**15.
****Narrative on the lecture Professor Graham B. Wallis
invited me to give in 1965, and the errors and lack of attribution in his
publications on thermal stability.**

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·
**Overview**

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·
**The lecture I gave on July 9, 1965 at Dartmouth. **

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My
correspondence with Professor Wallis began with my letter to him dated October
28, 1963. I had read one of
his articles on two phase flow and boiling, and I was so impressed by the
article that I felt moved to tell him that it was “*by far the most lucid and
straightforward article I have encountered . . .*” He replied in a letter dated November 21, 1963,
after which we corresponded several times.

In 1965, in response to my request, and on the basis of correspondence in which I presented unpublished, original work on thermal stability, Professor Wallis’ letter of June 30, 1965 invited me to lecture at his summer course on two phase heat and fluid flow. The lecture took place at Dartmouth on July 9, 1965.

Several
weeks after the lecture, Professor Wallis sent a letter to *Nucleonics* in
which he used (*without attribution*) original, unpublished material from
my letters and lecture, and expressed his agreement with my *Nucleonics *article. His letter was published in the October 1965
issue of *Nucleonics* under the title “A Vote for Adiutori”.

Professor
Wallis’ letter of July 8, 1966 enclosed the thermal stability
section of his notes for his 1966 summer course on two phase heat and fluid
flow. In the notes, he derived a
thermal stability criterion for a specific boiler type starting from the
general criterion in my *Nucleonics* article. An error in his derivation resulted in an erroneous criterion
that failed to account for the effect of the boiler plate on thermal stability.

In the Hale and Wallis article published in 1972, the above erroneous derivation is repeated, the error in the resultant criterion is recognized and described, and the error is erroneously attributed to a lack of rigor in the general criterion. The article then presents an alternative derivation that results in Criterion (24), the correct criterion for the subject boiler type. Criterion (24):

· Is
*identical* to Criterion (6) in my letter to Professor Wallis
dated June 14, 1965.

· Was presented in my lecture at Professor Wallis’ summer course on July 9, 1965, and its application to Berenson’s boiler and results was discussed.

· Was
the criterion Professor Wallis used to prepare his “A Vote for Adiutori” submitted to *Nucleonics* on or
about July 27, 1965, and published in its October, 1965 issue.

To my
surprise and dismay, the Hale and Wallis article contained *no attribution*
to my letter or my lecture.

The article also states

*The limitations imposed on Berenson’s data by the high wall
resistance were first discussed by Wallis in his *(“A Vote for Adiutori”) *comments on Audiutori’s (sic)
original paper. *

The above
statement is in error. It should state
that the limitations imposed on Berenson’s data by the high wall resistance
were first publicly discussed by me in ”Author’s reply” published in
the December, 1964 issue of *Nucleonics*, and privately in my letter
to Professor Wallis dated June 14, 1965, and in my lecture given on July 9, 1965 at Professor Wallis’ summer
course on two phase flow and heat transfer.

In my letter to the editor of *I & EC Fundamentals* dated August
18, 1972, I requested that he publish my “letter to the editor” that
corrected errors and described the lack of attribution in the article by Hale
and Wallis. Predictably, the editor saw
no need to publish such a letter.

**Correspondence that
resulted in an invitation from Professor Wallis to
lecture at his summer course on two phase flow and heat transfer held at
Dartmouth College.**

In May of 1965, I received a flyer from Professor Wallis announcing a two week summer course on two phase heat and fluid flow to be given at Dartmouth by Professor Wallis, Novak Zuber, and John Collier. My letter to him dated May 21, 1965 indicated that I did not wish to enroll in his course, and made the following offer:

*Some time near the end of the two weeks, I would be pleased
to present one or two one hour lectures dealing with the results of my
conceptual research on two-phase heat and mass transfer. . . . (I) offer to
present the lectures without fee and at my own expense.*

The reason
I offered to lecture “*without fee and at my own expense*” is because I
had tried to present and publish the application of the theory presented in my *Nucleonics*
article, but had been prevented from doing so by reviewers and editors who (I
feel) rejected my work because they correctly sensed that it was revolutionary,
and that I was not a member of the club.
As a result, I was extremely anxious to present the results of my work
to an audience competent in two phase heat and fluid flow, such as persons who
had completed Professor Wallis’ course.

Professor Wallis’ reply dated June 9, 1965 stated:

*There is a possibility that we might fit you in as a
“special topic” on the last day of the course.
Before deciding one way or another, I will need to consult with Collier
and Zuber about the amount of time they may be able to give up to make room for
you. Also, as I am not familiar with
your work, I find it hard to find a basis for a rational decision. Perhaps you can
supply me with more evidence which will convince me. I will try to be quite objective and not be
influenced either by your own opinion of your work or the opinions of those who
have resisted its acceptance.*

My
letter to Professor Wallis dated June 14, 1965 was my response to “*supply
me with* *more evidence which will convince me*”. The letter presents my view on the
relationship between heat flux and interface temperature difference in nucleate
boiling, and applies the thermal stability theory presented in my *Nucleonics *article to the boiler used in “Experiments on Pool-Boiling Heat Transfer” by P. J. Berenson, *Int J
Heat Mass Transfer*, v 5, pp 985-999, 1962. The letter gives the general criterion for
thermal stability, and then states:

*For a boiler such as Berenson used for his thesis, this
general form may be reworked into the particular form*

* *

* -(1/h _{s} + t_{w}/k_{w})^{-1}
<s dq/dT_{w} (6)*

* *

*where the right hand side of equation (6) of course refers
to the slope of the pool boiling curve.
From this criterion, it may easily be seen that:*

* *

*1.
**The statement that such a boiler is necessarily stable
at all points of the pool boiling curve is simply not true.*

* *

*2.
**The stability of such a boiler can be improved markedly
by simply increasing the steam side coefficient, decreasing
the thickness of the wall, or increasing the thermal conductivity of the
wall. . . . (Berenson) intentionally made the boiler plate very thick in spite of the fact
that he wanted the boiler to be as stable as possible since his thesis subject
was transition boiling.*

It is important to note that although Criterion (6) is quite simple, it was original. It was the result of the first application of my theory of thermal stability—the first thermal stability criterion derived for a specific type boiler. Nothing like it had ever appeared in the literature, although I had tried unsuccessfully to arrange its publication.

Professor Wallis’ letter of June 30, 1965 stated:

*Thank you for your letter of June 14 ^{th}.*

* *

*I would be glad to have you give a lecture on July 9 ^{th}
in the afternoon on a subject of your choice. . . . *

* *

*. . . I agree with your analysis and comments on Berenson’s
work which seems quite obvious once you have pointed it
out.*

Berenson’s article was derived from the Sc. D. thesis he submitted in 1960 at MIT. The thesis adviser was Professor Peter Griffith. The first sentence of the thesis abstract states:

*An experiment, utilizing a condensing fluid as the heat
source, was performed to determine the heat flux vs. temperature difference
curve for transition pool boiling from a horizontal surface.*

(Compare
Professor Wallis’ “*seems quite obvious once you have pointed it out*”
with the Argonne comment “*The most consistent fundamental
error throughout the paper treats temperature as an independent variable*”. In other words, the Argonne critics
considered it irrational to take derivatives with respect to temperature
because temperature is not an independent variable. Therefore, in their view, the “obvious” Eq. (6) was irrational
and of no use.)

**The lecture
I gave on July 9, 1965 at Dartmouth. **

My lecture
at Dartmouth on July 9^{th} is described in my lecture notes. The
first part of the notes is in the form of a manuscript. The second part of the notes is in the form
of an outline.

The lecture began with a review of the conventional view of thermal stability, and a description of what is wrong with the conventional view. The general criterion for thermal stability is given without derivation in the form

dQ_{in}/dT_{w} <s dQ_{out}/dT_{w}

in which Q is heat flow rate (not heat flux). (I usually express the general criterion in terms of heat flux rather than heat flow rate. In this case, I used heat flow rate because I feel that the criterion is easier to comprehend if it is first presented in terms of heat flow rate rather than heat flux.)

The notes state:

*The criterion results from idealizing a generalized system
and uncoupling it at the boiling interface. The uncoupled pieces are then analyzed to determine whether they
would fit together in a stable manner.
The derivative on the left hand side . . . answers the question “How is
the heat flow into the boiling interface affected by the temperature of the
interface?” The right hand side . . .
answers the question “How is the heat flow out of the boiling interface
affected by the temperature of the interface?”*

A boiler of the type used by Berenson is described, and its stability analysis is described analytically and graphically. It is shown that, for such a boiler,

*dQ _{in}/dT_{w} =
-A/(1/h_{s} + t/k)*

where A is the area of the boiler plate. Thus the stability criterion for this boiler type is given by

*-A/(1/h _{s}
+ t/k) <*

Berenson’s transition region article is discussed, and the lack of transition region data noted in the following:

*If you will plot up some of (Berenson’s) data on linear
graph paper, you will find that, in 17 of the 20 experiments, virtually no data
was obtained in the transition region, in agreement with the new theory of
thermal stability.*

With regard to the design of a boiler such as the one used by Berenson, the notes state:

*. . . the designer can exert a very strong influence on the
thermal stability of the boiler in any of the following simple ways:*

* *

*1.
**Minimize the thickness of the boilerplate*

*2.
**Maximize the thermal conductivity of the boiler plate.*

* 3. Maximize the heat transfer coefficient of
the fluid condensing on the heat source side of the boiler plate.*

* *

The phenomenon of burnout (ie a large increase in temperature resulting from an incremental increase in heat flux) in so-called constant heat flux systems such as nuclear reactors and electrically heated boilers was discussed, and it was pointed out that burnout does not necessarily result in such systems. For example, if the temperature coefficient of reactivity of a nuclear reactor were sufficiently negative, the stability criterion would be satisfied at all values of the boiling interface temperature, and there would be no burnout.

The manner in which thermal instability can result in undamped, oscillatory behavior was described.

The so-called dry wall phenomenon was discussed, and it was suggested that it is thermally induced rather than hydraulically induced.

Hydraulic stability and its resemblance to thermal stability were discussed.

I thoroughly enjoyed giving the lecture, and sensed that it was well received. I was particularly honored by John Collier’s request for my autograph.

** **

** **

**Professor
Wallis’ letter to Nucleonics published in the
October, 1965 issue under the title “A Vote for Adiutori”. **

Several
weeks after my lecture, I received a letter from Professor Wallis
dated July 27, 1965 in which was enclosed a copy of a “letter to the
editor” he had sent to *Nucleonics. *The
“letter to the editor” had obviously been prepared using (*without
attribution*) original, unpublished material on thermal stability from my
letters to Professor Wallis and my lecture of July 9, 1965. The “letter to the editor” discussed
Berenson’s boiler and results, and expressed agreement with my *Nucleonics *article. It was published in the October 1965 issue
of *Nucleonics* under the title “A Vote for Adiutori”.

I was dismayed that Professor Wallis’ “letter to the editor” did not state that it was based on the original, unpublished stability criterion in my letter to Professor Wallis dated June 14, 1965, and that I had discussed its application to Berenson’s boiler in the lecture I gave at his summer course on July 9, 1965. However, I was so elated that Professor Wallis had had the courage to publicly endorse my work that I made no effort to have the lack of attribution corrected.

I certainly
did not anticipate that Professor Wallis would one day present my Criterion (6)
as his own original work, or that he would credit himself with being the first
to consider the effect of boiler plate thickness on thermal stability, both of
which he did in Thermal Stability of Surfaces Heated by Convection and
Cooled by Boiling by Hale and Wallis, *I & EC Fundamentals*,
Vol. 11, No. 1, 1972.

**The fundamental error in Professor Wallis’ notes for his 1966
summer course on two phase flow and heat transfer.**

Professor Wallis’ letter of July 8, 1966 enclosed the section dealing with thermal stability in his lecture notes for his 1966 summer course on two phase heat and fluid transfer. At that time, I briefly perused the material, then filed it.

In
preparing this narrative, I examined the subject lecture notes more carefully,
and was amazed to find the following in Section 14.6.5 entitled “Pool Boiling From a SurfaceWhich
is Heated by Convection (Perhaps Condensation) from a Fluid at Constant
Temperature T_{1}”, the boiler type used by Berenson.

*The stability criterion now becomes *

* *

* -h _{1} – m_{b} < 0 (14.108)*

* *

*Thus a negative value of m _{b} can be counteracted
by having a suitably large heat transfer coefficient h_{1}. This was used experimentally by Berenson^{15}
and Owens^{29}.*

(m_{b}
is the slope of the boiling curve—ie is the slope of a curve of heat flux
versus the temperature difference at the boiling interface.)

Criterion
(14.108) states that, for the subject boiler type, the boiler plate has *no
effect* on thermal stability. This
violently disagrees with my “Author’s Reply” in the
December, 1964 issue of *Nucleonics*, my letter to
Professor Wallis dated June 14, 1965, and my lecture at
Professor Wallis’ summer course.
Criterion (14.108) also disagrees with the criterion that underlies
Professor Wallis’ “A Vote for Adiutori” published in the
October, 1965 issue of *Nucleonics*!

The correct expression of Wallis’ incorrect Criterion (14.108) is Criterion (6) in my letter to Professor Wallis dated June 14, 1965.

**The errors and lack of attribution in the article on thermal stability by Hale and Wallis published in I
& EC Fundamentals in 1972.**

The article by Hale and Wallis claims to demonstrate that

*dq _{in}/dT_{w}
< dq_{out}/dT_{w} (1)*

*. . . eq 1*
(the general criterion for thermal stability presented in my *Nucleonics*
article) . . . *is valid only if the thermal resistance of the wall is
neglected.*

This statement is simply *not true*. What the article by Hale and Wallis actually
demonstrates is that if the derivatives in Criterion (1) are not evaluated
correctly, the result will be a criterion that is incorrect.

The correct evaluation of the derivatives in Criterion (1) is quite simple. It requires only that both derivatives be evaluated at the boiling interface. (Note that I covered this on page 8 of my lecture notes for Wallis’ 1965 summer course.)

Hale and Wallis evaluated one of the derivatives in Criterion (1) at the boiling interface, and evaluated the other derivative at the opposite interface. Of course the result they obtained was incorrect. They erroneously concluded that Criterion (1) is incorrect, but they should have concluded that their analysis was incorrect.

The article by Hale and Wallis states that, for a convectively heated wall, Eq. 1 results in the stability criterion

*h _{in}
> - dq_{out}/dT_{w} (5)*

* *

The article also states

*Wallis and
Collier (1967) applied eq 1 to several different design situations . . .*

In other words, in the notes for
their 1967 summer course at Stanford, Wallis and Collier appraised the
stability of convectively heated boilers using Criterion (5), a criterion that
erroneously indicates the boiler plate has *no effect* on thermal
stability. This same erroneous
criterion had previously been presented in Professor Wallis’ notes for his 1966
summer course.

The article indicates that, sometime
between 1967 and 1972, Hale and Wallis deduced that Eq. (1) was incorrect. They then deduced alternative methodology
that resulted in their Criterion (24) which states that the boiler plate has a *strong
effect* on stability.

Criterion (24) in Hale and Wallis is *identical
*to Criterion (6) in my letter to Professor Wallis dated June
14, 1965. Criterion (24) is
presented as original work by Hale and Wallis, and there is no attribution to
my letter to Professor Wallis, or to my lecture at Professor Wallis’ summer course
in 1965.

Amazingly, the article also states

*Criterion (24)
was used by Wallis (1965) in analyzing Berenson’s data.*

This statement is amazing because it raises the questions:

· How could Professor Wallis deduce Criterion (24) in 1965, when he could not do so in 1966 or 1967?

· If Criterion (24) cannot be deduced from Criterion (1) as Hale and Wallis claim, how did Professor Wallis determine it in 1965?

The Hale and Wallis article also states:

*The limitations imposed on Berenson’s data by the high wall
resistance were first discussed by Wallis in his comments on Audiutori’s (sic)
original paper. *( Wallis’ comments were published under the title “A Vote for Adiutori” in the October, 1965 issue of *Nucleonics*).

The above
statement is not true. The truth is
that the limitations imposed on Berenson’s data by the high wall resistance
were first discussed publically by me in “Author’s Reply” in the
December, 1964 issue of *Nucleonics*, and privately in my letter
to Professor Wallis dated June 14, 1965, and in my lecture given on July 9, 1965 at Professor Wallis’ summer
course on two phase flow and heat transfer.

(Limitations
on Berenson’s data were also discussed in my manuscript entitled “Transition
Boiling—the Relationship Between Heat Flux and Thermal Driving Force” submitted
for publication to the *AIChE Journal* on March 19, 1964, and rejected on
May 5, 1964.)

The first public discussion of “the limitations imposed on Berenson’s data by the high wall resistance”.

The first public discussion of “the limitations imposed on
Berenson’s data by the high wall resistance” is the following from my “Author’s Reply” published in the letters section of the December, 1964
issue of *Nucleonics*:

*. . . Rohsenow states on p. 138 of *(*Modern
Developments in Heat Transfer, *W. Ibele, ed. (1963*): “With condensing vapor as the heat source on
one side of a wall, any point on the entire (pool boiling) curve can be reached
under stable conditions.” My concept of
thermal stability demonstrates that this conclusion is wrong and the
experiments by Berensen (sic) (“Transition boiling heat transfer from a
horizontal surface, Sc.D. thesis, MIT, [1960]; also Int. J. Heat Mass Transfer,
5, 985-999 [1962]) proved it, although apparently neither Berensen nor Rohsenow
realized it.*

* *

*In his experiments, Berensen built just such a boiler as
described above, and he reported the results of 20 experiments, each of which
purports to cover the entire pool boiling curve. If the reader will plot Berensen’s results on LINEAR graph paper,
he will find that there is essentially NO data in the so-called transition
region for 17 of the 20 experiments.
The reason for this predominant lack of data was that his boiler was
usually NOT thermally stable in the transition region. The fact that this was not recognized is
doubly important for the following reasons:*

* *

*1.
**Since nothing was known about thermal stability at that
time, Berensen understandably did not look for thermal instability, and as a
result he did not report it, even though it was there.*

* *

*2.
**Owing to a lack of understanding of thermal stability,
Berensen correlated the transition region “results” of the 17 experiments which
contained no such data! The three
experiments which contained the desired data did not “agree” with the majority
and were therefore treated as oddballs!*

* *

*3.
**Since nothing was known about thermal stability at that
time, Berensen understandably did not design his boiler with thermal stability
in mind. As a result, he INTENTIONALLY
built in a very thick boiler plate, virtually guaranteeing that he would not
get the desired data.*

Berenson made the boiler plate very thick (2.25 inches) in order to improve the accuracy of the heat flux results which were based on data from thermocouples imbedded in the boiler plate. Berenson’s results were presented on log log paper, and this obscured the fact that very little data had been obtained in the transition region. If the results had been plotted on linear paper, the lack of transition region data would have been readily apparent.

**My unsuccessful attempt to
correct the errors and cite the proper attribution in the article by Hale and Wallis.**

In a letter dated August 18, 1972
to the editor of *I & EC Fundamentals*, I requested that he publish my
“Letter to the Editor” that corrected errors in the Hale and Wallis article,
and cited the lack of proper attribution.

Predictably, the editor (Professor Pigford) saw no need to publish such a letter.

**Closing****
remarks**

When I read the article by Hale and Wallis, I was dismayed and resentful because:

· The stability criterion that was the main thrust of the article was my original work.

· I had been unable to arrange for the publication of the stability criterion.

· It was my guess that Hale and Wallis had no difficulty arranging for the publication of my criterion.

My response to the criticism
by the Argonne Seven and other critics, published in the December,
1964 issue of *Nucleonics*, closed with the following prophetic statement:

*That my concept
of thermal stability has not emanated from the universities or the national
laboratories is perhaps regrettable.
However, it is no less true that it represents new knowledge to the
science of heat transfer. It is now
incumbent on the universities and those who control the scientific literature
to see to it that this new knowledge is not wasted—and to make it possible for
me to publish my work in a less brief and more satisfactory manner. Whether they shall prove equal to the task
is a matter for their conscience—not mine.*

Persons who control the American
scientific literature have done nothing to make it possible for me to publish
my work in a less brief and more satisfactory manner. In fact, they have made it so difficult that, in spite of my many
attempts to arrange for the publication of my work in American Journals, *none
of my work has ever been published in an American peer reviewed Journal*.

In 1964, one of my articles was
accepted for publication in an American peer reviewed Journal (the *AIChE
Journal*), but it was *never *published there because a member of the
club (to whom I had naively mentioned the article) pressured the editor to
“unaccept” it prior to publication.
(The editor of the Journal, Professor Harding Bliss of Yale University,
told me it was the only article ever accepted for publication in the *AIChE
Journal*, and then not published.)
The article was finally published in a Japanese Journal *thirty years
after it was accepted for publication in the AIChE Journal*! And it was just as timely and important in
1994 as it had been in 1964!

The article was A
Critical Examination of the View that Nucleate Boiling Heat Transfer Data
Exhibit Power Law Behavior, *Japanese Society of Mechanical
Engineers International Journal*, Series B, Vol. 37, No. 2, 1994, pp
394-402.

The background on my
accepted-but-not-published article is related in Narrative on my 1964 paper accepted
for publication in the *AIChE Journal*, but never published there.

The fact
that researchers at MIT, a world class engineering school, did not know how to
optimize the design of an experimental boiler to operate stably in the
transition region was eloquent testimony to the originality of my *Nucleonics*
article. The fact that Berenson’s
boiler was unable to operate stably throughout most of the transition regions
tested is eloquent testimony to the validity of my view of thermal stability in
general, and the validity of my general criterion for thermal stability in
particular. Unfortunately, the originality
and validity of my work has served only to unite peer reviewers and journal
editors against its publication.