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Unformatted text preview: erence of less than 20°C. P = 1 atm EXAMPLE 10–3 Film Boiling of Water on a Heating Element Water is boiled at atmospheric pressure by a horizontal polished copper heating
element of diameter D 5 mm and emissivity
0.05 immersed in water, as
shown in Figure 10–17. If the surface temperature of the heating wire is
350°C, determine the rate of heat transfer from the wire to the water per unit
length of the wire. SOLUTION Water is boiled at 1 atm by a horizontal polished copper heating
element. The rate of heat transfer to the water per unit length of the heater is to
be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat losses from the boiler
are negligible.
Properties The properties of water at the saturation temperature of 100°C are
hfg 2257 103 J/kg and l 957.9 kg/m3 (Table A9). The properties of vapor at the film temperature of Tf (Tsat Ts)/2 (100 350)/2 225°C
498 K (which is sufficiently close to 500 K) are, from Table A16, 0.441 kg/m3
1.73 10 5 kg/m · s Cp
k 1977 J/kg · °C
0.0357 W/m · °C Note that we expressed the properties in units that will cancel each other in
boiling heat transfer relations. Also note that we used vapor properties at 1 atm
pressure from Table A16 instead of the properties of saturated vapor from Table
A9 at 250°C since the latter are at the saturation pressure of 4.0 MPa.
Analysis The excess temperature in this case is T
Ts
Tsat
350 100 250°C, which is much larger than 30°C for water. Therefore, film
boiling will occur. The film boiling heat flux in this case can be determined from
Eq. 10–5 to be 100°C Heating
element
Vapor
film FIGURE 10–17
Schematic for Example 10–3. cen58933_ch10.qxd 9/4/2002 12:38 PM Page 530 530
HEAT TRANSFER q·film 0.62 gk3 ( )[hfg 0.4Cp (Ts
D(Ts Tsat) l Tsat)] 9.81(0.0357)3 (0.441)(957.9 0.441)
[(2257 103 0.4 1977(250)]
0.62
(1.73 10 5)(5 10 3)(250)
5.93 104 W/m2 1/4 (Ts Tsat) 1/4 250 The radiation heat flux is determined from Eq. 10–6 to be q·rad 4
(Ts4 Tsat)
(0.05)(5.67...
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This note was uploaded on 01/28/2010 for the course HEAT ENG taught by Professor Ghaz during the Spring '10 term at University of Guelph.
 Spring '10
 Ghaz

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