This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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
temperaturetime 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/kgK, k = 398 W/mK 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 lfkgK, k = 398 W/rnK.
ANALYSIS: The timetemperature 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. <
”muI:
COMMENTS: Note that with LG 2 DO/6, 7 hLC Bi .— “1;“: 35.3 Win12 K>< 0.0127 6 mf398 WfrnKzl.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 notfor—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 bqoaodﬂmrpermmed 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 midplane (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 currentcarrying 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/mK.
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 WimzK. Assume that steadystate 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“; ~——— QhkJ —"'" __.——. no?!“ r he 0 W /»Wk§\ indirectioe air
iMKiﬁiﬂr°
"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) ...
View
Full Document
 Spring '11
 Dr.Carr

Click to edit the document details