514 Chapter 9: Heat transfer in boiling and other phase-change configurations9.9 Water at 100 atm boils on a nickel heater whose temperature is 6◦ C above Tsat.. 516 Chapter 9: Heat trans
Trang 1514 Chapter 9: Heat transfer in boiling and other phase-change configurations
9.9 Water at 100 atm boils on a nickel heater whose temperature
is 6◦ C above Tsat Find h and q.
9.10 Water boils on a large flat plate at 1 atm Calculate qmaxif the
plate is operated on the surface of the moon (at16of gearth−normal).What would qmax be in a space vehicle experiencing 10−4 of
gearth −normal?
9.11 Water boils on a 0.002 m diameter horizontal copper wire Plot,
to scale, as much of the boiling curve on log q vs log ∆T
coor-dinates as you can The system is at 1 atm
9.12 Redo Problem 9.11 for a 0.03 m diameter sphere in water at
10 atm
9.13 Verify eqn (9.17)
9.14 Make a sketch of the q vs (T w −Tsat) relation for a pool boiling
process, and invent a graphical method for locating the points
where h is maximum and minimum.
9.15 A 2 mm diameter jet of methanol is directed normal to the
center of a 1.5 cm diameter disk heater at 1 m/s How many
watts can safely be supplied by the heater?
9.16 Saturated water at 1 atm boils on a ½ cm diameter platinum
rod Estimate the temperature of the rod at burnout
9.17 Plot (T w − Tsat) and the quality x as a function of position x
for the conditions in Example9.9 Set x = 0 where x = 0 and
end the plot where the quality reaches 80%
9.18 Plot (T w − Tsat) and the quality x as a function of position in
an 8 cm I.D pipe if 0.3 kg/s of water at 100 ◦C passes through
it and q w = 200, 000 W/m2
9.19 Use dimensional analysis to verify the form of eqn (9.8)
9.20 Compare the peak heat flux calculated from the data given in
Problem 5.6with the appropriate prediction [The prediction
is within 11%.]
Trang 2Problems 515
9.21 The Kandlikar correlation, eqn (9.50a), can be adapted
sub-cooled flow boiling, with x = 0 (region B in Fig.9.19) Noting
that q w = hfb(T w − Tsat), show that
q w =1058 hloF (Gh fg ) −0.7 (T w − Tsat )1/0.3
in subcooled flow boiling [9.47]
9.22 Verify eqn (9.53) by repeating the analysis following eqn (8.47)
but using the b.c (∂u/∂y) y =δ = τ δ µ in place of (∂u/∂y) y =δ
= 0 Verify the statement involving eqn (9.54)
9.23 A cool-water-carrying pipe 7 cm in outside diameter has an
outside temperature of 40◦C Saturated steam at 80◦C flows
across it Plothcondensationover the range of Reynolds numbers
0 Re D 106 Do you get the value at ReD = 0 that you would
anticipate from Chapter8?
9.24 (a) Suppose that you have pits of roughly 0.002 mm
diame-ter in a metallic headiame-ter surface At about what temperature
might you expect water to boil on that surface if the pressure
is 20 atm (b) Measurements have shown that water at
atmo-spheric pressure can be superheated about 200◦C above its
normal boiling point Roughly how large an embryonic bubble
would be needed to trigger nucleation in water in such a state
9.25 Obtain the dimensionless functional form of the pool boiling
qmax equation and the qmaxequation for flow boiling on
exter-nal surfaces, using dimensioexter-nal aexter-nalysis
9.26 A chemist produces a nondegradable additive that will increase
σ by a factor of ten for water at 1 atm By what factor will the
additive improve qmax during pool boiling on (a) infinite flat
plates and (b) small horizontal cylinders? By what factor will
it improve burnout in the flow of jet on a disk?
9.27 Steam at 1 atm is blown at 26 m/s over a 1 cm O.D cylinder at
90◦ C What is h? Can you suggest any physical process within
the cylinder that could sustain this temperature in this flow?
9.28 The water shown in Fig 9.17 is at 1 atm, and the Nichrome
heater can be approximated as nickel What is T w − Tsat?
Trang 3516 Chapter 9: Heat transfer in boiling and other phase-change configurations
9.29 For film boiling on horizontal cylinders, eqn (9.6) is modified
9.30 Water at 47◦C flows through a 13 cm diameter thin-walled tube
at 8 m/s Saturated water vapor, at 1 atm, flows across the tube
at 50 m/s Evaluate Ttube, U , and q.
9.31 A 1 cm diameter thin-walled tube carries liquid metal through
saturated water at 1 atm The throughflow of metal is creased until burnout occurs At that point the metal tem-perature is 250◦ C and h inside the tube is 9600 W/m2K What
in-is the wall temperature at burnout?
9.32 At about what velocity of liquid metal flow does burnout occur
in Problem9.31if the metal is mercury?
9.33 Explain, in physical terms, why eqns (9.23) and (9.24), instead
of differing by a factor of two, are almost equal How do these
equations change when H is large?
9.34 A liquid enters the heated section of a pipe at a location z = 0
with a specific enthalpy ˆhin If the wall heat flux is q wand the
pipe diameter is D, show that the enthalpy a distance z = L
Since the quality may be defined as x ≡ (ˆ h − ˆ h f ,sat ) h fg, show
that for constant q w
x = hinˆ − ˆ h f ,sat
h fg + 4q w L
GD
9.35 Consider again the x-ray monochrometer described in Problem
7.44 Suppose now that the mass flow rate of liquid nitrogen
is 0.023 kg/s, that the nitrogen is saturated at 110 K when
it enters the heated section, and that the passage horizontal.Estimate the quality and the wall temperature at end of the
Trang 4References 517
heated section if F = 4.70 for nitrogen in eqns (9.50) As
before, assume the silicon to conduct well enough that the heat
load is distributed uniformly over the surface of the passage
9.36 Use data from AppendixAand Sect.9.1to calculate the merit
number, M, for the following potential heat-pipe working
flu-ids over the range 200 K to 600 K in 100 K increments: water,
mercury, methanol, ammonia, and HCFC-22 If data are
un-available for a fluid in some range, indicate so What fluids are
best suited for particular temperature ranges?
References
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[9.34] J R Ramilison and J H Lienhard Transition boiling heat transfer
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Trang 10Part IV
Thermal Radiation Heat Transfer
523
Trang 1210 Radiative heat transfer
The sun that shines from Heaven shines but warm, And, lo, I lie between that sun and thee:
The heat I have from thence doth little harm, Thine eye darts forth the fire that burneth me:
And were I not immortal, life were done Between this heavenly and earthly sun.
Venus and Adonis, Wm Shakespeare, 1593
Chapter 1 described the elementary mechanisms of heat radiation
Be-fore we proceed, you should reflect upon what you remember about the
following key ideas from Chapter1:
• Electromagnetic wave spectrum • The Stefan-Boltzmann law
• Heat radiation & infrared radiation • Wien’s law & Planck’s law
• Transmittance, τ • Transfer factor, F1–2
• e(T ) and e λ (T ) for black bodies
The additional concept of a radiation heat transfer coefficient was
devel-oped in Section2.3 We presume that all these concepts are understood
The heat exchange problem
Figure10.1shows two arbitrary surfaces radiating energy to one another
The net heat exchange, Qnet, from the hotter surface (1) to the cooler
525