Nucleate Boiling and Critical Heat Flux
1. A long, 1-mm-diameter wire passes an electrical current dissipating 3150 W/m and reaches
a surface temperature of 126°C when submerged in water at 1 atm. What is the boiling heat
transfer coefficient? Estimate the value of the correlation coefficient Cs,f.. Tsat = 100C, ρl = 1/vf
= 957.9 kg/m ,  = 1/vg = 0.5955 kg/m , cp,l = 4217 J/kgK, µl= 279 10 Ns/m , Prl = 1.76, h =
2257 kJ/kg, = 58.910-3 N/m. Assume n=1.0
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2. Estimate the nucleate pool boiling heat transfer coefficient for water boiling at atmospheric
pressure on the outer surface of a platinum-plated 10-mm diameter tube maintained 10°C
above the saturation temperature. Tsat = 100C, ρl = 1/vf = 957.9 kg/m ,  = 1/vg = 0.5955 kg/m ,
cp,l = 4217 J/kgK, µl= 279 10 Ns/m , Prl = 1.76, hfg = 2257 kJ/kg, = 58.910-3N/m. Assume
n=1.0 and Csf =.013
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3 Calculate the critical heat flux on a large horizontal surface for the following fluids at 1atm:
mercury, ethanol, and refrigerant R-134a. Compare these results to the critical heat flux for
water at 1 atm.
4 The bottom of a copper pan, 150 mm in diameter, is maintained at 115°C by the heating
element of an electric range. Estimate the power required to boil the water in this pan.
Determine the evaporation rate. What is the ratio of the surface heat flux to the critical heat
flux? Tsat = 100C, ρl = 1/vf = 957.9 kg/m ,  = 1/vg = 0.5955 kg/m , cp,l = 4217 J/kgK, µl= 279
10 Ns/m , Prl = 1.76, hfg = 2257 kJ/kg, = 58.910 N/m. Assume n=1.0 and Csf =0.013
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5 Copper tubes 25 mm in diameter and 0.75 m long are used to boil saturated water at 1 atm.
If the tubes are operated at 75% of the critical heat flux, how many tubes are needed to
provide a vapor production rate of 750 kg/h? What is the corresponding tube surface
temperature? Tsat = 100C, ρl = 1/vf = 957.9 kg/m ,  = 1/vg = 0.5955 kg/m , cp,l = 4217 J/kgK,
µl= 279 10-6Ns/m , Prl = 1.76, hfg = 2257 kJ/kg, = 58.910-3N/m. Take n=1.0 and Csf =0.013
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6 Estimate the current at which a 1-mm-diameter nickel wire will burn out when submerged
in water at atmospheric pressure. The electrical resistance of the wire is 0.129Ω/m.
7 What is the critical heat flux for boiling water at 1 atm on a large horizontal surface on the
surface of the moon, where the gravitational acceleration is one-sixth that of the earth?
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Minimum Heat Flux and Film Boiling
8 A steel bar, 20 mm in diameter and 200 mm long, with an emissivity of 0.9, is removed
from a furnace at 555°C and suddenly submerged horizontally in a water bath under
atmospheric pressure. Estimate the initial heat transfer rate from the bar. Water, liquid (1 atm,
T = 100C): ρl = 957.9 kg/m , h = 2257 kJ/kg; Water, vapor (Tf = (Ts + Tsat)/2 = 600K): v =
72.99 kg/m , cp,v = 8750 J/kgK, v = 22.710-6 Ns/m , kv = 0.0929 W/mK.
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9 A cylinder of 120-mm diameter at 1000 K is quenched in saturated water at 1 atm. Describe
the quenching process and estimate the maximum heat removal rate per unit length during the
process.
10 A sphere made of aluminium alloy 2024 with a diameter of 20mm and a uniform
temperature of 500°C is suddenly immersed in a saturated water bath maintained at
atmospheric pressure. The surface of the sphere has an emissivity of 0.25. Determine the tptal
heat transfer coefficient for the initial condition. Water, liquid (1 atm, T = 100C): ρl = 957.9
kg/m , h = 2257 kJ/kg; Water, vapor (Tf = (Ts + Tsat)/2 = 550K): v = 31.55 kg/m , cp,v = 4640
J/kgK, v = 18.610-6 Ns/m , kv = 0.0583 W/mK.
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11 A polished stainless steel bar of 50-mm diameter and an emissivity of 0.10 is maintained
at a surface temperature of 250°C while horizontally submerged in water at 25°C under
atmospheric pressure. Estimate the heat rate per unit length of the bar. Water, liquid (1 atm,
T = 100C): ρl = 957.9 kg/m , h = 2257 kJ/kg; Water, vapor (Tf = (Ts + Tsat)/2 = 450K): v =
4.81 kg/m , cp,v = 2560 J/kgK, v = 14.8510-6 Ns/m , kv = 0.0331 W/mK.
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Forced Convection Boiling
12 Saturated water at 1 atm and velocity 2 m/s flows over a cylindrical heating element of
diameter 5 mm. What is the maximum heating rate (W/m) for nucleate boiling? Assume high
velocity region flow and justify the assumption. Ts = 100C, ρl = 1/vf = 957.9 kg/m ,  = 1/vg =
0.5955 kg/m , cp,l = 4217 J/kgK, µl= 279 10 Ns/m , Prl = 1.76, hfg = 2257 kJ/kg, = 58.910
N/m.
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13 For forced convection boiling in smooth pipes, the heat flux can be estimated by
combining the separate effects of boiling and forced convection. The Roshnow and Dittus
–Boelter correlations may be used to predict nucleate boiling and forced convection effects
with 0.019 replacing 0.023 in the latter expression. Consider water at 1 atm with a mean
velocity of 1.5m/s and a mean temperature of 95°C flowing through a 15 mm diameter brass
tube whose surface is maintained at 110°C. Estimate the heat transfer rate per unit length of
the tube. Water Tm = 95C, ρl = 1/vf = 962 kg/m ,  = 1/vg = 0.500 kg/m , cp,l = 4212 J/kgK, µl=
296 10 Ns/m , Prl = 1.86, hfg = 2270 kJ/kg, = 6010 -3N/m,  = 3.0810-7 m /s
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Film Condensation
14 Saturated steam at 0.1 bar condenses with a convection coefficient of 6800 W/m2K on the
outside of a vertical brass tube having inner and outer diameters of 16.5 and 19 mm,
respectively. The convection coefficient for water flowing inside the tube is 5200 W/m2K.
Estimate the steam condensation rate per unit length of the tube when the mean water
temperature is 30°C. Water, vapor (0.1 bar): Tsat =320K, hfg = 2390x103 J/kg; Brass (T = (Tm +
Tsat ) / 2 = 300K): k = 110 W / mK
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15 Saturated steam at 1 atm condenses on the outer surface of a vertical, 100-mm-diameter
pipe 1 m long, having a uniform surface temperature of 94°C. Estimate the total condensation
rate and the heat transfer rate to the pipe. Water, vapor (1.0133 bar): Tsat = 100°C, rv = 0.596
kg/m3, hfg = 2257 kJ/kg; Water, liquid (Tf = 97°C): ρl= 960.6 kg/m3, µl = 289x10-6 N×s/m2, cp,l
= 4214 J/kgK, kl = 0.679 W/mK.
16 Saturated ethylene glycol vapor at 1 atm is exposed to a vertical plate 300 mm high and
100 mm wide having a uniform temperature of 420 K. Estimate the heat transfer rate to the
plate and the condensation rate. Approximate the liquid properties as those corresponding to
saturated conditions at 373 K. Ethylene glycol vapor (1 atm): Tsat = 470K, ρv » 0 kg/m3, hfg =
812 kJ/kg; Ethylene glycol, liquid (Tf = (Ts + Tsat)/2 » 445K; ρl = 1058.5 kg/m3, cp,l = 2742
J/kgK, µl = 0.215 ´ 10 -2 Ns/m2, kl = 0.263, W/mK.
17 Two configurations are being considered in the design of a condensing system for steam at
1 atm employing a vertical plate maintained at 90°C. The first configuration is a single
vertical plate L × w and the second consists of two vertical plates (L/2) × w, where L and w
are the vertical and horizontal dimensions, respectively. Which configuration would you
choose for laminar film condensation? Saturated water vapor (1 atm): T = 100C,  = (1/v ) =
0.596 kg/m , h = 2257 kJ/kg; Saturated water (T = (T + T )/2 = (90 + 100)C/2 = 95C = 368K):
ρl = (1/v ) = 962 kg/m , µl = 296 10 Ns/m , kl = 0.678 W/mK, cp,l = 4212 J/kgK.
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Radial Surface
18 An uninsulated 25 mm diameter pipe with a surface temperature of 15°C passes through a
room having an air temperature of 37C and relative humidity of 75%. Estimate the
condensation rate per unit length of the pipe assuming film rather than drop wise
condensation per unit length of the pipe. TA = 310K, PAsat= 0.06221 bar, Water vapor pressure
=ΦPAsat = 0.04666 bar, TAsat = 305K, ρv = 0.04 kg/m3, hfg = 2426kJ/kg; Water, liquid (Tf = (Ts +
Tsat)/2 = 297K): ρl = 997.2 kg/m3, cp,l = 4180 J/kgK, µl = 917X 10-6 Ns/m2, kl = 0.609 W/mK.
19 A horizontal tube of 50-mm outer diameter, with a surface temperature of 34°C, is
exposed to steam at 0.2 bar. Estimate the condensation rate and heat transfer rate per unit
length of the tube. Saturated steam (0.2 bar): Tsat = 333K, ρv = 0.129 kg/m3, hfg = 2358kJ/kg;
Water, liquid (Tf = (Ts + Tsat)/2 = 320K): ρl = 989.1 kg/m3, cp,l = 4180 J/kgK, µl = 577X 10-6
Ns/m2, kl = 0.640 W/mK.
Spherical Surface
20 Determine the rate of condensation on a 100-mmdiameter sphere with a surface
temperature of 150 °C in saturated ethylene glycol vapor at 1 atm. Approximate the liquid
properties as those corresponding to saturated conditions at 373 K. Saturated ethylene glycol,
vapor (1 atm): Tsat = 470K, ρv = 0 kg/m3, hfg = 812 kJ/kg; Ethylene glycol, liquid (Tf = 423K,
but use values at 373K, limit of data in table): ρl = 1058.5 kg/m3, cp,l = 2742 J/kgK, µl = 0.215
X10-2 Ns/m2, kl = 0.263 W/mK.
Condensation in Tubes
21 The saturated refrigerant vapour at 310 K is condensed as it flows through a 25 mm
diameter, 2 m-long tube whose wall temperature is maintained at 290 K. If vapor enters the
tube at a flow rate of 0.010 kg/s, what is the rate of condensation and the flow rate of vapor
leaving the tube? The relevant properties of R-12 at Tsat = 310 K are ρv = 50.1 kg/m3, hfg = 160
kJ/kg, and µv = 150 × 10-7 Ns/m2 and those of liquid R-12 at Tf = 300 K are ρl = 1306
kg/m3, cp,l = 978 J/kgK, µl = 2.54 × 10-4 Ns/m2, kl = 0.072 W/mK.
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Dropwise Condensation
22 An uninsulated 25 mm diameter pipe with a surface temperature of 15°C passes through a
room having an air temperature of 37C and relative humidity of 75%. Estimate the
condensation rate per unit length of the pipe assuming drop wise condensation per unit length
of the pipe. TA = 310K, PAsat= 0.06221 bar, Water vapor pressure =ΦPAsat = 0.04666 bar, TAsat =
305K, ρv = 0.04 kg/m3, hfg = 2426kJ/kg; Water, liquid (Tf = (Ts + Tsat)/2 = 297K): ρl = 997.2
kg/m3, cp,l = 4180 J/kgK, µl = 917x10-6 Ns/m2, kl = 0.609 W/mK.
23 A beverage can with a diameter of 65 mm and a height of 120 mm has a uniform
temperature of 5°C when it is removed from the refrigerator. The can is set on a table in a
room with an ambient air temperature of 32C and a relative humidity of 75%. Estimate the
condensation rate assuming dropwise condensation. TA = 305K, PAsat= 0.04712 bar, Water
vapor pressure =ΦPAsat = 0.03534 bar, TAsat = 300K, hfg = 2438 kJ/kg; Water, liquid (Tf = (Ts +
Tsat)/2 = 289K), cp,l = 4185 J/kgK
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