TWO PH A SE H EA T TRA N SFER
TWO PHA SE H EA T TRA TRA N SFER
Objectives 1.
Dete Determ rmin inee the the heat heat flu flux x and and surf surfac acee heat heat tra trans nsfe ferr coef coeffi fici cien entt as fun funct ctio ions ns of of the the temperature excess at constant pressure; i.e., construct a boiling curve.
2.
Determ Determine ine the the maxi maximum mum heat heat flux flux (criti (critical cal heat heat flux flux)) as as a functi function on of pressu pressure; re; compar comparee the value with the theoretical data generated using the Zuber and T ribus correlation.
3.
Determine and explain the effect of system pressure on the maximum heat flux
4.
Determine and explain the effect of system pressure on the heat transfer coefficient. 5. Perfo Perform rm a hea heatt bal balan ance ce on the the app appar arat atus us and and com compa pare re to theo theory ry.. Can Can you you appl apply y the heat balance to the film boiling region to get a more accurate estimate of max heat flux? For extra credit, model a similar system in Polymath or Excel to show how pressure can affect the heat transfer transfer coefficient. Hint: you may have to assume a simplified simplified distribution of discreet surface cavity sizes.
Theory Boiling Heat Transfer When a liquid at the saturation temperature is in contact with the surface of a solid (usually a metal) at a higher temperature, heat is transferred to the liquid, and a phase change (evaporation) (evaporation) of some of the liquid occurs. occurs. The nature and rate of this heat transfer changes considerably as the temperature difference between the metal surface and the liquid is increased. Convective Boiling When the metal surface is slightly hotter than the liquid, convective currents carry the warmed liquid to the surface, and evaporation is largely at the surface with little ebullition (turbulence). Nucleate Boiling As the metal surface temperature is increased, small bubbles of vapor appear on the heating element surface. surface. At first, some of these bubbles may may collapse, giving up their latent heat heat to the liquid. The rest of the bubbles rise to the surface where they burst and and release the vapor. As the temperature difference difference increases further, almost all of the bubbles make it to the surface without condensing. Surface tension in the liquid offers great resistance to the birth of a bubble. Initially the bubbles form at nucleation sites on the surface where minute local cavities or gas pockets exist. exist. The ability of these vapor bubbles to form, form, expand, and rise to the surface depends on the size of the surface cavity (note that for a given surface there is a unique range or distribution of cavity sizes), the system pressure, the liquid vapor pressure and surface tension, and the
temperature difference between the heating element and the liquid. The dependence of bubble formation on these variables can be seen by combining a force balance on the gas-liquid interface of the bubble with the ClausiusClapeyron equation which you should recall from physical chemistry and thermodynamics classes. In full nucleate boiling, bubbles form vigorously with considerable turbulence. This action leads to very high heat transfer rates. From an industrial point of view, this is by far the most important and most used regime of boiling. Film Boiling Above a critical surface-liquid temperature difference, the surface becomes “vapor-locked” and the liquid is unable to wet the surface. When this happens, there is a considerable reduction in the heat transfer rate. If the heat input to the metal is not reduced to match the lower ability of the surface to transfer heat, the metal temperature will rise until radiation heat transfer plus the limited film boiling heat transfer from the surface is equal to the energy input. This condition can result in a failure or “burn-out.” In this experiment, film boiling is reached and sustained for a limited period of time.
Heat flux
Q = V I
Heat Flux =
Q A
The heat transferred and the heat flux are calculated using the equations below. Remember that Q is calculated in Watts. The exact dimensions of the heating element will be required to calculate the area A. These dimensions are indicted on the experiment casing.
h =
Q A ∆T
The heat transfer coefficient ( h) is then given by
q A max
=
π
24
h f g ρ v
σ g ( ρ l - ρ v ) 2 ρ v
Zuber and Tribus Correlation
Brock and Bird Method for Computing Surface Tension (σ)
1/4
ρ v 1 + ρ l
1/2
σ
where,
11/9
2/3 1/3 = Pcr T cr B (1 - T r )
Pcr = T ln Pcr B = 0.1207 1 + br T cr = 1 - T br h fg boiling (fluid-gas) B = Brock and Bird parameter (dimensionless) T br = T b / T cr (dimensionless) σ = Surface tension (dynes/cm = mN/m)
- 0.281
Critical pressure (atm) Critical temperature K =Latent heat of
OPERATING INSTRUCTIONS During Use Control the saturation pressure to the desired level b y: a.
Varying the cooling water flow rate. Increasing the water flow rate results in a decrease in the vapor pressure.
b.
Varying the power supplied to the heater. Increasing the power supplied to the heater results in an increase in the vapor pressure.
High Temperature Cut-Off Under no circumstances should the setting on this control be above 300 °C. For normal operation, it is advisable that the control be set to shut the system off at 250 °C.
After Use a.
Switch off the electrical supply.
b.
Circulate cooling water until the pressure has dropped to atmospheric.
Note Initial readings from the voltmeter and ammeter should be taken from the lowest scales (low power inputs). When the power input is sufficient enough to exceed this scale, the two pole switch should be adjusted to allow the larger voltmeter and ammeter scales to be utilized. The switch is labeled to indicate which scale relates to each switch position.
EXPERIMENTAL APPARATUS
VISUAL DEMONSTRATION OF THE THREE MODES OF
BOILING EXPERIMENT 1 Objective:
To visually demonstrate the three modes of boiling: convective, nucleate, and film boiling using R-113 refrigerant.
Procedure: 1.
Turn on the electric and water supply. Adjust the power output to 100-150 Watts and maintain the pressure at 5 psig by switching buttons 1 and 3 (button 1 is the power button; it should always be turned on). Carefully watch the liquid surrounding the copper heating element. Convection currents will be observed and at the same time, liquid will be seen to collect on the condenser coils, indicating that evaporation is proceeding at a low rate. When the pressure reaches 5 psig, purge air until the pressure reaches 2.5 psig.
2.
Increase the wattage in increments (around 15 Watts). Observe the surface temperature of the heating element and the liquid temperature at each increment. Nucleate boiling will be seen, and as the power input is increased, vigorous boiling will occur. The temperature difference between the liquid and the heating element surface at this point should still be below 70°C.
3.
Increase the power in smaller increments and observe the liquid to heating and 75 °C, the temperature of the heating element will rise quickly. This indicates that film boiling is occurring. At this point watch the temperature CLOSELY. As it approaches 250 degrees, reduce the electrical power input to about 100 Watts. When film boiling occurs, the rate of evaporation falls to a low level. Observation of the heater surface will show that it is now enveloped in an almost unbroken film of vapor.
4.
The power output at which film boiling occurs will be used in Experiment 2 to determine the size of increments to obtain the proper number of data points.
DETERMINATION OF THE HEAT FLUX AND SURFACE HEAT TRANSFER COEFFICIENT EXPERIMENT 2 Objective: A) and the surface heat transfer coefficient ( h) up to and beyond the To determine the heat flux ( Q / critical temperature difference point at a constant pressure.
Procedure: 1.
After reaching steady-state, start taking the data according to the data table. Increase the power input in increments. Continue the increments until film boiling is reached.
2.
When film boiling is reached, reduce the heat input to about 100 Watts. Go to the next pressure (7.5 psig) by switching off button 3 and switching on button 4.
DETERMINATION OF THE HEAT FLUX AND SURFACE HEAT TRANSFER COEFFICIENT EXPERIMENT 3 Objective: To determine the maximum heat flux at four pressures.
Procedure: 1.
Follow the procedure from Experiment 2 for pressures of 5.0, 7.5, 10.0, and 12.5, psig to determine the maximum heat flux at these pressures. Remember that at each pressure you need to reach film boiling and maintain up to 250 °F. Choose the appropriate heat input increments so that you will have enough data to make a graph.
2.
After the 12.5 psig run is completed, reduce the wattage (or turn it off). Then set the pressure down to 10.0 psig by switching button 5. After 2 minutes, set it to 7.5 psig. Then wait 2 more minutes before setting it to 5.0psig, etc.. This prevents the sudden contraction of the glass tube. Let the GTA know that the experiment is finished.
MINIMUM REPORT REQUIREMENTS 1.
Plot the log (heat flux) vs. log (temperature difference) at each pressure, and obtain the maximum heat flux values from these graphs.
2.
Compare values determined from (1) above to theoretical values determined using the Zuber and Tribus correlation. For calculation of the surface tension, use the Brock and Bird method.
3.
Plot log (heat transfer coefficient) on a linear axis vs. the temperature difference on a log axis at each pressure.
4.
Obtain a correlation between the heat transfer coefficient and pressure for nucleate boiling (see below).
Correlation between heat transfer coefficients and pressure At some constant pressure, heat transfer coefficient (W/m 2 - °C) is a function of ∆T x (temperature
h = a′ ( ∆ T x )
b′
difference between the heating element and the saturated liquid, in °C) as follows: where, a′ and b′ are constants. To obtain these constants, make a plot of ln ( h) vs. ln (∆T x). The slope of the linear regression is b′ and the y-intercept is ln a′. Since we have 4 different pressure runs, we can take the average of the a′ and b′ values (assuming the standard deviation is not too great). Use the data analysis- regression routines in Excel to get 95% confidence level estimates of the parameter values.
h = href
p pref
c
The following equation takes into account the variation of pressure in the heat transfer coefficients where, c is a constant, and href is the heat transfer coefficient at a reference pressure pref .
h = a ( ∆ T x )
Combining the above two equations gives
b
p pref
c
This time, use multiple variable linear regression in Polymath to determine the constants a, b, and c. You will need to first transform the equation to get a linear form:
ln h = ln a + b ln ( ∆ T x ) + c ln
p p ref
Polymath (on PCs in 228 Textile has an example problem of this type that is easily accessed through the menu system. By tabulating all combinations of ln( ∆Tx ), ln(p/pref), and the dependent variable ln(h), and using the regression routine, you will get least squares estimates of ln(a), ln(b), and ln(c) along with 95% confidence levels on these parameters. By taking the antilogs of these values and uncertainties (95% confidence intervals), you will be able to get estimates of a, b, and c from our original equation. The confidence interval tells you what range of values are likely to be the actual parameter values with 95% certainty. Compare the results to experiment. Try graphing as a surface plot in Excel, or (preferably) Sigma Plot. How do the values for a and b compare to those calculated for a’ and b’?
SAMPLE DATA SHEET: Experiment 2 PRESSURE: 5 psig Temperatures (°C) Run No.
Voltage (Volts)
Current (Amps)
Coolant H 2O Liquid
Metal In
Out
Flow Rate of H 2O
SAMPLE DATA SHEET: Experiment 3 PRESSURE: 7.5 psig Temperatures (°C) Run No.
Voltage (Volts)
Current (Amps)
Coolant H 2O Liquid
Metal In
Out
Flow Rate of H 2O
PRESSURE: 10 psig Temperatures (°C) Run No.
Voltage (Volts)
Current (Amps)
Coolant H 2O Liquid
Metal In
Out
Flow Rate of H 2O
PRESSURE: 12.5 psig Temperatures (°C) Run No.
Voltage (Volts)
Current (Amps)
Coolant H 2O Liquid
Metal In
Out
Flow Rate of H 2O
PRESSURE: 12.5 psig
PRESS URE: 15.0 psig Temper atures (° C) Run No.
Voltage (Volts)
Current (Amps)
Coolant H 2 O Li qui d
Metal In
Out
Flow Rate of H 2O
