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exam2soln

exam2soln - The appropriate temperature from which to...

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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)= “Of-57.7 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 - ” r4 Q‘- r— » 9;, “3ng ._ 1-)ther Loewe l“ CL; {in‘A :- ("ﬂ #9714477. ) . If" .' in“ 32"” / c f a ’3- w ,; = E} "W “A” 1* {Wm 17:}; n ,_,_ :2. ~ t “r CF at m Mm!) _: rlc 4 ‘ I”: L ’ -‘ I”! (7%: IL”- ‘ LC"; : : bl LEIEEQHZ/ "’ rm.”- b: {63:39 A /°“ ’9‘)" /s new, if “a” 3 [c manta)? Nata yme: tannin : 2 l2..m_ I V ’7 a A, - -5 . .,, <- - :m .c‘.» "r (Wkti’ﬂb‘y- [VHS-xix , L 3’ ("WE-‘9 (fwm‘jt )' ' 2 L0 “7 Sat? «em/F’j (~43; we": 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' {rm-M. L(m): 0mm 5 3 “L t W” l“ "r “it = r. 2% in @mrbulent, or mixed? (circle one) 2., _ I Luau-w“ vzﬁg “(KGB r ﬁ‘ﬂeLch-txsw *- - ( O-T’éz Nusselt: EU“ :2 '37 av— : 3- (, ' c (5 m - ﬁE—x‘d; (quitmﬁcE' i NHL 1 Si. \$3363) L Fig H. p 0:674 y (we) Nu» 1 0 “*1? Ramos . iRe. r ' 0357*! 5 ; 9"”?- : l 1% (C3342?) ﬁﬁénf Pt” ‘- .. Q .2/ 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. ,. egg-Lerofq (lit-51a) -- Ital-m 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 (Qt-55:"? Kai-Ely" \$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 {Jo-K 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 0-00? 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"F-7-"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‘fT-édﬂﬂ ‘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 MAP-0303 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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exam2soln - The appropriate temperature from which to...

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