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Unformatted text preview: The appropriate temperature from which to determine fluid properties The appropriate length scale from which to calculate the Reynolds, Rayleigh, or Grashof
number Whether the flow is laminar, turbulent, or mixed The appropriate correlation from which to calculate the Nusselt number — write out the
full form of the correlation including speciﬁc coefﬁcients and expenents. (7 pts) Fresh outside air at 19°C ﬂows through a duct of triangular cross section that is
heated on all sides with a uniform heat ﬂux of 18.3 W/mz. The duct is 10 cm on a side
and 10 m long. The air exits at 23°C. Tl‘lujd :ngiw “Eml ; p U T _ . ' nan—3; .
L(m)= “Of57.7 v: '2, if:
turbulent, or mixed? (circle one)
. H Li A
Nusselt : E. H van" 1:324; l—<:~}9LL (3.1 : fail? : “5‘3"” Exit) . ELMLFA
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n ,_,_ :2. ~ t “r
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Ml" ebLnresc—Hiwvt" b. (8 pts) Warm air at 34°C is incident on a staggered tube bank with a velocity of 1.33 rats.
The tube bank is comprised of 25.4 mm diameter tubes, spaced 76.2 mm apart in the
transverse direction and 76.2 mm apart in the longitudinal direction. Each (vertical)
column of tubes contains 10 tubes, and there are 25 columns of tubes. The surface
temperature of the tubes is 5°C, and the outiet temperature of the air is 20°C. ‘ = A. I. I’ FF‘ — T Ig‘fT L w t: I
Tmag): 333% ca? :53 K. If: 2‘m" it“ {Pi:3!“ “ “fie: 3am
Labia"1 ‘ 1  7 "' A" 09' {rmM.
L(m): 0mm 5 3 “L t W” l“
"r “it = r. 2% in
@mrbulent, or mixed? (circle one) 2., _
I Luauw“ vzﬁg “(KGB r ﬁ‘ﬂeLchtxsw
*  ( OT’éz
Nusselt: EU“ :2 '37 av— : 3 (, ' c (5
m  ﬁE—x‘d; (quitmﬁcE' i NHL 1 Si. $3363) L Fig
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(we) Nu» 1 0 “*1? Ramos . iRe. r
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: l 1% (C3342?) ﬁﬁénf Pt” ‘
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u—«— p (.1 0 L. \n 3&2. F ‘f
.. r" _~ ,., _
7°67 N“ "O'x’ w Pr (ﬁrs) i — i big—7
, 14— : :2»
rmwh;( MDT/5L) 2:”. (xi) bill C. t. ,.
eggLerofq (lit51a)  Italm mom“ I
(7 pts) Water with a free stream velocity and temperature of 3.69 mfmin and 23°C
respectively flows over a 7 m long flat plate that is held at 53°C. The critical Reynold’s
number associated with the surface roughness of the plate is 5 X 105. The average heat
transfer over the whole plate is desired. . h T  ﬂ 0 I ‘
Tﬂuidﬁ)=i\<_ 133* 5:11:23“ : 5C0) (— 53“ K
L(m)=_7m_ p “tr. .' .2 ,1 AL
Kw : “2L '1' v L z: 23:!
Laminar, turbulent, 0 mixed. (circle one) )1. '
y ._ Gem's» f 1 M
Nusselt = Kilo "1 (Qt55:"? KaiEly" $271)?” 5 5’ ’mﬁwlyc‘gi‘lest’
: (smegma;
12'}: '? 'Z‘w a: S’ x155; d. (7 pts) A warm copper disk with a diameter = 0.1 m and thickness 0.01 m is cooled by
placing it in the bottom of a large bath of water. The initial temperature of the disk is 90
°C, and the water is maintained at 24°C. — J... ‘_.~.—a...« _.. v‘ \__..—. 1! .rj m f 4r“ ' c: h a“?
I Tﬁuid = __DDQ— f” '—' C. :7 m: . M a
m Lam —H—*—~—3 L5, — :— ‘Tp :; T774 ‘: Qibé‘: m
. _ . t” <4 ~er
Laminar, turbulent, or m1xed‘? (Circle one)
item??? ﬁnk, i434" _ use.) Hart‘ﬁsrri'tiﬂ (:1; coir S; iw.“ Rama, "* W‘e‘l” Mé—t “'9 '  rS—m' ' . a ' I .4. UL “CAI‘69
Nusselt = b m _ maxi Ci Pt I P“ w— y
Nb. 1:. “(ML
{JoK
7.  . ‘ i!
2. Rog: IO lo 6. ('7 pts) Hot gas (which mayr be modeled as air) is cooled as it ﬂows through a 50 m long
by 0.01 In diameter tube immersed in an ice—bath. The initial temperature and mass
ﬂow rate of the gas are respectively 154°C and 2.0 g/s. (7 pts) The inside (vertical) surface of an oven door is 0.8 m wide by 0.7 m tall. When
the air inside the oven reaches the desired temperature of 400°F, the temperature on the inner wall is 150°C. elm 35:
Tm 1" Nusselt: .7 . _ V2“, an r. rattan w——————————.— (j‘f' ! (7 pts) A refrigerated semi—truck is traveling along the freeway at 65 mph. The
temperature all along the 10 m long top of the truck is 20°C, while the ambient
temperature is 34°C. The local heat transfer coeffi cient at the back end of the truck’s top
is desired. Tﬂuid : _—SOQ 3“ L (m) = l O Laminar, @r mixed? (circle one)
"3 Nusselt : 1‘31. I’.
_ km.
N we *1 O .DKQQKPKFP 5 2. Water moves at a flow rate of 7i11=0.005 kg/s through a coiled, thin walled, 5—mm diameter
tube submerged in a large water bath maintained at 340K. The water enters the tube at 280K. Your final goal is to estimate the length of the tube required to provide an exit temperature of Tm‘02320K. Assume that the ﬂow is hydrodynamically developed, and the thermal entry length
is not important. The following questions will guide you through the solution. TOTAL ENERGY TRANSFERRED TO THE FLUID INSIDE THE PIPE: a) (5 pts) Calculate the total energy reguired to increase the temperature of the water inside
the pipe from 280K to 320K. $1 2 M if m N : 300k :i) C: 4nqu C K
16)
f 1 000? li'érr— » 4301:”) v ( 6W ~280') Al Q. q (W) = ﬂ
HEAT TRANSFER INSIDE THE PIPE: b) (5 pts) Calculate Reynolds number. Specify the characteristic length and film
temperature that you used to estimate the ﬂuid properties. pi] 9:3 ., ,1, am.
L? “a u 4‘ ‘rr/D/N lit/u V c) (3 pts) Is this laminar or turbulent flow? What critical Reynolds number did you use? Ed 2 2300
‘C
QC 4 $251 ~——> wam d) (4 pts) Determine the average Nusselt number for this ﬂow. \meaa. 1" W, GWEN! Em: fr: TWF‘3Y"F7"a": m: 3.66 e) (4 pts) Find the average heat transfer coefficient. (If you were unable to determine a value of M, assume a value of 4 for this part of the
problem.) E‘ if; in. 9 U K 1: =0.él3/\_N_
a v, M i} (W/mzK) z 445 “‘J/ ml ll: f) (5 pts) Calculate the log mean temperature difference associated with the internal ﬂow.
{T ~ T P (Twit ~ (ls‘TVWB‘ (T5
’T _ \ 1° 3 ’_ _ r__ i __ _ __ : ______.,_’______ ........... a
A 1% ‘ (Tm I It) (M (15— 1W,
\n r —14 Aw
TM \( t i 5 (320K’ 5400 — {I z 5_ __ _ ___. __ _
AHA \ n>
V‘ 250K ' 340K
Asz (K) =__34_;ﬂ<_ g) (5 pts) Calculate the length of the pipe required to increase the temperature of the water inside the pipe from 280K to 320K.
If you did not calculate the heat transfer rate in part a, assume that it is equal to 850W. If you did not find the heat transfer coefficient in part e, assume that it is equal to
4OO[W/m2K].
If Em did not find AT 1m in part f assume that it is equal to 30K. ' {ML  Wk»
5.) x O__ W A) ’
16¢; _ L. —————— a:
31: l A ADM ,_
p  ’ A l
'4: l’l’ICr’f’ero ~Tm;\ : V m) L ’6‘”
L : W‘ Tm” p lM'l) USWA THC l‘fTédﬂﬂ ‘5‘er P"
L‘ T!“ ‘17 A PM Sit/WM:
L: 832%... .. _ _ .t . i _
448 W Y T!“ Outfit/mm 344K
le
32!: M L(m)= HEAT TRANSFER TO THE ENVIRONMENT The constant temperature bath is contained in a vessel that is exposed to air at Tm 2300K. The air is moving at 5m/s. The vessel is a cylinder With diameter 0.8m and height 1m. The surface of
the cylinder has a temperature of 340K and an emissivity 8 :06. Neglect heat transfer from the
top and bottom surfaces of the cylinder. h) (5 pts) Calculate the Reynolds number corresponding to the air moving across the
cylinder. Indicate the characteristic length and film temperature. 0 1,
'  ,é
j>l0ﬂ£kﬂilﬁ\yloﬁﬁ
“ﬁg 514—)
\ 01134;” S NA, O$m
/,  a ‘5 F_ﬁ:_._r~#—~ :
l‘p m X'HoikaA/ S
r r 52
Re: 2,73 xlO LIV: 0.3M TF r/OK i) (5 pts) Calculate the average Nusselt number for this flow. ” W\ V2, {cm Fl 3’ Y 5 ram T'FbLé ‘77. ‘.
NV 1 C RC ?Y ‘ — / .
V ‘7 @944 r :05 C s 0‘02”)
9v}, 0.7 /Fr MAP0303
TU“?'31:.':r' 2%: P’ if Nu : 4010 j) (4 pts) Find the average heat transfer coefficient. (If you were unable to find an average
Nusselt number in part i, assume a value of 500) ENE"? k .’ 0,027 WK 2 (W/mzK) = l 6 ~ 3/ k) (5 pts) Calculate the total heat'transfer from the cylinder to the air. (If you were unable to
determine an average heat transfer coefficient, assume a value of ZOW/mzK). 4: I A(:'Tm\1' 0‘8 A (7?“ m
:Tl/VL ("13” i F 6 (TS ’— g 1 n (mm A i m (163% (340K 'JUOK) + YWWH’W V0 (, elf—900) q<W> w H 10 ...
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This note was uploaded on 08/08/2008 for the course ME 364 taught by Professor Rothamer during the Spring '08 term at Wisconsin.
 Spring '08
 Rothamer
 Heat Transfer

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