10-101
333 kg/m 141.6)2.35(kg/m0.86)1(kg/m99786011 =+−=+−= .).()( gltp
10-102
10-103
10-104
10–111 Water is boiled at 84.5 kPa pressure and thus at a saturation (or boiling) temperature of Tsat = 95C in a mechanically
polished AISI 304 stainless steel pan placed on top of a 3-kW electric burner. Only 60% of the heat (1.8 kW) generated is
85.1Pr
N/m 0599.0
kg/m 50.0
kg/m 5.961
3
3
=
=
=
l
v
l
Kc
h
pl
l
fg
=
=
=
−
J/kg 4212
m/skg 10297.0
J/kg 102270
3
3
Also, ksteel = 14.9 W/mK (Table A-3),
=
sf
C
0.0130 and n = 1.0 for the boiling of water on a mechanically polished stainless
steel surface (Table 10-3). Note that we expressed the properties in units specified under Eq. 10-2 in connection with their
definitions in order to avoid unit manipulations.
Analysis The rate of heat transfer to the water and the heat flux are
222
222
kW/m 25.46= W/m25,460=)m 69 W)/(0.0701800(/
m 07069.04/m) 30.0(4/
W1800=kW 8.1kW 360.0
==
===
==
s
s
AQq
DA
Q
Then temperature difference across the bottom of the pan is determined directly from the steady one-dimensional heat
conduction relation to be
C3.10 =
==→
=Kk
Lq
T
L
T
kq W/m9.14
m) )(0.006 W/m460,25(
2
steel
steel
The Rohsenow relation which gives the nucleate boiling heat flux for a specified surface temperature can also be used to
determine the surface temperature when the heat flux is given.
Assuming nucleate boiling, the temperature of the inner surface of the pan is determined from Rohsenow relation to be
3
sat,
2/1
nucleate Pr
)(
)(
−
−
=n
lfgsf
slp
vl
fglhC
TTc
g
hq
3
3
1/2
33
85.1)102270(0130.0
)95(4212
0599.0
0.50)9.81(961.5
)10)(227010297.0(460,25
−
−
= −s
T
It gives
C100.9=
s
T
Electric burner, 3 kW
P = 84.5 kPa
95C
Water
10-105
10-106
10–113 Water is boiled at Tsat = 100C by a chemically etched stainless steel electric heater whose surface temperature is
maintained at Ts = 115C. The rate of heat transfer to the water, the rate of evaporation of water, and the maximum rate of
evaporation are to be determined.
75.1Pr
N/m 0589.0
kg/m 60.0
kg/m 9.957
3
3
=
=
=
=
l
v
l
CJ/kg 4217
m/skg 10282.0
J/kg 102257
3
3
=
=
=
−
pl
l
fg
c
h
Also,
=
sf
C
0.0130 and n = 1.0 for the boiling of water on a chemically etched stainless steel surface (Table 10-3). Note that
we expressed the properties in units specified under Eq. 10-2 in connection with their definitions in order to avoid unit
manipulations.
Analysis (a) The excess temperature in this case is
C15100115
sat =−=−= TTT s
which is relatively low (less than 30C).
3
1/2
, sat
nucleate
3
1/2
33
3
2
()
()
Pr
9.81(957.9 0.60) 4217(115 100)
(0.282 10 )(2257 10 ) 0.0589 0.0130(2257 10 )1.75
474,900 W /m
p l s
lv
l fg n
sf fg l
c T T
g
qh
Ch
rr
ms
–
æö
éù–÷
–ç÷
ç
êú ÷
=ç÷
êú
ç÷
ç÷
ëû
èø
æö
éù
—
÷
ç÷
êú
= ´ ´ ç ÷
ç÷
êú ÷
ç
è ´ ø
ëû
=
2
Water, 100C
115C
100C
10-107
10–114 The initial boiling heat transfer coefficient and the total heat transfer coefficient, when a heated steel rod was
submerged in a water bath, are to be determined.
10-6. Therefore, film boiling will occur. The film boiling heat flux in this case can be determined from
24
4/1
5
33
sat
4/1
sat
sat
3
filmfilm
W/m10476.6
)400(
)400)(02.0)(10045.2(
)]400)(1997(4.0102257)[3831.09.957)(3831.0()04345.0(81.9
62.0
)(
)(
)](4.0)[(
=
+−
=
−
−
−+−
=
−
TT
TTD
TTchgk
Cq s
sv
spvfgvlvv
Using the Newton’s law of cooling, the boiling heat transfer coefficient is
film
q
10-108
10–115 The boiling heat transfer coefficient and the total heat transfer coefficient for water being boiled by a cylindrical
metal rod are to be determined.
kv = 0.04345 W/m·K
Analysis The excess temperature in this case is
ΔT = Ts − Tsat = 400°C, which is much larger than
30°C for water from Fig 10-6. Therefore, film boiling
25
4/1
5
33
sat
4/1
sat
sat
3
filmfilm
W/m10152.1
)400(
)400)(002.0)(10045.2(
)]400)(1997(4.0102257)[3831.09.957)(3831.0()04345.0(81.9
62.0
)(
)(
)](4.0)[(
=
+−
=
−
−
−+−
=
−
TT
TTD
TTchgk
Cq s
sv
spvfgvlvv
Using the Newton’s law of cooling, the boiling heat transfer coefficient is
film
q
10-109
10-116 Water is boiled at Tsat = 100C by a spherical platinum heating element immersed in water. The surface temperature is
Ts = 350C. The boiling heat transfer coefficient is to be determined.
10-110
10-111
10-112
10-113
10-120 Saturated refrigerant-134a vapor condenses on the outside of a horizontal tube maintained at a specified temperature.
The rate of condensation of the refrigerant is to be determined.
10-114
10-115
10-122 Steam at a saturation temperature of Tsat = 40C condenses on the outside of a thin horizontal tube. Heat is transferred
to the cooling water that enters the tube at 10C and exits at 30C. The rate of condensation of steam, the average overall heat
transfer coefficient, and the tube length are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The tube can be taken to be isothermal at the bulk mean fluid
5.42=Pr
C W/m615.0
CJ/kg 4178
/sm10801.0/
skg/m10798.0
kg/m 0.996
26
3
3
=
=
==
=
=
−
−
l
pl
lll
l
l
k
c
:C30At
7.01Pr
C W/m598.0
CJ/kg 4182
/sm10004.1/
skg/m10002.1
kg/m 0.998
26
3
3
=
=
=
==
=
=
−
−
l
pl
lll
l
l
k
c
:C20At
Analysis The mass flow rate of water and the rate of heat transfer to the water are
W118,000=C)10C)(30J/kg kg/s)(4182 411.1()(
kg/s 411.1]4/m) 03.0(m/s)[ )(2kg/m 998(23
water
−=−=
===
inoutp
c
TTcmQ
VAm
Condensate