ME410_HW4_FALL_2010_Solution

ME410_HW4_FALL_2010_Solution - ME 410-2 Name: Homework #4...

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Unformatted text preview: ME 410-2 Name: Homework #4 (due October 4, 2010) Homework Format l. 2. 3. @999? 1. Use this page as a cover sheet. One problem per page. Always state what is given, your assumptions, provide a sketch, and analysis. Circle your answer. Include units. Write legibly. No late homework accepted. Work independently. Use paper with four straight edges. Staple together your work. A type K Chromel-Alumel thermocouple is quickly placed into a hot air flow to measure its temperature. In particular, it is desired to know the response time of the thermocouple to attain 99% of the initial temperature difference between the hot air and the initial temperature of the thermocouple junction. The thermocouple junction can be modeled as an isolated sphere with a diameter of 0.6 mm and the properties: ksond = 35 W/m-K, p = 8500 kg/m3, and c = 320 J/kg-K. The convection heat transfer coefficient, h, between the flow and the sphere is 65 W/mz-K. i) What is the Biot number associated with this problem? ii) Derive the appropriate differential equation for T(t). iii) Solve this equation to attain the time for thermocouple junction to attain 99% of the initial temperature difference between the hot air and the initial temperature of the thermocouple junction. A long circular shaft of 0.2 m diameter and thermo physical properties k = 21 W/m-K, p = 7900 kg/m3, and c = 570 J/kg-K is initially at a uniform temperature of 600°C and is cooled in a convective flow maintained at 200°C. What is the shaft centerline temperature after exposure to the convective flow for 45 minutes? The convection heat transfer coefficient, h, is 80 W/mz-K. You must check the validity of your answer. A thick steel slab (k = 50 W/m-K, p = 7800 kg/m3, and c = 480 J/kg-K) is initially at 300°C and is cooled by water jets impinging on one of its surfaces. The temperature of the water is 25°C, and the jets maintain an extremely large, approximately uniform convection coefficient at the surface. Assuming that the surface is maintained at the temperature of the water throughout the cooling, how long will it take for the temperature to 50°C at a distance of 25 mm from the surface? l. Given A L Assume MS 3 j g gum WWGQTES A T M Qfiom'l'lom ( fi“23/ 2\ (2/ '0 8; = AS = 5 Li. ksoh'J kph}! ksp‘fll .. 5 w 620003 m/S -— LEA/:JKk—L : M<< m LHC \Memw VAuo Q 0 .. I D '13) %'Eou‘r+z 305535;” 5;,“ marge) (£9, , V¢JT I: T 7.7; I” 07; I4 ,. .41. " ’0'th Jt — fT-‘Ea 0 Ti thm,‘ ,. x __ _. JET In ( "7—90) “ [file 13 twig: 1.4% = \h(@)=—M&m\h(vw 2. Ghent Lang ska“ Tarmac ( ' T;=éoo'( w 8% ED Q: 0.1m 7 ,0: WMW /777 k: 210%.2 ionis— WW ( c : WOWflfl-K PC rm”) kw)" (57037“ K) : 4,1,6 Klo‘k m2]; Fw'é 1 TOM) Q 1-,: 4smwk£ kaask: (3; : Viv/A53 _ h(m23'Ly/(Z"Q'L): MHz/A .; L o q - ma ' REM km: 2| ’ “ °‘ ,'. LHC NOT VAUD fisswne F0201 HM) use THé \—'r£nM soumom F0: g1: : 4ww‘m2/g “mos/«R a LZSQ 27' ifld WOL T (wk) — TOB Tc — Tc} mew‘w; m) ) 70(th (Tame 9.43 Vim Tad: 5.! Ea» W3 : ng/M‘k)(0“"“ = 0.3? 13.1 (2‘ WM) C‘t Law at is 052309 2 ; CI EXPC’ 7: =~ 374 "c 0‘5va sol (“at = 75an 0“: .5. ’} SD : \lgggx‘ak Nils ’0‘ (mo V‘Hm3) (490 mark) Use semi- (“Rub 9W “\U‘WR “03“ T; :comghmf T‘X-lc) '— T5 .1- 7? ’ ‘2 (NEE So — 2: A 300 * 2s ' e4 X 0. = 05 243:; Sa‘m‘xs ¢vr t '2 - 7‘. W = 4 0L (005)" 4 (mssxfi‘m‘g (0,0531 _ :. 30.5 MM ...
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ME410_HW4_FALL_2010_Solution - ME 410-2 Name: Homework #4...

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