, (for time = 240s, the values are out of range, hence another reading is required)

(T-Tair)/(Ti-Tair) = 35.7/97.2 = 0.367

(t)/r = 0.24

From chart,

k/(hro) = 0.05 (approximately)

From Graph 5,

k/(hro) = 3/5.5035 = 0.545

The two values are completely different and hence it is not possible to approximate using lumped-heat-capacitymethod.

Calculation of convective heat transfer coefficient

METHOD 1

FOR ALUMINIUM:

Graph 1-3 (hro/k) = -0.0403

h = 0.0403(k/3ro)

= 0.0403(206/(30.025))

= 110.7 W/(m2.K)

FOR BRASS:

Graph 3-3 (hro/k) = -0.0595

h = 0.0595(k/3ro)= 0.0595(128/(30.025))= 101.5 W/(m

2.K)

FOR ALUMINIUM: (NOT APPLICABLE)

Graph 5-3 (hro/k) = -5.5035

h = 5.5035(k/3ro)

= 5.5035(0.35/(30.025))

= 25.7 W/(m2.K)

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METHOD 2

FOR ALUMINIUM:

Ts = Ts,ave = 333K

Ta = Tambient,ave = 295K

Graph 2Gradient of graph, dT/dt = -0.172

Qt = CsVdT/dt

= 2707 896 (4 0.0253/ 3) 0.172

= 27.3 W

Qr = ..A.(Ts4-Ta

4)

= 0.8 5.67 10-8

(4 0.025) (3334295

4)

= 1.68 W

Qc = Qt - Qr= h.As.(Ts-Ta)

Qc = 27.31.68

= 25.62 W

= h (4 0.025) (333295)

h = 85.8 W/m2.

K

FOR BRASS:

Ts = Ts,ave = 336K



Qt = CsVdT/dt= 8522 385 (4 0.025

3/ 3) 0.1279

= 27.5 W

Qr = ..A.(Ts4-Ta

4)

= 0.8 5.67 10-8 (4 0.025) (33642954)= 1.84 W

Qc = Qt - Qr

= h.As.(Ts-Ta)

Qc = 27.51.84= 25.66 W

= h (4 0.025) (336295)

h = 79.7 W/m2.

K

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FOR TEFLON:

Ts = Ts,ave = 336K



Qt = CsVdT/dt

= 2200 1046 (4 0.0253/ 3) 0.0487

= 7.33 W

Qr = ..A.(Ts4-Ta

4)

= 0.8 5.67 10-8

(4 0.025) (3364295

4)

= 1.84 W

Qc = Qt - Qr= h.As.(Ts-Ta)

Qc = 7.331.84

= 5.49 W

= h (4 0.025) (336 295)

h = 17.0 W/m2.

K

METHOD 3

FOR ALUMINIUM:

Ta = 295K 300 K

Ti = 403K 400 K

Viscosity of air at Ti,

400K = 2.286 10-5

kg/(m.s)

Density of air at ambient temperature,

a = 300K

= 1.1774 kg/m3

Viscosity of air at ambient temperature,

amb 300K= 1.846 x 10

-5kg/(m.s)

2

2UgH w

Velocity of flow at ambient temperature, (zero error of -0.1x10-3

m/s initially)

U = ((13.3 + 0.1) 10-3

x 1000 x 9.81 x 2 / 1.1774)0.5

= 14.94 m/s

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02RerU

= 1.1774 x 14.94 x 2 x 0.025 / (1.846 x 10-5

)

= 47645

Prambient = 0.708 0.71

kambient = 0.02624 W/(m.K)

Conditions:

35000 < Re=47645 < 76000

Pr = 0.708 , 0.71 Pr < 380

< 1 (Condition not met)

Nui

2 0 4 0 060 5 2 3 0 4 0 25( . Re . Re ) Pr ( ). / . .

= 2 + (0.4 476450.5

+ 0.06 476452/3

) 0.7080.4

[(1.846 10-5

) /( 2.286 10-5

)]0.25

= 139.2

krhNu o /2.

h = 139.2 x 0.02624 / (0.025 2)= 81.9 W/(m

2.K)

FOR BRASS:

Ta = 295K 300 K

Ti = 429K


429K =

400450

400450400

KKK

( 429400 )

= 2.401 10-5

kg/(m.s)

Density of air at ambient temperature,a = 300K

= 1.1774 kg/m3


amb 300K= 1.846 x 10

-5kg/(m.s)

2

2UgH w


m/s initially)

U = ((13.3 + 0.1) 10-3

x 1000 x 9.81 x 2 / 1.1774)0.5

= 14.94 m/s

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02RerU

= 1.1774 x 14.94 x 2 x 0.025 / (1.846 x 10-5

)

= 47645



Conditions:

35000 < Re=47645 < 76000

Pr = 0.708 , 0.71 Pr < 380


Nui

2 0 4 0 060 5 2 3 0 4 0 25( . Re . Re ) Pr ( ). / . .

= 2 + (0.4 476450.5

+ 0.06 476452/3

) 0.7080.4

[(1.846 10-5

) /( 2.401 10-5

)]0.25

= 137.5

krhNu o /2.

h = 137.5 x 0.02624 / (0.025 2)= 72.16 W/(m

2.K)

FOR TEFLON:

Ta = 290.7K 300 K

Ti = 392K


392K =

350400

350400350

KKK

( 392350 )

= 2.252 10-5

kg/(m.s)

Density of air at ambient temperature,

a = 300K

= 1.1774 kg/m3


amb 300K

= 1.846 x 10-5

kg/(m.s)

2

2UgH w


m/s initially)

U = ((13.0 + 0.1) 10-3

x 1000 x 9.81 x 2 / 1.1774)0.5

= 14.77 m/s

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02RerU

= 1.1774 x 14.77 x 2 x 0.025 / (1.846 x 10-5

)

= 47102



Conditions:

35000 < Re=47102 < 76000

Pr = 0.708 , 0.71 Pr < 380


Nui

2 0 4 0 060 5 2 3 0 4 0 25( . Re . Re ) Pr ( ). / . .

= 2 + (0.4 471020.5

+ 0.06 471022/3

) 0.7080.4

[(1.846 10-5

) /( 2.252 10-5

)]0.25

= 138.8

krhNu o /2.

h = 138.8 x 0.02624 / (0.025 2)= 72.84 W/(m

2.K)

METHOD 4

With reference to Heisler Temperature Chart

FOR ALUMINIUM:

At time = 240s,

(T-Tair)/(Ti-Tair) = 34.2/108 = 0.32

(t)/r = 32.6

From chart,


h = k / (75 x ro)

= 206 / ( 75 x 0.025 )

= 109.9W/(m2.K)

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FOR BRASS:

At time = 240s,

(T-Tair)/(Ti-Tair) = 57.8/134 = 0.431

(t)/r = 14.98

From chart,k/(hro) = 50 (approximately)

h = k / (50 x ro)

= 128 / ( 50 x 0.025 )

= 102.4W/(m2.K)

FOR TEFLON: (NOT APPLICABLE)

At time = 840s, (for time = 240s, the values are out of range, hence another reading is required)

(T-Tair)/(Ti-Tair) = 35.7/97.2 = 0.367

(t)/r = 0.24

From chart,k/(hro) = 0.05 (approximately)

h = k / (0.05 x ro)

= 0.35 / ( 0.05 x 0.025 )

= 280W/(m2.K)

Table 4: Experimentally determined convective heat transfer coefficients

Spheres Reynolds Number Convective Heat Transfer Coefficient, W/m2

K

Method 1 Method 2 Method 3 Method 4

Aluminium 47645 110.7 85.8 81.9 109.9

Brass 47645 101.5 79.7 72.16 102.4

Teflon 47102 25.7

(N.A.)

17.0 72.84 280

(N.A.)

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DISUSSION

1. Compare the convective heat transfer coefficients of the methods 1, 2 and 4 with that

obtained from the method 3. Give a brief account on possible causes of the

discrepancy in the values of the heat transfer coefficient obtained from method #3

The differences in heat transfer coefficients may be due to the following reasons:

1. The lumped-heat-capacity method assumes that the temperature in the sphere is uniform. However, inthe actual experiment, the temperature may not be completely uniform. Hence the data obtained from

the experiment will be inaccurate and the plots may not reflect the actual values correctly.

2. The values obtained for all three materials from method 2 are not likely to be very accurate. Averagedvalues are used in calculations. This will generate errors in the calculated heat transfer coefficients.

3.

The flow past the sphere is assumed to be smooth. But in the experiment, there is a wake present at theend of the sphere as the flow not laminar and smooth. Thus, there will be heat losses at the flow at the

end of the sphere due to this wake and this will affect the values of the heat transfer coefficients,

causing discrepancies.

2. Comment on the values of heat transfer coefficients obtained from method 1, 2, 3 and

4.

Method 1

The most reliable assumption and method of calculation as Bi is far from the critical value of 0.1, with the

exception of Teflon. There is minimal error in this method of analysis. Hence the h value calculated is relativelyaccurate.

Method 2A best fit linear line is used to approximate the values plotted. This is not very accurate as the plot is supposed

to be a curve. The linear plot averaged out the spread of values in the calculations and hence the heat coefficient

obtained will be less accurate than that of Method 1.

Method 3

The least reliable analysis method as all 3 materials do not satisfy the initial conditions to utilize the empirical

relation (Whitaker). All 3 materials violate the initial condition of 1

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e8 edited lab 3122