AER423 Lab - Thermal Conductivity and Contact Resistance (1)

Time Water Tin °C Water Tout °C T1°C T2°C T3°C T4°C OBSERVATIONS

0 [min] 19.1 ± 0.05 24.9 ± 0.05 75.1 ± 0.05 132.9 ± 0.05 168.1 ± 0.05 184.7 ± 0.05

2 [min] 19.1 ± 0.05 24.9 ± 0.05 75.2 ± 0.05 132.2 ± 0.05 168.6 ± 0.05 185.2 ± 0.05

4 [min] 19.2 ± 0.05 25 ± 0.05 75.4 ± 0.05 132.6 ± 0.05 168.9 ± 0.05 185.6 ± 0.05

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"

m ´=

0.4900 ± 0.0005 kg 360 s ± 0.3

=1.361 × 10− ± 0.00025 3

 kg s

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

(

100 ×

 0.0005 0.49

)( +

100 ×

0.3 360

)=

0.18537  error

,-so"ute *rror )ro+a'ation$ −3

1.361 × 10

× 0.18537  = 0.00025 kg / s| Error  Error| Propagation  Propagation

,era'e era'e Tem+. m+. °C °C

´

Water Tin

19.

1

Water Tout

24.

9

T1

75.

4

T2

132.

T3

168.

T4

185.

´ ´

´ 6 ´ 8

´ 4

5 ± 0.05

,era era'e 'e Te Tem+. m+. °/  °/  292.3 ± 0.05

5 ± 0.05

298.1 ± 0.05

5 ± 0.05

347.6 ± 0.05

75 ± 0.05

405.8 ± 0.05

75 ± 0.05

442.0 ± 0.05

2 ± 0.05

458.6 ± 0.05

RESULTS

6 [min] 19.2 ± 0.05 25 ± 0.05 76.1 ± 0.05 133 ± 0.05 169.9 ± 0.05 186.2 ± 0.05

eat transfer rate trou' te !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 = 4185.5  H 2 O

J  (k g ∙ K ) 

q =m∙ ´ C  p ( T out −T ¿ )

¿

(

 kg −3 1.361 × 10 ± 0.00025 s

)(

 J  q =33.04 ± 6.4 =33 ± 6.4 W  s

4185.5

)(

J  kg∙K 

−292.3 ± 0.05 K )

298.1 ± 0.05 K 

: 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

i'. 1

i'. 1

*tra+o"ation of interfa!ia" tem+erature #ifferen!e$ T1 $ 6.5mm 347.6/ T2 $ 31.5mm 405.8/ Tinterfa!ia" $ 38mm Tint. ss

T3 $ 45mm 442/ T4 $ 95mm 458/ Tinterfa!ia" $ 38mm Tint. a"

Tint ss & [38mm  6.5mm405.8/347.6/:31.5mm6.5mm]  347.6/  & 420.9 ± 0.05 /  Tint a" & [38mm  45mm458.6/442/:95mm45mm]442/  & 439.7

±

0.05/ 

;nterfa!ia" Tem+.
& Tint a"  Tint ss

Interfacia! Temp "ifference # $%&' 

*tra+o"ation of interfa!ia" tem+erature #ifferen!e$ T1 $ 6.5mm 347.6/ T2 $ 31.5mm 405.8/ Tinterfa!ia" $ 38mm Tint. ss

T3 $ 45mm 442/ T4 $ 95mm 458/ Tinterfa!ia" $ 38mm Tint. a"

Tint ss & [38mm  6.5mm405.8/347.6/:31.5mm6.5mm]  347.6/  & 420.9 ± 0.05 /  Tint a" & [38mm  45mm458.6/442/:95mm45mm]442/  & 439.7

±

0.05/ 

;nterfa!ia" Tem+.
& Tint a"  Tint ss

Interfacia! Temp "ifference # $%&' 

Interfacia! Therma! Resistance: q =33 ± 6 . 4 W 

,-oe re+resents te amount of eat a-sor-e# -= te !om+osite materia"s. Tis i"" -e use# to !a"!u"ate te interfa!ia" terma" resistan!e$

 Rt , c =

T  A −T  q

 !nter"acia# Temperature $i""erence  Rt , c = q

 Rt , c =

18.7 ± 0.05 K  33 ± 6.4 W 

 Rt , c =0. 6 ± 0.1

K  W 

Heat Transfer (oefficient q =%i A ( T  A−T  )

%i

 A =

%i =

q

 & $ 4

2

2

=

=

 & ( 0.025 m )

 A ( T  A −T  ) (

4

= 4.908 × 10− m 4

2

33 ± 6.4 W  −4 2 4.908 × 10 m 18.7 ± 0.05  K 

)(

)

=3500 ± 707

W  2

m ∙ K 

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

q =k a A

k a =  A

¿ 26 ± 5

[

T 4 −T 3  ' q = T 4 −T 3

]

 '

33 ± 6.4 W 

[

−

−3 2 458 ± .05 K  442 ± .05 K  4.908 × 10 m 0.064 m

]

W  m∙ K 

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

k ( =  A

[

q = T 2−T 1  '

]

33 ± 6.4 W  −3

4.908 × 10

m

2

¿ 4. 4 ± 0.9

[

405.8 ± . 05 K −347.6 ± . 05 K  0.038 m

]

W  m∙ K 

Terma" Con#u!tiit= "IS(USSION

Te !"osest materia" -ase# on terma" !on#u!tiit= for >+e!imen , is ?ranium it a terma" !on#u!tiit= of ( ?ranium & 29.6 [W:m/] an# Titanium -ein' se!on# !"osest it ( Titanium & 20.4 [W:m/]. Te +er!enta'e mat! of uranium to (  - is 88@ -eteen teir res+e!tie terma" !on#u!tiit= a"ues at 400 /e"in. Te !"osest materia" -ase# on terma" !on#u!tiit= for >+ e!imen A is te 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+ -eteen te a"ues eists oeer of 32@. Te a"ues for ( a an# (  - are si'nifi!ant"= #ifferent en !om+are# to teir ta-u"ar +ro+erties. Te terma" !on#u!tiit= of +ure ,"uminum is 240 [W:m/] an# ,"uminum a""o= 2024T6 is 186 [W:m/]. Tis !om+are# to a a"ue of 26

±  5 [W:m/] >os si'nifi!ant #ifferen!e -eteen

te ta-u"ar an# e+erimenta""= #erie# a"ues. %i(eise te 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! o f te 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/]

tere "ies a #ifferen!e of minimum 63.3 @ an# maimum #ifferen!e of 79.7@ #e+en#in' on te a""o= an# u++er an# "oer ran'e of errors se"e!te#. Te sour!es of error for tis e+eriment ere te fo""oin'$ 1 Time as !a"!u"ate# it a sto+ at! on !e""u"ar #ei!e i! a""os for uman error  2 Te +erson o+eratin' te Cussons Terma" Con#u!tiit= #ei!e as #oin' it for te first time an# an error !ou"# ae -een ma#e in rea#in' an# !one=in' te instrument rea#in's to te "a-orator= +arti!i+ants 3 Tree +eo+"e ere ino"e# in$ te ater !o""e!tion en to start te sto+ at! an# en to rea# te instrument rea#in' i! ou"# resu"t in te !om+oun#in' of minor errors. 4 Te Cussons Terma" !on#u!tiit= a++aratus as +rese"e!te# an# te inerent manufa!turin' #efe!ts or or(a-i"it= of te #ei!e are un(non. ;t !ou"# -e er= a!!urate an# +re!ise an# te "a- as +erforme# it a mista(e or it !ou "# -e te o++osite ere te #ei!e ma= not -e 'iin' a!!urate rea#in's an# te termo!ou+"es insi#e ere not o+eratin' +ro+er"=. ;#ea""= if tis "a- as re+eate# it to of tese #ei!es un#er same !on#ition it ou"# a""o for a -etter #ia'nosti! of ere te sour!es of error arose from. 5 Te meta" a""o=s ma= not ae -een stain"ess stee" an# a"uminum as in#i!ate# -= te "amanua" it is +ossi-"e te= ere oter a""o=s. ´  as er= sma"" an# its !ontri-ute# error +ro+a'ation to te rest of te 6 Te a"ue of m "a- !a"!u"ations as fair"= "ar'e at an aera'e of 20@ error +ro+a'ation ere eer te a"ue as ino"e# an# !ertain"= "e# to "ar'e error +ro+a'ation in man= ste+s of te !a"!u"ation. 7 Te s+e!ifi! eat a"ue of ater C + use# in te !a"!u"ation as a stan#ar#iBe# a"ue of ater at 15 #e'rees an# 101.325 ()a. Tis a"ue as s"i't"= #ifferent tan te one use# in a!tua" e+erimenta" !on#itions an# ou"# !ontri-ute a sma"" +ortion to te sour!es of errors. Te to s+e!imens ere !"ame# to'eter in te a++aratus. ;f te= a# -een sta!(e# tere ou"# ae -een a 'reater #ifferen!e of interfa!ia" tem+erature an# su-seuent"= a 'reater terma" !onta!t resistan!e. ,s sma"" surfa!e im+erfe!tions an# 'a+s are minimiBe# #ue to te resu"tant  +ressure from !"am+in' tat ou"# ae a 'reater im+a!t at +reentin' te transfer of eat from  -ot s+e!imens if te= ere sim+"= sta!(e#. To meto#s tat !ou"# -e use# to #e!rease te terma" !onta!t resistan!e are as fo""os$

1 Ma!ine te matin' surfa!e to a smoot mirror "i(e finisin' a""oin' te ti'test  +ossi-"e seam u+on !"am+in'. ,"so te use of 'reater +ressure ou"# #e!rease terma" !onta!t resistan!e. 2 urtermore -eteen te to !onta!t surfa!e use a si"i!one -ase# terma" +aste s+rea# een"= an# tin"= oer -ot matin' surfa!es -efore !"am+in'. Te terma" +aste a!ts as a terma" !on#u!tor a""oin' for -etter eat transfer from one s+e!imen to te oter. >imi"ar to te a++"i!ation of terma" +aste on C)?Ds of mo#ern !om+uters (onc!usion

Te Cussons terma" !on#u!tiit= a++aratus as use# to measure te terma" !on#u!tiit= of stain"ess stee" an# a"uminum s+e!imens. ?sin' te tem+erature #ifferen!es -eteen -ot matin' surfa!es an# etra+o"atin' te #ata as son in te 'enerate# 'ra+ terma" !onta!t resistan!e as a"so #etermine# -eteen te to materia"s.