Problems (Ch. 2)

1. Derive the Clausius-Clapeyron equation from the Gibb's equation,

Tds = dh - dp/ρ .

2. Estimate the enthalpy to evaporate the water of 525oF using the Clausius -Clapeyron equation and compare to the result from the steam table.

3. Find the minimum liquid superheat required for nucleate boiling from a horizontal surface in water at atmospheric pressure where,

(a) cavities of all radii are present and the heat flux is,

q" = 1.0x106 Btu/hr-ft2.

(b) only cavities of 1/2 mil(0.0005") radius are present

(c) How does the result in Part (b) change as the system pressure is             increased ?

4. Prob. 4-1 of Collier's book.

5. For 665.6 F water, calculate the amount of liquid superheat necessary to generate 4.68x10-3 in diameter bubble at 2250 psia.

6. Consider the data presented on the next three figures concerning the actual frequency distribution of departing bubbles from a platinum wire, where F(Db)dDb is the number of bubbles leaving the surface per nucleation site   per unit time with diameter between Db and dDb.

1) Obtain the average departure diameter, Db, and the average departure

frequency, f, for the two heat flux

2) Compare the frequency from the model derived in class, the Cole and         Rohsennow's model and Mikic model with that of experiments.  And describe

the dependence of heat flux on Db and f.

7. Derive the Rayleigh equation(Eq.5) by inserting Eq.4 into Eq.2 in Handout.

8. Plot the radius as a function of time for the isothermal and isobaric bubble dynamic model as well as the spherical bubble model of Rosenow and Mikic for  the two cases below.  Briefly discuss the results.

	CASE 1	CASE 2
Pliq Tliq(>Tsat) Ro	0.1831 psia 79.1 oF 0.0	12.7 psia 217.6 oF 0.0

9. For initially nonuniformly superheated liquid(i.e. presence of condensing

heat flux), the rate equation of bubble radius was given in class as,

ρghfg (dR/dt) = hf(T -Tsat)/√(παft) - q"cond

Determine the time-dependent bubble radius and express with the maximum

bubble radius.

10.Starting with the postulate that energy is conserved, derive the spherically symmetric liquid phase energy equation in spherical coordinates.

[eqn: {T_l} over t + u_l~(r)~{{∂T_l} over {∂r}} = {α_l over r^2}{{∂} over {∂r}}[r^2{{∂T_l} over {∂r}}]]

where ul(r) is the radial velocity of the liquid phase and the subscript,l,

represents the  liquid phase.

11. Following parameters were measured in a subcooled pool boiling test at 1 atm.

q" = 1.04x106 Btu/hr-ft2,       Tbulk, Twall = 98, 270 oF

Bubble departure frequency     =  1000 bubbles/sec

Bubble population              =   280 bubbles/cm2

Average radius of departing bubbles bubbles = 0.01187 in

Obtain the amount of evaporative heat transfer, q"evap .