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Unformatted text preview: An aluminum can having the diameter of6 cm and the height of 10 cm contains fruitjuice at 1“C.
Using a lumpedcapacity analysis, estimate the time required for the contents to warm to 15“C
when the can is placed in a room at 22°C with a convection coefﬁcient of4 Wltn 2 “Cl Assume the fruitjuice has the same properties as water. Also validate the assumption ofthe lumped—capacity
analysis employed. 999a duds P g ' c = 42.2.5 
k' n 0's; L: 0.!
A: ald‘KL'f'leJ— zonal+5 M
V “ ﬁdtL. "' 0 9092.85 M3
3 = )3:— = bani; AV = 4. I: 0"“; ‘—' [La guns
P‘ 9&9} x +1.15 K «Lu 1&3 T— T9. is — [L t 5.30 Inclr4: 1LT... ' I 1L 't. 2. laaqa' S 3" 3.?‘111
. ‘i Knows
0.3! Chadv. : 51 3%: =c.ast <0" A concrete column (an inﬁnite circular cylinder) with radius 1"” = 0.3 m initially has a uniform
temperature of 30"C. Now the atmospheric environment is suddenly changed to 20°C. The
convection heat transfer coefﬁcient is estimated to be 5 Who 2 DC. What will be the temperatures
ofthe concrete at r = 0.0 (center) and 0.3 m (surface) after 24 hours? The properties ofthe
concrete are as follows: a = 7 x10 ‘7 m l is and k = l W/m.°C. NOTE: For a cylinder with a convection boundary, the one—term approximation is given as
follows: T —‘ Tab 2 I”
T; _ T1, = Cl Fl) )Jn (4] The values for Bessel function are given in Table 8.4. Bi — hr _ §X°.3 K I =l.§' Fm 'hblgfl’ cl = _¢.l.?_;;
(;I = Layzit db 4“. a! LEI$364.
r... = °.6?L 70.1. 1'... To. _ T 36 I Lam‘s u ( tH‘H4L b >
———. . = .  . X 0. $2» =
T14.” and P 0.32.35 T(r=e) = goat. tuko,3l3$ : L3.z'c_
4 Io<§ '0‘? = ELIAZWJ = angler. : 0.32.3: wastti = allHS TLr:o.3) = Llﬁl‘L
o On a hot summer day a concrete driveway may reach a temperature of SOT. Suppose that a stream
ofwater is directed on the driveway so that the surface temperature is suddenly lowered to 20°C.
How long will it take to cool the concrete to 30°C at a depth of 5 cm From the surface? {A = ? xahf M75 T1: 561C , T; = zo'c. Tts.a9.t) : 33'; T 1; _ 35‘ ~19
T1 :1: ~ e.» ‘24:! 2 0'55” : eff &
i: ‘6er
E '—" 950‘“: 95° oszféj
2 x = “.5 D. 5& use9:3 ngt ;J ?A5+t t= 9543 5‘ ...
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 Spring '11
 nezihtopaloglu
 Heat Transfer

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