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quiz+2+key+2008 - PTFE 3210 QUIZ#2 Spring 2008 Name KEy...

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Unformatted text preview: PTFE 3210 QUIZ #2 Spring 2008 Name KEy TURN IN YOUR QUESTiON SHEET ALONG'WITH YOU ANSWERSEI 1. The heat transfer coeficient for air flowing over a sphere is to be determined by observing the temperature-time history of a sphere fabricated from pure copper. The sphere, which is 12.7 mm in diameter, is 66°C before it is inserted into an airstream having a temperature of 27°C. A thermocouple on the outer surface of the sphere indicates 55°C at 69 seconds afier the sphere is inserted in the airstream. Properties of pure copger: p = 8933 kg/m3, C3, = 389 J/kg-K, k = 398 W/m-K Calculate the heat transfer coefficient. Justify the method you use to solve the problem, (35 points) Sod. MTIDN --13 ON NEXT fees . PROBLEM 5.7 KNOWN: The temperamentirne history of a pure copper sphere in an air stream. FIND: The heat transfer coefficient between the sphere and the air stream. SCHEMATIC: 77695) =55°Cé To 266°C 7;,=27°C ( ) % ASSUMPTIONS: (1) Temperature of sphere is spatially uniform, (2) Negligible radiation exchange, (3) Constant properties. PROPERTIES: TabEeA—I, Pure copper (333K): p = 8933 kgfms, cp = 389 lfkg-K, k = 398 W/rn-K. ANALYSIS: The time-temperature history is given by Eq. 5.6 with Eq. 5.7. 6 t ():exp — t where Rt: 1 As=er2 9i tht hAS 3 a: D C = Vc V 2 —— t 10 p 6 6 m r- — rm. Recognize that when t = 695, a t 55 — 27 ° C ()=—( )0 :0.718+exp[—i]xexp[—@] 91 (66—27) c It a and solving for T find Hence, m _. ._ chp 8933 kgz’m3 (30.01273 m3 1’6)389Jfkg -K Asa 7:0.012721113 x 208s 11:35.3 W/m2 -K. < ”mu-I: COMMENTS: Note that with LG 2 DO/6, 7 hLC Bi .— “1;“: 35.3 Win12 -K>< 0.0127 6 mf398 Wfrn-Kzl.88><10‘4. Hence, Bi < 0.1 and the spatially isothermal assumption is reasonable. «-——-’ Excerpts from this work may be reproduced by instructors for distribution on a not-for—profit basis for testing or instructional purposes oniy to stuécnis enrolied in courses for which the textbook has been adopted. Any other reproducrion or fi'mzsfarion qfritis work bq-oaodflmrpermmed by Sections 107 or 108 ofh’ie 1976 United States Camv'fghrAct without the permission ofrfze copyright owner is zrm’mqfiri'. 2. A glass plate, which is initially at a uniform temperature of 210°C, is cooled by suddenly reducing the temperature of both surfaces to a temperature of 10°C. The plate is 20 mm thick, and the glass has a thermal diflhsivity of 6 x 10'7 111213. How long will it take for the mid-plane (i.e., plane at center of plate) temperature to reach 110°C? (35 points) r. M: 0‘ @113 X4} " mow/o S ., , 3 g .., £57071: 7%.0'94 Cl“ '72.}? {q 3. Consider a long solid cylinder, which could represent a current-carrying wire or a fuel element in a nuclear reactor. The outer radius of the cylinder is re. The rate of heat generated in the cylinder per unit voiume is (1 , a constant with units W/m3. The thermal conductivity of the cylinder is k, a constant with units W/m-K. Heat is convected from the cylinder by a moving fluid at a temperature Ta, and the heat transfer coefficient is h, an unknown constant with units Wimz-K. Assume that steady-state conditions exist. The surface temperature of the cyiinder is Ts. A. Start by writing the general governing equation for the heat transfer process that will allow you to determine the temperature distribution. Epoints) riflKfi Jii+i3§6il<jflgia Ziki‘jiti “is B. Write assumptions that will allow you to reduce the general governing equation so that you will be able to solve the equation. Of course, your assumptions must be reasonable!! fipoints) /, /’9/MGNS‘ID/V#L 1»! tr— éweabow C. Using your assumptions, simplify the governing equation. (5 points) 9 Q 7. 1&(kyfiw-‘ri A Kieth afté—T)+g :EGDQ“; ~—-—-— Qhk-J —"'" __.——--. no?!“ r he 0 W /»Wk§\ indirectioe air iMKifi-iflr° "F air "” g/K D. Write the boundary conditions and initial conditions, if needed, to solve for the temperature distribution as a function of radial distance from the center of the cylinder. (6 points) .4- a... '/ 13.5.! @W—‘i’; f: i a .. M “9%; Brian @ gash, ~KfiL—k” A[7’[fi°_.}~w.) ”j 5 h / 5.325 @icra filtzrazo mfisw E. Solve the governing equation and determine the distribution, "f(r)_ Show all steps of your world! (53 points) ...
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