aer423 lab - thermal conductivity and contact resistance (1)

8/20/2019 AER423 Lab - Thermal Conductivity and Contact Resistance (1)

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Time 0 [min] 2 [min] 4 [min] 6 [min]

Water Tin °C 19.1 ± 0.05 19.1 ± 0.05 19.2 ± 0.05 19.2 ± 0.05

Water Tout °C 24.9 ± 0.05 24.9 ± 0.05 25 ± 0.05 25 ± 0.05

T1°C 75.1 ± 0.05 75.2 ± 0.05 75.4 ± 0.05 76.1 ± 0.05

T2°C 132.9 ± 0.05 132.2 ± 0.05 132.6 ± 0.05 133 ± 0.05

T3°C 168.1 ± 0.05 168.6 ± 0.05 168.9 ± 0.05 169.9 ± 0.05T4°C 184.7 ± 0.05 185.2 ± 0.05 185.6 ± 0.05 186.2 ± 0.05

OBSERVATIONS

Mass of ater !o""e!te#$

490. ± 0.5 m%

& 490. ± 0.5 '

& 0.4900 ± 0.0005 ('

Co""e!tion time$ 6.00 ± 0.005 min & 360 ± 0.3 se! tota"

ḿ=0.4900±0.0005kg

360s ±0.3=1.361×10−3±0.00025

kg

s

)er!enta'e *rror )ro+a'ation$

(100× 0.00050.49 )+(100× 0.3360 )=0.18537 error

,-so"ute *rror )ro+a'ation$

1.361×10−3×0.18537 =0.00025 kg /s| Error| Propagation

RESULTS

,era'e Tem+. °C ,era'e Tem+. °/

Water Tin 19. 1́ 5 ± 0.05 292.3 ± 0.05

Water Tout 24. 9́ 5 ± 0.05 298.1 ± 0.05

T1 75. 4́ 5 ± 0.05 347.6 ± 0.05

T2 132. 6́ 75 ± 0.05 405.8 ± 0.05

T3 168. 8́ 75 ± 0.05 442.0 ± 0.05

T4 185. 4́ 2 ± 0.05 458.6 ± 0.05


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eat transfer rate trou' te !om+osite -ar$

,era'e Water Tin & 19.15 ± 0.05 °C 273.15 ± 0.05 & 292.3 ± 0.05 /

,era'e Water Tout & 24.95 ± 0.05°C 273.15 ± 0.05 & 298.1 ± 0.05/

C p H 2 O=4185.5

J

(k g ∙ K )

q= ḿ∙ C p (T out −T ¿)

¿(1.361×10−3 ±0.00025 kgs )(4185.5 J kg∙K )(298.1±0.05 K −292.3±0.05 K )

q=33.04±6.4 J

s=33±6.4W

: Heat transfer rate through the composite bar

Error propagation: Like above error propagation percentage errors were added

and then converted to absolute error to determine the ± 6.4W value


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i'. 1


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*tra+o"ation of interfa!ia" tem+erature #ifferen!e$

T1 $ 6.5mm 347.6/ T3 $ 45mm 442/

T2 $ 31.5mm 405.8/ T4 $ 95mm 458/

Tinterfa!ia" $ 38mm Tint. ss Tinterfa!ia" $ 38mm Tint. a"

Tint ss & [38mm 6.5mm405.8/347.6/:31.5mm6.5mm] 347.6/

& 420.9 ± 0.05 /

Tint a" & [38mm 45mm458.6/442/:95mm45mm]442/

& 439.7 ±

0.05/

;nterfa!ia" Tem+.


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A= & $

2

4=

& (0.025m)2

4=4.908×10−4 m2

%i= q

A(T A−T )

= 33±6.4W

(4.908

×10

−4

m

2

)(18.7

±0.05

K )

=3500±707 W

m

2

∙ K


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Therma! con)ucti*it+ of A!uminum ,- a.

q=k a AT

4−T

3

'

k a= q

A [ T 4−T 3 ' ]= 33±6.4W

4.908×10−3

m2[ 458± .05 K −442±.05 K 0.064m ]

¿26±5 W

m∙ K

Therma! con)ucti*it+ of Stain!ess Stee! ,- b.

k (= q

A [T 2−T 1 ' ]=

33±6.4W

4.908×10−3m

2[405.8± .05 K −347.6± .05 K 0.038m ]

¿4.4±0.9

W

m∙ K

Terma" Con#u!tiit=

"IS(USSION

Te !"osest materia" -ase# on terma" !on#u!tiit= for >+e!imen , is ?ranium it a terma"

!on#u!tiit= of ( ?ranium & 29.6 [W:m/] an# Titanium -ein' se!on# !"osest it ( Titanium & 20.4

[W:m/]. Te +er!enta'e mat! of uranium to ( - is 88@ -eteen teir res+e!tie terma"

!on#u!tiit= a"ues at 400 /e"in.

Te !"osest materia" -ase# on terma" !on#u!tiit= for >+e!imen A is te ni!(e"!romium -ase#a""o= !a""e# ;n!one" it a a"ue of ( in!one" & 13.5 [W:m/]. , si'nifi!ant 'a+ -eteen te a"ues

eists oeer of 32@.

Te a"ues for ( a an# ( - are si'nifi!ant"= #ifferent en !om+are# to teir ta-u"ar +ro+erties. Te

terma" !on#u!tiit= of +ure ,"uminum is 240 [W:m/] an# ,"uminum a""o= 2024T6 is 186

[W:m/]. Tis !om+are# to a a"ue of 26 ± 5 [W:m/] >os si'nifi!ant #ifferen!e -eteen


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te ta-u"ar an# e+erimenta""= #erie# a"ues. %i(eise te ta-u"ar a"ue of stain"ess stee" ran'es

from 17.3[W:m/] to 15.8 [W:m/] #e+en#in' on i! of te four t=+es of stain"ess stee" a"ues

are se"e!te# for !om+arison. Wit an e+erimenta""= #etermine# a"ue 4.4 ± 0.9 [W:m/]

tere "ies a #ifferen!e of minimum 63.3 @ an# maimum #ifferen!e of 79.7@ #e+en#in' on te

a""o= an# u++er an# "oer ran'e of errors se"e!te#.

Te sour!es of error for tis e+eriment ere te fo""oin'$

1 Time as !a"!u"ate# it a sto+ at! on !e""u"ar #ei!e i! a""os for uman error 2 Te +erson o+eratin' te Cussons Terma" Con#u!tiit= #ei!e as #oin' it for te first

time an# an error !ou"# ae -een ma#e in rea#in' an# !one=in' te instrument

rea#in's to te "a-orator= +arti!i+ants

3 Tree +eo+"e ere ino"e# in$ te ater !o""e!tion en to start te sto+ at! an#

en to rea# te instrument rea#in' i! ou"# resu"t in te !om+oun#in' of minor

errors.

4 Te Cussons Terma" !on#u!tiit= a++aratus as +rese"e!te# an# te inerent

manufa!turin' #efe!ts or or(a-i"it= of te #ei!e are un(non. ;t !ou"# -e er=

a!!urate an# +re!ise an# te "a- as +erforme# it a mista(e or it !ou"# -e te o++osite

ere te #ei!e ma= not -e 'iin' a!!urate rea#in's an# te termo!ou+"es insi#e ere

not o+eratin' +ro+er"=. ;#ea""= if tis "a- as re+eate# it to of tese #ei!es un#er

same !on#ition it ou"# a""o for a -etter #ia'nosti! of ere te sour!es of error arose

from.

5 Te meta" a""o=s ma= not ae -een stain"ess stee" an# a"uminum as in#i!ate# -= te "a-

manua" it is +ossi-"e te= ere oter a""o=s.

6 Te a"ue of

ḿ

as er= sma"" an# its !ontri-ute# error +ro+a'ation to te rest of te"a- !a"!u"ations as fair"= "ar'e at an aera'e of 20@ error +ro+a'ation ere eer te

a"ue as ino"e# an# !ertain"= "e# to "ar'e error +ro+a'ation in man= ste+s of te

!a"!u"ation.7 Te s+e!ifi! eat a"ue of ater C + use# in te !a"!u"ation as a stan#ar#iBe# a"ue of

ater at 15 #e'rees an# 101.325 ()a. Tis a"ue as s"i't"= #ifferent tan te one use#

in a!tua" e+erimenta" !on#itions an# ou"# !ontri-ute a sma"" +ortion to te sour!es of

errors.

Te to s+e!imens ere !"ame# to'eter in te a++aratus. ;f te= a# -een sta!(e# tere ou"#

ae -een a 'reater #ifferen!e of interfa!ia" tem+erature an# su-seuent"= a 'reater terma"!onta!t resistan!e. ,s sma"" surfa!e im+erfe!tions an# 'a+s are minimiBe# #ue to te resu"tant

+ressure from !"am+in' tat ou"# ae a 'reater im+a!t at +reentin' te transfer of eat from

-ot s+e!imens if te= ere sim+"= sta!(e#.

To meto#s tat !ou"# -e use# to #e!rease te terma" !onta!t resistan!e are as fo""os$


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1 Ma!ine te matin' surfa!e to a smoot mirror "i(e finisin' a""oin' te ti'test

+ossi-"e seam u+on !"am+in'. ,"so te use of 'reater +ressure ou"# #e!rease terma"

!onta!t resistan!e.

2 urtermore -eteen te to !onta!t surfa!e use a si"i!one -ase# terma" +aste s+rea#

een"= an# tin"= oer -ot matin' surfa!es -efore !"am+in'. Te terma" +aste a!ts as a

terma" !on#u!tor a""oin' for -etter eat transfer from one s+e!imen to te oter.

>imi"ar to te a++"i!ation of terma" +aste on C)?Ds of mo#ern !om+uters

(onc!usion

Te Cussons terma" !on#u!tiit= a++aratus as use# to measure te terma" !on#u!tiit= of

stain"ess stee" an# a"uminum s+e!imens. ?sin' te tem+erature #ifferen!es -eteen -ot matin'

surfa!es an# etra+o"atin' te #ata as son in te 'enerate# 'ra+ terma" !onta!t resistan!e

as a"so #etermine# -eteen te to materia"s.

aer423 lab - thermal conductivity and contact resistance (1)

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