I will always be grateful to Rossi and Wong for encouraging me to learn about heat exchangers. The maths, which I had when young always avoided as being unpleasantly messy, is in fact remarkably beautiful. And the engineering trade-offs behind the device which Rossi told Wong he used are fascinating. It is those, not properly debated anywhere yet, that I thought might be of interest. Academic only, now the Trial is cancelled.

The background (for those new here) is that Rossi needed to find a way to dispose of 1MW of claimed heat from his claimed 1MW power plant in the IH long-term test. Otherwise, IH experts argued convincingly, the factory would have overheated. Rossi and his expert appeared to accept this in depositions. Rossi's expert explained how a heat exchanger no longer present, which Rossi had described to him, would be sufficient to blow 1MW (in fact Wong calculated 1.4MW) of heat out of an upstairs window.

I realise that not everyone here will be as interested in these details as me, but I'm sure some will. For those who just want the conclusions, they are as follows. The first few are old material, recapped here for those new to the story:

- The Wong calculations for heat exchangers depend on the total surface area of tubing, the temperatures of piping (to be cooled) and flow rate of air (doing the cooling) and the
*heat transfer coefficient*(HTC) which shows how effective is the tube surface, on average, at dissipating heat. - Wong uses a fixed HTC which he quotes from a source in the text of his report.
- If Wong's HTC is correct then, even though his calculation is ball-park, it shows the heat exchanger to be of the right size to dissipate 1MW. The air coming out of that window would be very hot, close to 100C, thereby reducing the exchanger efficiency. Nevertheless most of that 1MW could be so dissipated.

When presented with these calculations my first thought was to question the HTC. Although indeed a number of internet references agree with Wong about this, it is very vague. It is pretty obvious that HTC should vary with wind velocity (sort of 101 of heat exchanger theory). Wong ignores this, using the value quoted for *moderate velocity*. And, anyway, I suspected this convenient figure to come not from Wong but from Rossi, because the reference was unusually for Wong's references a non-English-language one and appeared to be Italian. Maybe the value was being misused?

The first thing to do was to track down Wong's reference:

*Overall heat
transmission coefficient between moderate air cross flow and carbon 1.5 steel.
See [OPPO Conductibita Termica] The value is 200W/m ^{2}C.*

to see the figure in its real context. The reference is difficult to track down. Unlike all Wong's other references (properly stated in a bibliography) this is added into the report text as an off-hand remark. It is from an Italian web-site which however does not anywhere provide this data - although it does tabulate a vast amount of similar engineering data, specifically it shows the thermal conductivity coefficients for many materials. Other web references give this figure but with very vague context: it seems to be an internet myth.

So then I went to source material to determine how HTCs are calculated. Basically, there are two dimensionless numbers that determine the HTC: *Nusselt number *describes the gas characteristics (viscosity, density, specific heat capacity). For air it varies with temperature relatively little, and can easily be computed for the relevant temperature here of 50C or so. The *Reynolds number *describes the speed of flow relative to the typical dimensions of the problem (the diameter of the pipe) and the time of the interaction. It determines how turbulent is the flow. It can be easily worked out from the air velocity and the tube diameter. The HTC dependence on Reynolds number is complex and non-analytic. Various approximate formula are available each correct within different ranges of Reynolds Number. I looked at several and for the problem here they agree.

I constructed a spreadsheet (see attachment for this with some things added as noted later) that would work out HTC (and then using Wong's simple formula the overall dissipation) from the pipe diameter - fixed and given by Rossi - the pipe length (the same) and the air flow velocity and total flow. Total flow rate is fixed by the fans and given by Wong from information provided by Rossi. Velocity is not given by Rossi and must be determined.

Wong's value of 200W/m^2C requires an insanely high wind speed over the tubes. 75m/s or **Hurricane cat 1**. The reason for such high speed is that large tubes (as Rossi used) give lower HTCs than small tubes. The internet myth figure is possible at reasonable speeds but only for very thin tubing as for example in a vehicle radiator.

Even de-rating by 1/3 to give 500kW total diSsipation requires a high wind speed of 20m/s or force 8 gale.

Can Rossi's fans deliver this high wind speed? this depends on the area they are blowing wind through. For a given air flow the smaller the area the higher the speed. But the air must blow over all the tubes. If the area of the passage through which it blows is small, it must move multiple times over each tube.

This is a standard construction for heat exchangers using baffles. They force the air to move across the hot rods in multiple separate boxes. At the end of each box there is a passage way through to the next box, inside which the air blows across the same tubes in the opposite direction.

To get the 20m/s 500kW speed we need to have 10 separate boxes to run the air 10X over the tubes. That reduces the flow area by 10X, and speeds up the velocity from 2m/s to 20m/s as needed.

Such a design is just about defensible. So it looks as though Wong is right?

**Power it up, Scottie!**

In fact as intuition would tell you (1MW heat exchangers are big beasts) Wong was wrong. But his calculations are all justifiable. The weird HTC does not matter because (as he would know) you can get whatever HTC you want by varying wind speed and you can make speed arbitrarily high by increasing the number of baffles.

So what is the engineering trade-off? Why can we not make small cheap heat exchangers this way just by having a very large number of baffles?

It turns out that the key problem is the power needed to push the air through the heat exchanger. Obviously, the faster it moves, the more drag you get and the more power is needed. Also, whenever the air changes direction, power is lost due to the turbulence in the momentum change, though that is difficult to quantify. I used standard calculations for the air pressure drop over tubes. There are 22 tubes in Rossi's design. But if the air criss-crosses them 10 X the total drag is as from 220 tubes. You can see the trade-off here. As the number of baffles increases so the drag increases at a very fast rate from two separate effects. The number of tubes the airflow crosses increases (linear) and the wind velocity and hence turbulence also increases (faster than linear).

I added this into the spreadsheet - *attached to this post *- and modelled the airflow fan back-pressure due to the air speed and the total drag on the air as a function of the number of baffles.

As the number increases so does the heat exchanger power dissipation, but also the necessary air pressure. it is easy to compute the mechanical power output of the fans, and hence their electrical input. For even 500kW dissipation, 3X lower than Wong's suggestion,* the total power output by the heat exchanger fans is much larger than the total power drawn from the FPL supply!*

Those with access to specialised heat exchanger design tools could repeat this modelling - perhaps with more accuracy. I'm confident that my results are correct to within 30% or so, and the proposed design is so far from possible even de-rated to 500kW that I'm confident it could not have done what Rossi claims.

Most here won't be interested because they believe the heat exchanger to be fictional. So do I. What I find interesting is how a superficial theoretical analysis of a real possible product (Wong) can leave out the actual trade-offs and generate totally unrealistic conclusions.

**Wong HTC reference - the details**

The word *Conductibita* does not translate to English, although *Termica* is Italian for Thermal, and it
seems likely that *Conductibita* is
meant to mean Conductivity. This title does not exist on the web.

Wong’s background is not Italian
and I find the insertion of an Italian reference here weird, especially when he
gives as the reference he used for Heat Exchangers (the topic here) a perfectly
good reference from which the exact value of **h** could easily be derived (more later on that).

The Italian for Thermal
Conductivity is *Conduttività Termica* and this appears to be what Wong meant. From this
and the word OPPO we find a web reference page of data, etc, which is certainly
the reference he meant:

http://www.oppo.it/tabelle/conducibilita_termica.htm

This unfortunately does not give the coefficient Wong claims to have found here. It gives thermal conductivity of mild steel (something quite different, and has no value any where near what is stated). Nor do any other pages under the OPPO site give the required coefficient. In any case Wong would need to translate this Italian site to read it. My view is that Rossi gave Wong this coefficient, and this incorrect reference from a site with data but not the required data. The figure he uses is a RossiSays!

The value used 200W/m^{2}K is however found in many *other* places on the web with the vague
definition close to what Wong uses. It is *a
typical value* for any surface – not as Wong states specific to mild steel. (In
this case the surface has no effect on the answer. Roughness matters but not as much as other things). So as with all Rossisays
the stated figure has some loose resemblance to fact. For example:

http://thermopedia.com/content/660/

This *typical value* is ill-defined
and not found in serious books on Heat Exchangers. I can nowhere find a
definition of precisely what it means. Thus: *what is moderate air flow?* *What
size pipe* (both air flow rate and pipe diameter make a big difference) does
the value apply to? It appears to be a web myth copied from one place to another
with original source lost. Note that many web sites supply the correct, precise
equation used to calculate the correct figure:

http://www.engineersedge.com/h…_air_convection_13963.htm

**Calculations - details**

See the enclosed spreadsheet. I have not given a good explanation for the numbers and formulae (though there is some). I'll answer questions if anyone is interested.