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10-41
10-47E Water is boiled at 1 atm pressure and thus at a saturation (or boiling) temperature of Tsat = 212F by a horizontal
polished copper heating element whose surface temperature is maintained at Ts = 988F. 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.
3
(Table A-9E). The properties of the vapor at the film temperature of
F6002/)988212(2/)( sat =+=+= sf TTT
are, by
interpolation, (Table A-16E)
FftBtu/h 02640.0
FBtu/lbm 4799.0
hlbm/ft 0.05099slbm/ft 10416.1
lbm/ft 02395.0
5
3
=
=
==
=
−
v
pv
v
v
k
c
Also, g = 32.2 ft/s2 = 32.2(3600)2 ft/h2. 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 A-16E instead of the properties
of saturated vapor from Table A-9E since the latter are at the saturation pressure of 1541 psia (105 atm).
Analysis The excess temperature in this case is
F776212988
sat =−=−= TTT s
, which is much larger than 30C or 54F.
Therefore, film boiling will occur. The film boiling heat flux in this case can be determined from
2
4/1
32
sat
4/1
sat
3
film
ftBtu/h 147,25
)212988(
)212988)(12/5.0)(05099.0(
)]212988(4799.04.0970)[02395.082.59)(02395.0()0264.0()3600(2.32
62.0
)(
)(
)](4.0)[(
62.0
=
−
−
−+−
=
−
−
−+−
=TT
TTD
TTChgk
qs
sv
satspvfgvlvv
The radiation heat flux is determined from
44428
4
sat
4
rad
)(
−=
−
TTq s
Btu/h 3433=
P = 1 atm
Water, 212F
Heating element
10-42
10-43
10-44
10-45
10-46
10-52 Cylindrical stainless steel rods are heated to 700°C and then suddenly quenched in water at 1 atm. The convection heat
transfer coefficient and the total rate of heat removed from a rod at the instant it is submerged in the water are to be
700)/2 = 400°C are, from Table A-16,
skg/m 10446.2
kg/m 3262.0
5
3
=
=
−
v
v
K W/m05467.0
KJ/kg 2066
=
=
v
pv
k
c
2
4/1
5
33
W/m92097
)100700(
)100700)(025.0)(10446.2(
)]100700)(2066(4.0102257)[3262.09.957)(3262.0()05467.0(81.9
62.0
=
−
−
−+−
=
−
Thus, the convection heat transfer coefficient is
)( satfilm TThq s−=
→
K W/m153.5 2=
−
=K )100700(
W/m92097 2
h
The radiation heat flux is determined from
2
444428
4
sat
4
rad
W/m14917
K )373973)(K W/m1067.5)(3.0(
)(
=
−=
−=
−
TTq s
Then the total heat flux becomes
2522
radfilmtotal W/m100328.1) W/m14917(
4
3
W/m92097
4
3=+=+= qqq
The total rate of heat removed from a rod at the instant it is submerged in the water is
W2028=== ) W/m100328.1)(m 25.0)(m 025.0()( 25
totaltotal
qDLQ
Discussion Convection heat transfer coefficient in film boiling is generally lower than that of nucleate boiling, because the
excess temperature of film boiling is much larger than that of nucleate boiling.
10-47
10-48
10-54 A cylindrical heater is used for boiling water at 1 atm. The film boiling convection heat transfer coefficient at the
burnout point is to be determined.
0.0589 N/m (Tables 10-1) and, from Table A-9, ρl = 957.9 kg/m3, ρv,sat = 0.5978 kg/m3, hfg = 2257 × 103 J/kg.
The properties of vapor at the film temperature of Tf = 1150°C are, from Table A-16,
skg/m 10283.5
kg/m 1543.0
5
3
=
=
−
v
v
K W/m1588.0
KJ/kg 2571
=
=
v
pv
k
c
cylinder) large thusand 1.2 > * (since 12.0
1.2 >997.1
0589.0
)5978.09.957(81.9
)2/01.0(
)(
2
*
2/1
2/1
sat,
LC
g
D
L
cr
vl
=
=
−
=
−
=
The burnout point occurs at the maximum heat flux, which is
4/1
sat,
2
sat,max
)]([
−= vlvfgcr ghCq
10-49
10-50
Ts = 2192°C
The film boiling heat flux is
25
4/1
5
33
film
sats
4/1
satsv
satspvfgvlv
3
v
filmfilm
W/m 108366.6
)1002192(
)1002192)(003.0)(10283.5(
)]1002192)(2571(4.0102257)[1543.09.957)(1543.0()1588.0(81.9
62.0
)cylindershorizontal(62.0Cwhere
)TT(
)TT(D
)]TT(c4.0h)[(gk
Cq
=
−
−
−+−
=
=
−
−
−+−
=
−
Thus, the film boiling convection heat transfer coefficient is
K W/m327 2=
−
=
−
=K )1002192(
W/m108366.6 25
sat
film
TT
q
h
s
Discussion The nucleate boiling convection heat transfer coefficient is about 175 times higher than that of film boiling. This
is because the vapor film surrounding the heater surface during film boiling impedes convection heat transfer.
Note that the film temperature Tf = (2192 + 100)/2 = 1146C, is close to the assumed value of 1150C used in film boiling for
the evaluation of vapor properties.
10-51
10-56 Water is boiled at 1 atm pressure and thus at a saturation (or boiling) temperature of Tsat = 100C by a horizontal nickel
plated copper heating element. The maximum (critical) heat flux and the temperature jump of the wire when the operating
10-52
10-57 Prob. 10-56 is reconsidered. The effects of the local atmospheric pressure and the emissivity of the wire on the
D=0.004 [m]
epsilon=0.3
P=101.3 [kPa]
"PROPERTIES"
Fluid$='steam_IAPWS'
T_sat=temperature(Fluid$, P=P, x=1)
rho_l=density(Fluid$, T=T_sat, x=0)
g=9.81 [m/s^2] “gravitational acceleraton"
sigma_rad=5.67E-8 [W/m^2-K^4] “Stefan-Boltzmann constant"
"ANALYSIS"
"(a)"
10-53
10-54
10-55
10-56
10-66 The local heat transfer coefficients at the middle and at the bottom of a vertical plate undergoing film condensation are
to be determined.
Assumptions 1 Steady operating condition exists. 2 The plate surface has uniform temperature. 3 The flow is laminar.
Properties The properties of water at the saturation temperature of 100°C are hfg = 2257 kJ/kg (Table A-2) and ρv = 0.5978
kg/m3 (Table A-9). The properties of liquid water at the film temperature of Tf = (Tsat + Ts)/2 = 90°C are, from Table A-9,
J/kg 102314
3
=
The local heat transfer coefficient can be calculated using
)675.0)(102314)(5978.03.965)(3.965)(81.9(
)(4
)(
4/1
33
4/1
sat
3
−
−
−
=
xTT
khg
h
sl
lfgvll
x
10-57
10-58
10-59
10-60
10-70 Saturated steam at a saturation temperature of Tsat = 100C condenses on a plate which is tilted 60 from the vertical
and maintained at 90C by circulating cooling water through the other side. The rate of heat transfer to the plate and the rate
