14-29
14-37 A glass window is considered. The convection heat transfer coefficient on the inner side of the
window, the rate of total heat transfer through the window, and the combined natural convection and
radiation heat transfer coefficient on the outer surface of the window are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Air is an
Glass
ideal gas with constant properties. 3 The local atmospheric
Ts = 5qC
pressure is 1 atm.
Room
H = 0.9
Properties The properties of air at 1 atm and the film
Tf = 25qC
temperature of (Ts+Tf)/2 = (5+25)/2 = 15qC are (Table A-22)
Q
L = 1.2 m
k 0.02476 W/m.qC
1.470 u 10 5 m 2 /s
Pr 0.7323
1
1
E
(15 273)K
Tf
Q
Outdoors
-5qC
0.003472 K -1
Analysis (a) The characteristic length in this case is the height of the window, Lc
Ra
gE (Tf Ts ) L3c
Q2
Pr
(9.81 m/s 2 )(0.003472 K -1 )(25 5 K )(1.2 m) 3
(1.470 u 10 5 m 2 /s) 2
2
L 1.2 m. Then,
(0.7323)
½
­
½
­
°
°
°
°
°
°
°
9 1/ 6 °
1/ 6
0.387(3.989 u 10 )
0.387Ra
°
°
°
°
Nu ®0.825 ®0.825 8 / 27 ¾
8 / 27 ¾
°
°
ª § 0.492 · 9 / 16 º
°
°
ª § 0.492 · 9 / 16 º
°
°
«1 ¨
»
°
°
«1 ¨
»
¸
¸
°¿
°¯
«¬ © 0.7323 ¹
»¼
°¿
°¯
«¬ © Pr ¹
»¼
k
0.02476 W/m.qC
h
Nu
(189.7) 3.915 W/m 2 .qC
L
1.2 m
As (1.2 m)(2 m) 2.4 m 2
3.989 u 10 9
2
189.7
(b) The sum of the natural convection and radiation heat transfer from the room to the window is
Q
hA (T T ) (3.915 W/m 2 .qC)(2.4 m 2 )(25 5)qC 187.9 W
convection
Q radiation
Q total
s
s
f
HAs V (Tsurr Ts 4 )
4
(0.9)(2.4 m 2 )(5.67 u 10 8 W/m 2 .K 4 )[(25 273 K ) 4 (5 273 K ) 4 ] 234.3 W
Q
Q
187.9 234.3 422.2 W
convection
radiation
(c) The outer surface temperature of the window can be determined from
kAs
Q t
(422.2 W )(0.006 m)
(Ts ,i Ts ,o ) 
5qC o Ts ,o Ts ,i total
Q total
t
kAs
(0.78 W/m.qC)(2.4 m 2 )
3.65qC
Then the combined natural convection and radiation heat transfer coefficient on the outer window surface becomes
Q total
or
hcombined
hcombined As (Ts ,o Tf ,o )
Q
422.2 W
total
As (Ts ,o Tf,o )
(2.4 m )[3.65 (5)]qC
2
20.35 W/m 2 .qC
Note that 'T Q R and thus the thermal resistance R of a layer is proportional to the temperature drop
across that layer. Therefore, the fraction of thermal resistance of the glass is equal to the ratio of the
temperature drop across the glass to the overall temperature difference,
Rglass
'Tglass
5 3.65
0.045 (or 4.5%)
R total 'TR total 25 (5)
which is low. Thus it is reasonable to neglect the thermal resistance of the glass.
PROPRIETARY MATERIAL. © 2008 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
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14-29 window, the rate of total heat transfer through the window,... 14-37