12-17
12-46 Water flows over a large plate. The rate of heat transfer per unit width of the plate is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 The critical Reynolds number is Recr = 5u105. 3
Radiation effects are negligible.
Properties The properties of water at the film temperature of (Ts + Tf)/2 = (10+43.3)/2 = 27qC are (Table
A-15)
U
k
P
Pr
996.6 kg/m 3
0.610 W/m.qC
Water
V =30 cm/s
Tf =43.3qC
0.854 u 10 3 kg//m ˜ s
5.85
Ts = 10qC
L=1m
Analysis (a) The Reynolds number is
Re L
VLU
(0.3 m/s)(1.0 m)(996.6 kg/m 3 )
P
0.854 u 10
3
2
m /s
3.501u 10 5
which is smaller than the critical Reynolds number. Thus we have laminar flow for the entire plate. The
Nusselt number and the heat transfer coefficient are
Nu
h
0.664 Re L 1 / 2 Pr 1 / 3
k
Nu
L
0.664(3.501u 10 5 )1 / 2 (5.85)1 / 3
0.610 W/m.qC
(707.9)
1.0 m
707.9
431.8 W/m 2 .qC
Then the rate of heat transfer per unit width of the plate is determined to be
Q
hAs (Ts Tf )
( 431 .8 W/m 2 .qC)(1 m)(1 m)](43.3 10) qC = 14,400 W
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