solution4 - An aluminum can having the diameter of6 cm and...

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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 lumped-capacity 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 gun-s P‘- 9&9} x +1.15 K «Lu- 1&3 T— T9. is — [L t-- 5.3-0 Incl-r4: 1LT... ' I -1-L 't. 2. laaqa' S 3"- 3.?‘11-1 .- ‘i- Knows 0.3!- Chadv. : 51 3%: <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 'hblgf-l’ cl = |_¢.l.?_;; (;I = Lay-zit db 4“. a! LEI-$364. r... =- °.6?L 70.1. 1'... To. _ T-- 3-6 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‘? = ELIA-ZWJ = angler. : 0.32.3: wast-ti- = all-HS 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 = ? x-ahf M75 T1: 561C , T; =- z-o'c. Tts.a9.t) : 33'; T- 1-; _ 35‘ ~19 T1 :1: ~ e.» ‘24:! 2 0'55” : eff & i: ‘6er E '—" 950‘“: 95° oszfé-j 2 x = “.5 D. 5&- use-9:3 ngt ;J ?A|5+t t= 9543 5‘ ...
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