## Introduction

This discussion responds to the recently published commentary presented by Webb 1 in this journal. Several simple, but important misrepresentations were made in his commentary about the flow pattern/flow structure flow boiling model of Kattan et al. 2,3,4 and all *four* other prediction methods 5,6,7,8 he discusses, creating confusion in the state-of-the-art and perpetuating his misconceptions about these flow boiling models. In fact, it is quite surprising that his comments about the paper by Kattan et al. 2,3,4 survived a peer review, given that they received the ASME 1998 Heat Transfer Division Best Paper Award for their work. While it is essential to expose new methods to critical and objective examination, on the other hand purposely incorrect or uninformed comments are not appropriate and hence that is what I would like to set straight below for the heat transfer community.

## Correct Heat Flux to be Used in Flow Boiling Correlations

Regarding 1, Webb’s thesis is that in a flow boiling model describing intube evaporation, the nucleate boiling contribution (through the nucleate boiling heat transfer coefficient) should be calculated in a nucleate boiling correlation using the residual heat flux, that is the total heat flux at the wall minus that taken away by the two-phase convection or the so called convective boiling heat flux. He refers to several published sets of flow boiling data measured under nucleate boiling dominated conditions and under convective boiling dominated conditions as his proof for this thesis. Clearly, for nucleate boiling dominated test conditions, the nucleate boiling mechanism dominates and hence the total heat flux can be used for calculating the nucleate boiling heat transfer coefficient since the convective boiling heat flux is negligible. Furthermore, it is self evident that for convective boiling dominated test conditions, it does not make much difference what heat flux is used to calculate the nucleate boiling heat transfer coefficient, since it is in any case negligible. Between these two extremes, neither mechanism is dominant. Following the asymptotic approach widely and successfully employed by Churchill and others in numerous single and two-phase processes, each heat transfer coefficient of the contending mechanisms is calculated separately at the local conditions (that is, at the local total heat flux in the present case for nucleate boiling) and are then combined together using an asymptotic law with a selected exponent. It should be noted that the asymptotic approach is itself empirically based and experience shows that it works well. This asymptotic approach is in fact what Steiner and Taborek 8 applied so nicely in the flow boiling method they presented for vertical tubes, evaluating a very large, diversified database and finding the best exponent for their asymptotic model to be 3. However, they did not calculate their nucleate boiling heat transfer coefficient based on $Tw-Tsat$ nor based on the residual heat flux, which is what Webb claims to support his thesis. In fact, Steiner and Taborek used the total heat flux just like in the other methods 4,5,6,7,8 enounced by Webb. This fact is evident by simply referring to their example calculation presented in 8 where the local design heat flux of 60 kW/m^{2} is directly input to their nucleate boiling correlation or to their Eq. (3*a*), defining their flow boiling heat transfer coefficient obtained from their asymptotic equation. Secondly, Steiner and Taborek did not use the Gorenflo 9 nucleate pool boiling correlation as Webb incorrectly claims. In fact, they used a Gorenflo-like nucleate pool boiling correlation of their own, something they stated quite clearly to avoid confusion, that used different standard reference conditions, different standard heat transfer coefficients and an additional residual correction factor based on the molecular weight of the fluid; refer to Chapters 4 and 7 (and Tables 4.3 and 7.5) in Collier and Thome 10 to see the two different sets of tabular values, conditions and methods. Hence, Webb misrepresents simple facts in the literature to try to support his residual heat flux thesis.

Proceeding to a physical view point of the situation at flow boiling conditions with significant contributions of both nucleate boiling and convective boiling, the surface of the tube must be covered by a layer of closely packed growing and departing bubbles. Hence, all the heat flux must first pass from the heated wall through this “nucleate boiling layer” of bubbles attached to the heated wall, where some of it is converted to latent heat, and the remaining heat flux flows out towards the vapor-liquid interface where convective evaporation converts liquid into vapor. Hence, the nucleate boiling process sees the total heat flux, not the *residual* heat flux. It is not physically clear how the convective boiling heat flux could circumvent the nucleate boiling layer on the wall packed with bubbles, which is Webb’s thesis, without first being made available to the nucleate boiling process. This physical situation is also similar to the nucleate pool boiling process taking place in an otherwise stagnant pool, where only a fraction of the heat is absorbed by the bubbles at the surface and the rest departs in the rising superheated liquid; here, again, the total heat flux is used to calculate the local nucleate boiling heat transfer coefficient, not the residual latent heat flux. In contrast, Webb presented no physical interpretation of this process to support his thesis.

## Literature Ignored in Commentary

In an additional attempt to support his thesis and discredit a flow boiling model counter to it, Webb states that “the Kattan et al. correlation was based on a small refrigerant data base.” In their original three-part publication, 702 flow pattern observation data points were obtained in 2 while 1141 flow boiling heat transfer coefficients were reported in 3 and used in the Kattan et al. heat transfer model in 4. Their database covered five refrigerants (R-134a, R-123, R-502, R-402A, and R-404A) and a wide range of mass velocities (100–500 kg/m^{2}s), pressures (1–9 bar) and vapor qualities (0.15–0.98), in particular with numerous data at high vapor qualities and in stratified-wavy flow that are the most difficult to predict. In citing this work for an award, the ASME Heat Transfer Division must have considered this to be an exemplary database. Relative to state-of-the-art in 2002 when writing his comments, Webb also ignored numerous new additions to the database, appearing after peer review in widely cited journals. For example, in 1998 in 11 the database was extended to include R-407C with its mixture effects, additional R-134a data, and even to refrigerant-oil mixtures up to 50 percent wt percent oil (achieved by only introducing the local liquid viscosity of the refrigerant-oil mixture into the model without any changes to the heat transfer equations). In 1999 in the *J. Heat Transfer*, Zu¨rcher et al. 12 presented a large new heat transfer database for evaporation of ammonia in a stainless steel tube at numerous mass velocities and showed the same heat transfer model still worked without change, only making minor fixes to the flow pattern map using the new database that went to very low mass velocities (down to 20 kg/m^{2} s), along with a largely successful comparison to an older, independent ammonia database. In 2000, Zu¨rcher et al. 13 presented a new general version of the Steiner-Taborek onset of nucleate boiling criterion to use in their model to distinguish the heat flux threshold at which nucleate boiling ceases to occur, extending the ammonia heat transfer database to 11 mass velocities to look also at the flow transition effects. In an independent study in 2001 in another widely read journal, Kabelec and de Buhr 14 found that their ammonia flow boiling data agreed quite well with the Kattan et al. heat transfer model. In early 2002, Zu¨rcher et al. 15,16 presented new developments on the flow pattern map and heat transfer model. Hence, the original “small refrigerant database” that by the year 1999 included seven fluids plus refrigerant-oil mixtures is actually a huge database, all gone missing in his commentary in 2002. It is true, and we have stated this, that for the most part we have avoided including other flow boiling data measured using electrically heated tubes, which we do not think are appropriate for stratified types of flows.

More recently, R-22 and R-410A have also been added to the database behind this method in 17 and also the maverick fluid $CO2$ over a very wide range of reduced pressures 18, i.e., currently a total of 10 fluids plus oil mixtures. We have also recently submitted for review a two-part paper in which we compare the void fraction model we use in our heat transfer model and flow pattern map to about 250 time-averaged void fraction measurements (very good results) based on processing 227,000 dynamic void fraction images using a new measurement technique, images now being newly processed to provide experimental data on the dry angle around the upper tube perimeter in stratified-wavy flows. Furthermore, our sister method for in tube condensation, based on the same basic approach used in our flow boiling model, has recently been completed, covering a database of 15 fluids from 9 independent laboratories 19,20, and captures 85 percent of the heat transfer data to within ±20 percent.

In summary, this two-phase flow pattern, simplified two-phase flow structure approach has shown promise over the years and, being realistic, has the potential to continue to evolve and improve to attain higher accuracies and reliability as we and others learn more about the influence of two-phase flows on flow boiling heat transfer. This flow pattern/flow structure type of heat transfer model so far appears to be a sound, unified approach to predict local two-phase heat transfer coefficients for both evaporation and condensation that also correctly captures the trends in the data quite well too. Notably, our two-phase flow pattern, simplified two-phase flow structure papers reflect an attentive reading and referencing of the state-of-the-art in heat transfer and two-phase flow published by others.

Professor, Laboratory of Heat and Mass Transfer, Faculty of Engineering Science and Technology, Swiss Federal Institute of Technology Lausanne, CH-1015 Lausanne, Switzerland. E-mail: john.thome@epfl.ch

*Multiphase Transport and Particulate Phenomena*, T. Nejat Veziroglu, ed., Hemisphere Publishing Co., New York,

**1**, pp. 419–432.

*VDI Wa¨rmeatlas*, Section Ha, VDI Verlag, Du¨sseldorf, (English ed.).

*Convective Boiling and Condensation*, Oxford University Press, Oxford, England.

*Int. Congress of Refrigeration*, Washington, D.C., August.

**26**in press.