Int. J . Heat Ma ss Transfer. Vol. 25, No. 6, pp 771-779,1982 0017-9310/82/060771-09 $03.00/0 Printed in Great Britain © 1982 Pergamon Ptess Ltd. ON THE EXISTENCE OF TWO 'TRANSITION' BOILING CURVES L. C. WITTE and J. H. LIENHARD Heat Transfer and Phase-Change Laboratory, Mechanical Engineering Department, University of Houston, Houston, TX 77004, U.S.A. (Re ceived 18 September 1981) Abstract-The idea that there are two 'transition' boiling curves accessible to a given liquid boiling on a given surface, is advanced. A variety of saturated, subcooled, pool, and flow boiling data are shown to be consistent with, and explainable in terms of, the idea. Some of the data are hitherto unpublished results. The two boiling curves are extensions of the nucleate and film boiling curves, and they are related to nucleate and film boiling phenomenologically. NOMENCLATURE a given boiled liquid on a given surface. We shall also specific heat at constant pressure; show how the two curves serve to explain some of the latent heat of vaporization; seemingly anomalous behavior we have witnessed in the past. Jakob number, PrCp(Tliquid - Tsa,)JPghrg; j, probability of nucleation in a molecular collision ; T, temperature; THE TWO- URVE PH YSICAL MODEL I'lT, Tw - T sa,; q, heat flux. We first present our conceptual model without rationalization or justification. We then otTer the Subscripts evidence for the model. The two curves in Fig. are simply labeled nucleate w, wall; 1 sat, saturation; andfilm boiling. As the heat flux is increased, in the conventional nucleate boiling regime, to a value be­ hn, homogeneous nucleation; yond the hydrodynamic peak, qm." the collapse of the liquid, liquid bulk; vapor escape path will be catastrophic. On the other max, peak nucleate boiling q ; hand, if I'l T is increased independently, the vapor min, minimum film boiling q. removal path is observed to change in a continuous manner. Therefore the 'jets-and-columns' mechanism INTRODUCTION should not disappear all at once. TRADITION has it that the heat flux, q, is a single valued There will instead be an increase in the number of function of the liquid superheat, I'l T , during boiling­ nucleation sites and an increased tendency to separate particularly during saturated pool boiling. However, a the liquid from the surface, just beyond the peak of the great accumulation of evidence forces us to the con­ curve. As the surface grows hotter, the duration of viction that there are two boiling curves that typically liquid contact will be reduced. When liquid moves into relate to one another as shown in Fig. 1. These curves a dry patch, heavy nucleation will tend to blow it away change in different ways as system variables are quickly. The hydrodynamic 'jets-and-columns' me­ altered. Together they form the various continuous chanism is still admissible because the vapor pro­ represen tations that have been advanced as 'the boiling duction is below the critical value, but the disruptive curve'. situation at the surface leads more and more to Nukiyama's independent q experiments [IJ re­ oscillating liquid contact-to batchwise explosions of quired that he terminate his nucleate and film boiling vapor into the liquid bulk. curves at the extreme heat fluxes, qm., and qmin' He The film boiling curve is also extended (to the left) speculated that these extrema would be connected by a beyond its conventional hydrodynamic limit. The single line element if I'lT could be varied indepen­ minimum heat flux in this curve, qmin' is the value at dently. Three years later, Drew and Mueller [2J which vapor is no longer generated rapidly enough to obtained a few data that suggested Nukiyama was keep the film from falling into the heater. When q is correct, and the notion of a single boiling curve was varied independen tly and reduced below qmin' film solidified. boiling collapses catastrophically into nucleate boil­ The objective of this paper is to show how the ing. Bu t when I'l Tis independen tly reduced beyond the massive intervening accumulation ofdata suggests that minimum, change is almost imperceptible as long as there are, in fact, two q vs I'l T relationships available to the system continues to change along the film boiling 771 772 L. C. WITTE and 1. H. LIENHARD qmax _____~~---;,...---- nucleate boiling from left accessible from right L film boiling ~~---=-==- (system thermal resist)-I FIG. 1. The two boiling curves. The 'transition region' denotes all states between the local maximum and the local minimum-wherever they occur. curve. There is some liq uid-solid contact to the left of with these photographs is that they can only approxi­ the minimum, and even the slightest contact will lead mately be related to a boiling curve for lack of actual to substantial increases in the rate of the generation of surface temperature data. vapor. Thus q begins to rise. The basic film boiling We turn next to Berenson's 'infinite' flat plate data process is preserved in this region; however, it is [4J, which include surface temperature data and increasingly augmented by instances of liquid-solid represen t very close con trol of a variety of surface contact. conditions. Figure 2 shows data for six of Berenson's The reader will note that we have not used the term surfaces on linear q vs !:lT coordinates. 'transi tion boiling', and we suggest that region ough t Berenson's system for regulating!:l T independently to be viewed as an ex tension of either film boiling or had an important weakness that was brought to light nucleate boiling. Drew and Mueller simply identified in other systems by Stefan and Kovlev and by Grass­ the region as a part of the film boiling regime and did man and Ziegler during thela_tter 1960s (see discussion not use the word 'transition'. Later such terms as by Hesse [5J). Berenson heated the lower side of a 'partial' or 'unstable' film boiling were first introduced, copper block, which was heavily finned, with condens­ and then dropped, in favor of the term 'transition' that ing steam. He boiled more volatile fluids on the did not commit anyone to a hypothetical mechanism. top of the block. The block placed a thermal resis­ For the sake of clarity we shall speak of transitional tance equal to (block thickness/conductivity) = nucleate, and transitional film boiling to distinguish 0.OOO860ft 2 hOF Btu-I, o r 0.0001514 m 2 °C W-l, be­ the two curves. tween the condensing steam and the surface. Accord­ We now turn our attention to two aspects of ingly, if the line: verification of the mechanism: Observations of the two (Tcond st m - T ,a.) - !:IT mechanisms, and demonstration of ways in which (1) given systems elect one or the other of the two q = 0.00086 processes. expressed in the units of Btu, ft , h, and OF, should happen to intersect the boiling curve in more than one point, then on ly one poin t can be reached in an SOME OBSERVATIONS IN SATURATED experiment. If the system is initially in film boiling, POOL BOIU G then reduction of the condensing steam temperature The classical photos of transition boiling on tubes will only allow one to observe the lowest curve that can given us by Westwa ter and Santangelo [3J have been be reached along a line of negative slope equal to widely reproduced. They are interesting because they (conductivityJblock thickness). If one starts with the clearly display both mechanisms in the transition system in nucleate boiling then he can only reach the region. Their Fig. 5, showing high-q 'transition' boiling highest curve that such a line intersects. at tlT only a little beyond the peak, reveals a vapor Figure 2 shows three cases (Berenson's Runs No.2, 3 removal mechanism that clearly consists ofjets such as and 4) where certain sta tes are inaccessible, and one those that collapse when q:> qmax' Their Fig. 7, more case (Run N o. 25) where some states might have showing low-q ' transition' boiling, at!:lT about 3/4 of been inaccessible. Runs No.2, 3 and 4 do not reveal the value giving qmin' is indistinguishable from film anything about the existence of the two 'transition' boiling. They also provide a photograph for a state boiling curves hypothesis although they dramatize a between these two pictures. It shows a completely basic limitation of Berenson's system. The reader blanketed, but very ragged, surface in what could be should note that we avoid Berenson's use of logarith­ film boiling with a lot of local con tact. The problem mic coordinates in reproducing these results. On the existence of two 'transition' boiling curves 773 • Run #2 • Run #4 x Run # 3 (rough bUI Clean) (mirror finish) Ihe camplele curve 5 X104 the complete curve is nol accessible is not accessible 00 100 200 100 toT (OF) toT(OF) 200 lOS 1:, x ® Run # S • Run # 7 N ® reported but not (rough, oll.idized, plotted (or mi s­ and not cleaned) ::::: plotted I in [4J .2 CD 5xl04 (rough,O)!'ldized, not clear whether and not cleaned) or not the curves r:r "'Jam ~ >< " .... ".o, . 2 " -.~-...... °0~----~------10~0------~--~-2~0-0-- c; 00 200 toT(OF) toT (OF) .c'" lOS 10 5 Run # 2S(surface rough and clean ~ .. • Run # 8 with traces of oleic acid in liQuid . o Run # 9 Numbers denote sequence af ..~,. (rough, oxidized, observations .) 4 and not cleaned) 5xl0 "~. • afler oleic acid has had 4 " " 0 chance 10 boil away • ........not plotted @ immediately after addition S 4 "\' '"( J of 3 dropS of oleic ocid 2 I °OL------L~~--~L----L------L--- 200 100 200 toT (OF) to T(OF) FIG.