GRAPHICAL ESTIMATION OF NUCLEATE BOILING HEAT TRANSFER W A L T E R F R O S T A N D G E R A L D S. D Z A K O W I C The University of Tennessee Space Institute, Tullahoma, Tenn.
A method for graphically presenting fully developed nucleate boiling heat transfer correlations currently being used for design purposes enables the engineer to compute a numerical value of the boiling heat flux, or corresponding wall superheat, rapidly and without knowledge of the physical properties of the fluid, other than at one arbitrary reference state.
method is illustrated for presenting boiling heat transfer correlations in engineering handbooks or design manuals. This method is applicable to such correlations as those given by Engelberg-Forster and Grief (7), Rohsenow (3),and Seader, Miller, and Kalvinskas ( 4 ) . If the ratio of the functions f(q/A,AT,) and f(q/A,ATJref,which are determined from the chosen boiling correlation, are plotted against reduced pressure, it forms a single curve for a number of different fluids. The method is, thus, analogous to the law of corresponding states and is demonstrated here with the Engleberg-Forster and Grief correlation, for which j ( q / A,AT,) becomes A T s / a . A curve of ( A T , / d G ) / ( A T , / us. reduced pressure, p,, is established and a table of ( A T , / a ) r e for f a number of different fluids compiled. From the plot and the tabled values, AT,/* for a given fluid at any system pressure is computed by a simple multiplication. This technique greatly reduces the work of the design engineer by providing a means of computing a boiling heat flux or corresponding wall superheat without the problem of finding physical properties of the fluid or the tedious numerical computation generally required in evaluating nucleate boiling heat transfer correlations.
4.0
ACONVENIENT
2.0
I
> 0.8 \
2
0.6
dz)ref
\
c
0.4
s. 0.2
0.1
I
0.001
Proposed Method
I
I
l l l l l l l
0.M)5 0.01
I
I 1 1 1 1 1 1 1
0.05
0.1
I
I
IIOOI
0.5
1.0
REDUCED PRESSURE, P,
Values of AT,/*
are determined from
which is Engelberg-Forster and Grief's (7) Equation 30 with side is a AP set equal to ( / L I ~ / V , ~ T ~ ~The ~ ) Aright-hand T,. function of fluid properties only. The value ( A T , / d G ) r e f is determined from Equation 1 a t an arbitrarily chosen reduced pressure of 0.05. Table I shows values of (AT,/ d G ) / ( A T s / a ) r eforf nine fluids a t a number of reduced pressures. The ratio for all fluids obeys satisfactorily the principle of corresponding states up to reduced pressures of 0.8. Discrepancies at higher reduced pressures are attributed to a scarcity of reliable property data in this pressure range. The reduced pressure a t which ( A T 8 / a ) r eisfevaluated is arbitrary to the extent that it can be assigned any value with the exception of values near unity. T o satisfy physical requirements A T , / d G must approach zero at the critical pressure; hence, reduced pressures near unity are not suitable reference 346
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
Figure 1. Engelberg-Forster and Grief ( 7 ) correlation in terms of reduced coordinates
values. The value of P, = 0.05 was used as a reference because property values for most fluids are best known at reduced pressures of this magnitude. Accordingly the most accurate computation of ( A T s / G A ) r e fwhich , is dependent solely on the properties of the fluid, is obtained at or near this pressure. Figure 1 is a plot of the best fit curve for the values of (AT8/ The tabulated values have a two standard deviation of 3=0.08 with respect to this curve. The curve in Figure 1 is identical to the Engleberg-Forster and Grief correlation. Thus, comparison of Figure 1 with experimental data is unnecessary, as this is extensively done in the literature. There it is generally reported that agreement between predicted values and experimental values is *25y0 (2). Since the present work is not an extension of the theory but only a convenient method of presenting it, no greater accuracy can be expected with the technique proposed here. Moreover,
d q ~ / ( A T , / ~ ) given , e f in Table I.
Table
Pr 0.002 0.005 0.01 0.02 0.05 0.10 0.20 0.40 0.50 0.60 0.80 0.90 0.95
1.
Calculated from the Correlation of Engelberg-Forster and Grief ( I ) Hydrogen (Para) Neon Nitrogen Oxygen n-Pentane Water 2.303 1.813 1.527 1.220 1.265 1.205 1.270 1.271 1.272 1.000 1.000 1.000 1.000 1.000 1.000 0.858 0.839 0.859 0.812 0.814 0.679 0.671 0.719 0.723 0.621 0.669 0.502 0.518 0.508 0,600 0.473 0.515 0.443 0.439 0.453 0,522 0.411 0.466 0.385 0.392 0.387 0.349 0.420 0.217 0.292 0.255 0.309 0.233 0.292 0.159 0.247 0.197 0.241 0.161 0.217 0.101 0.203 0.152 0.103 0.149
Values of (4T,/l/q/A)/(4T,/1/S/A)ref
Ammonia
Freon- 12
1.258
1.300 1 .ooo 0.818 0.637 0.480 0.409 0.390 0.255 0.145 0.130
1.000
0.837 0.671 0.525 0.446
Helium
1.000 0,835 0.655 0.479
Table II. Reference Values Determined from EngelbergForrter and Grief Correlation for Fully Developed Boiling at P, 0.05 (ATA/ (AT*/
=
%mref 5
1/4/A)ref
5
703,
Fluid
Ammonia Argon Carbon dioxide Carbon tetrachloride Ethanol Freon-1 2 Helium Hydrogen (para)
R.l [B.t.u.)Hr. sq. Ft.]’/* 66.8
Kerosine
96.5 141.2 187 . O 123.7 113.6 41 .O 44.8
Mercury Neon Nitrogen Oxygen n-Pentane Propane Water
Fluid
these two values gives 4TJ= 0.137. Therefore, Tzo T,,, = 13.7’ F., and since Teat= -22’ F., the surface temperature is determined as approximately -8’ F. Of course, the reverse problem of finding q / A with ATsatknown is handled with equal simplicity.
-
103,
R.l [B.t.u.jHr. Sq. Ft .]l / * 196.0
(JP-4) 52.0 49.8 80.9 86.5 153.8 195.2 61.9
Conclusions
A method of numerically evaluating the heat flux or the corresponding wall superheat of a boiling system a t any given pressure for fluids which reasonably obey the correspondence principle is embodied in Figure 1 and Table 11. This method is ideally suited for design purposes, in that without loss of accuracy it significantly reduces the time required to compute boiling heat transfer parameters. Nomenclature
thermal diffusivity specific heat this technique is subject to the limitations imposed on the corproportionality constant relation it represents. Typical limitations are clean commerlatent heat of vaporization cially finished heating surfaces, wetting fluids, etc. conversion factor (778 lb,f-ft./B, t .u .) The Engleberg-Forster and Grief correlation is used in the thermal conductivity reduced pressure present work because it is reported (7,3)to predict boiling heat fully developed nucleate boiling heat flux transfer for a number of fluids reasonably well. Should one, saturation temperature however, have a preference for some other nucleate boiling heat wall temperature transfer correlation such as given by Rohsenow (3),KutateTw - Tsat volume of saturated vapor minus volume of saturated ladze [reported in (41, etc., the above procedure should be liquid readily adaptable. viscosity Table I1 lists values of (4Tsj’d&)ref for 16 fluids. The density surface tension ratio ( A T s / d Z ) / ( 4 T s / d & & for only eight has been evaluated over the complete pressure range, but it is anticipated Literature Cited that the remaining fluids also obey the correspondence prin(1) Engelberg-Forster, K., Grief, R., J. Heat Transfer, Trans. ciple. Values of ( A T s / d z ) r e ffor fluids other than those ASME, Ser. C, 81,43-53 (1959). listed can be accumulated as needed by evaluating the right(2) Perry, R. H., Chilton, C. H., Kirkpatrick, S. C., “Chemical hand side of Equation 1 at P, = 0.05. Engineer’s Handbook,” 4th ed., McGraw-Hill, New York, i*I-.,. wn The following example illustrates the use of Figure 1 and (3) Rohsenow, W. M., Trans. ASME 74,969-75 (1952). Table I1 in solving a physical problem. Consider a heat flux (4) Seader, J. D., Miller, W. S., Kalvinskas, L. A., Natl. Aeronaut. of 10,000 B.t.u./hr. sq. ft. from a solid commercial surface to Space Admin., Rept. NASA CR-243 (1964). Freon-1 2 a t atmospheric pressure where the temperature of the RECEIVED for review August 29, 1966 surface is to be computed. ACCEPTED January 17,1967 One atmosphere is equivalent to a reduced pressure of 0.025; Research sponsored by the Arnold Engineering Development hence, from Figure 1, ( A T s / d ~ ~ ) / ( 4 T s / = d 1.2, ~ ) ~ ~ ~Center (AEDC) Air Force Systems Command (AFSC) under Contract AF 40(600)-1200 with ARO, Inc. (subcontract 67-17and from Table I1 (AT,/dB/A),,t = 0.114. The product of TS/OMD).
VOL. 6 NO. 3
JULY 1967
347
