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Boiling Heat Transfer Fundamentals
During the past few decades, great interest has developed in boiling as a method of increasing heat transfer rates at moderate temperature differences. Boiling heat transfer is especially effective at high heat fluxes. Thus, it finds application in cooling of nuclear reactors and rocket engines where heat transfer rates may be of the order of 3 × 106 to 3 × 107 W/m2 (106 to 107 BTU/hr-ft2). See "Boiling" by W.M. Rohsenow, in Handbook of Heat Transfer Fundamentals, 2nd ed. W.M. Rohsenow, J.P. Hartnet and E.N. Ganic, McGraw-Hill, New York, 1985.
Saturation boiling takes place at a surface situated in a liquid which is at the saturation temperature. The average liquid temperature may remain well below the saturation value, producing local boiling at the wall with subsequent condensation of the vapor as it departs the wall and moves into the colder bulk of the fluid. This is known as subcooled boiling. When the heated surface is submerged in a container of liquid where there is no motion except that induced by the boiling process, the process is called pool boiling. If, on the other hand, a liquid is forced over the heated surface and boils, it is called forced convection boiling.
In your experiment, saturated liquid pool boiling on an electrically-heated, horizontal wire in a saturated liquid is to be studied and observed.
Figure 1: Representative boiling curve, saturated pool boiling [CRC Handbook of Thermal Engineering. Edited in chief Frank Kreith, 1999 pp.3-94]
Figure 1 shows a representative boiling curve obtained from an experiment involving an electrically heated horizontal wire submerged in a pool of water at saturation temperature, Tsat. As the wire surface temperature, Tw, is first raised above the saturation temperature, convective currents circulate the superheated liquid, and vapor is produced by evaporation at the free surface of water. In this region of the curve, indicated as ac in the figure, heat transfer is mainly by single-phase, free convection. The temperature difference (Tw - Tsat) which drives the heat transfer is given the symbol ΔTsat , the wall "superheat." The q=f(ΔTsat) relation for region ac may be correlated as q ~ (ΔTsat)5/4. It depends strongly on the wire diameter. Point c is called "the first bubble point" and reflects the onset of bubble production in the fluid at the heated surface. Under certain conditions, a higher superheat isrequired to initiate boiling over that required to maintain boiling. If so, point c will be to the right and the onset of boiling is marked by a drop in wall temperature below the temperature of point c associated with a slight rise in heat flux to point d above that of point c. As point c is passed, the effect of boiling manifests itself, sometimes rather abruptly. In region de, vapor bubbles are formed at favored spots on the heating surface and rise to the free liquid surface. The formation cycle and the size of the bubbles are fairly regular. This is called the region of isolated bubbles for the bubbles remain isolated from one another as they rise to the free surface. This portion of the curve is quite steep because, as heat flux is increased, more bubble formation sites become active and each existing site becomes more active (releasing bubbles at a higher rate). Thus, the heat transfer coefficient rises steeply with rising heat flux.
In region ef, larger and more numerous bubbles are formed which begin to interfere with one another while rising. Further increases in the wire temperature produce continuous vapor columns above the wire. This is called the region of bubble coalescence.
Region def is called the nucleate boiling regime. Note that the entire boiling curve is such that the wall temperature is above the saturation temperature. To the right of the peak of the curve lies the transition boiling regime fg where an unstable vapor film forms around the wire. If the wire temperature were controlled, the film would collapse and reform rapidly giving the time-average behavior shown as the fg line. The presence of this film provides additional resistance for heat transfer and reduces the heat transfer coefficient with increasing surface temperature. In this experiment, the voltage to the wire is controlled. Under a condition of controlled heat flux, no stable state can be attained in the fg portion of the curve and there will be an immediate jump from point f to point h at the same heat flux.
In region gh, the film around the wire becomes stable in the sense that it does not break up and reform cyclically but, instead, it always envelops the heating surface, although its shape is not necessarily smooth. This regime is called stable film boiling. Usually within the film boiling regime, particularly when in water where values of ΔTsat are often beyond 600oC, the influence of radiation becomes pronounced.
As noted, when an electrically controlled, heated wire is used, the regime fg cannot be obtained. In region df, an increase in the electric energy input (and hence q") results in an increase in ΔTsat due to occasional formation of large vapor patches intermittently on the surface. When the peak value of heat flux is reached at f, and then exceeded slightly, the boiling process cannot remove heat as fast as is necessary to maintain a stable wire temperature. The difference between the energy that must be removed and the energy that can be removed causes a rapid rise in the temperature of the wire. Unless the electrical input is quickly reduced, the system will proceed toward point h. The stable point temperature may be above the melting point of the wire material and, if so, the wire melts before the stable point is actually reached. For this reason, the peak heat flux in nucleate boiling is sometimes called the "burnout" heat flux. A more universal term is the "Critical Heat Flux," since it represents a critical point in the boiling performance. However, as the temperature rises, so will the resistance. Thus, if voltage is controlled, the power will drop according to P=V2/R, as will the heat flux. Therefore, the stable point will be below h on the gh line.
Kutateladze (in 1950) proposed the following expression for estimating the burnout, or critical, heat flux, q"max, in saturated pool boiling as:
C = a constant analytically determined by hydrodynamic stability analysis to be 0.1309 by Zuber
hfg = latent heat
ρv = density of saturated vapor
ρL = density of saturated liquid
σ = surface tension
g = gravitational acceleration
This expression is obtained by dimensional analysis. Insight was gained by analyses which assumed that burnout, or the critical point, can be associated with the instability of the interface between the departing vapor streams and the liquid streams moving toward the heating surface.
With an electrically heated wire, both nucleate and film boiling can exist simultaneously on different portions of the length of the wire. This, of course, introduces some error in our analysis, since the wire temperature is actually an average wire temperature.