Results and Discussion Practice HEAT TRANSFER BY RADIATION

7/23/2019 Results and Discussion Practice HEAT TRANSFER BY RADIATION

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RESULTS AND DISCUSSION: First experiment 12 V

During the pratie! "e ma#e t"$ #i%%erent experiments "ith #i%%erent &$'tages! in

this %irst part $% $ur resu'ts "e sh$" the $(taine# #ata %$r the heat trans%er ()

ra#iati$n at #i%%erent #istanes "ith a &$'tage e*ua' t$ 12 V+

The $n#ense# #ata %$r this %irst experiment is sh$"n in the %$''$"ing ta('e:

Obtained Data (At 12 Volts):

Distance(mm)

Temperature (C)

Temperature (K)

Radiometerreading(!m"2)

Voltage (V)

#eaterCurrent

(A)

AmbientTemperatur

e(K)

134 197.2 470.35 310 12 4 301.25

200 196.6 469.75 151 12 4 301.45

220 197.2 470.35 126 12 4 301.35

240 197.2 470.35 108 12 4 301.35

T$ ma,e the $rresp$n#ing a'u'ati$ns "e nee# t$ ta,e in $unt s$me p$ints:

Ratio: 50mm

Area: -./0 mm

Stefan-Boltzman Constant: /+/ E3. 45m62760

An# a's$:

Distance (mm) /

x

R (Radiometer

reading)

Ln R Lnx

!" 813 /+-8/-229- 0+.9-.89.

#00 1/1 /+31-2-9.8- /+29.81-8-

##0 12 0+.82.193- /+8982-/0

#"0 13. 0+.218122- /+0.38.928


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4.6 4.8 5 5.2 5.4 5.6 5.8

4.6

4.7

4.8

4.9

5

5.1

5.2

5.3

5.4

5.5

5.6

f(x) = - 0.55x + 8.07

R = 1

lnx

Linear (lnx)

ln $

ln R

N$"! ma,ing a graph $% 'n R &s 'n x t$ he, the s'$pe:

As "e an n$te! the s'$pe in#iates the temperature #i# n$t sta(i'ie (e%$re "e

t$$, the #ata+

The next step is a'u'ate the shape %at$r! t$ #$ that! "e nee# t$ ,n$" the existing

ang'e (et"een the #istane $% the ra#i$meter an# the #is, rati$+

F$r that! "e supp$rt $n the next #iagram:

Or the next $ne:


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As "e ,n$"! the %$rmu'a t$ a'u'ate the ang'e is:

=arctan (Rx)

;a,ing an examp'e %$r the %irst #istane:

=arctan( 50mm134mm )=0.357134

An# the shape %at$r:

F=(sin())2

F$r the ang'e $% the %irst #istane:

F=(sin(0.357134011))2=0.12221

An# %$r the $ther #istanes an# its $rresp$n#ing ang'es an# shape %at$rs:

A1($!O%C)!mm

#&potenuse(mm) R(mm)

'()arctan(R!$) *sen"2 *

134 143.0244734 50 0.357134011 0.122213531 F1

200 206.1552813 50 0.244978663 0.058823529 F2

220 225.6102835 50 0.223476601 0.049115914 F3

240 245.1530134 50 0.205395389 0.041597338 F4

T$ $(tain *( "e use# the %$''$"ing %$rmu'a:

qb=sb(Tsuf4

Tenv4

)

C$ntinuing the examp'e %$r the %irst #istane:

qb=5.67x108 W

m2K

4(470.35K4301.25K4)


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qb=2308.206726W

m2

A'' the *( $(taine# are in the next ta('e:

Distance+b,sb-(Ts"./

Ten0".)

134 2308.206726

200 2292.831654

220 2307.586331

240 2307.586331

N$"! the emmisi&it) is a'u'ate# as:

= R

qbF

A's$ %$r the %irst #istane


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* +bmmisi0it&

0.357134011

0.122213531

2308.20673 1.0989241

0.244978663

0.058823529

2292.83165

1.119576309

0.223476601

0.049115914

2307.58633

1.111707053

0.205395389

0.041597338

2307.58633

1.125123669

SECOND E>?ERI;ENT 10 V:

The $n#ense# #ata %$r this %irst experiment is sh$"n in the %$''$"ing ta('e:

Distance(mm)

Temperature (C)

Temperature (K)

Radiometerreading(!m"2)

Voltage (V)

#eaterCurrent(A)

AmbientTemperatu

re

134 236.4 509.55 333 14 4.6 301.95

200 236.7 509.85 217 14 4.7 301.95

220 236.1 509.25 184 14 4.6 302.15

240 235.8 508.95 158 14 4.7 302.35

T$ ma,e the $rresp$n#ing a'u'ati$ns "e nee# t$ ta,e in $unt s$me p$ints:

Ratio: 50mm

Area: -./0 mm

Stefan-Boltzman Constant: /+/ E3. 45m62760

An# a's$:

Distance($

)

R(Radiometer

Reading) ln R ln$

134 3335.808142

49 4.8978398

200 2175.379897

354 5.298317367

220 1845.214935

758 5.393627546240 158 5.062595 5.480638923


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033

5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9

4.6

4.7

4.8

4.9

5

5.1

5.2

5.35.4

5.5

5.6

f(x) = - 0.79x + 9.53

lnx

Linear (lnx)

Linear (lnx)

ln $

ln R

N$" ma,ing a

p'$t 'n R an# 'n x t$ he, the s'$pe:

As "e an n$te! the s'$pe in#iates the temperature #i# n$t sta(i'ie (e%$re "e

t$$, the #ata+

The next step is a'u'ate the shape %at$r! t$ #$ that! "e nee# t$ ,n$" the existing

ang'e (et"een the #istane $% the ra#i$meter an# the #is, rati$+

F$r that! "e supp$rt $n the next #iagram:


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As "e ,n$"! the %$rmu'a t$

a'u'ate the ang'e is:

=arctan (Rx)

;a,ing an examp'e %$r the se$n# #istane! (eause "e $(taine# a &a'ue e*ua' t$

888 "hih is the maximum gi&en () the e*uipment:

=arctan( 50mm200mm)=0.244978663

An# the shape %at$r:

F=(sin())2

F$r the ang'e $% the se$n# #istane:

F=(sin(0.244978667))2=0.058823529

An# %$r the $ther #istanes an# its $rresp$n#ing ang'es an# shape %at$rs:

$!mm#&potenuse

(mm) R(mm)'()arctan

(R!$) *sen"2 *

134 143.0244734 50 0.357134011 0.122213531 F1

200 206.1552813 50 0.244978663 0.058823529 F2

220 225.6102835 50 0.223476601 0.049115914 F3

240 245.1530134 50 0.205395389 0.041597338 F4

T$ $(tain *( "e use# the %$''$"ing %$rmu'a:

qb=sb(Tsuf4Tenv

4)


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C$ntinuing the examp'e %$r the se$n# #istane


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A'' the a'u'ate# in%$rmati$n is sh$"n in the next ta('e:

* +b mmisi0

it&

3%561

.311

0.122213

531

3351.23

746

0.813054

6493%2..76

899

0.058823

529

3360.24

77

1.097835

7333%22.6

9931

0.049115

914

3340.99

304

1.121295

363%2357

587

0.041597

338

3330.76

202

1.140375

678

;a,ing a $mparis$n (et"een the emissi&it) "e %$un# %$r the %irst experiment an#

the se$n# $ne:

mmisi0it&mmisi0it&2 rror

1.09892410.8130546

490.260135

756

1.1195763091.0978357

330.019418

575

1.1117070531.1212953

60.008551

099

1.1251236691.1403756

780.013374

548

4e an see that the emissi&it) is appr$ximate#+ This is (eause the %irst

in%$rmati$n an# se$n# in%$rmati$n "ere ta,en "ith #i%%erent $n#iti$ns+

It@s neessar) t$ (e 'ear "ith the emmisi&it) &a'ues! the rep$rte# &a'ue %$r the

materia' "e "$r,e# "ith is 3+..! an# the &a'ues "e $(taine# are $&er 1! "hih

in#iate# "e #i# n$t "ait en$ugh time t$ 'et the s)stem sta(i'ie+

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Results and Discussion Practice HEAT TRANSFER BY RADIATION