Thermal Dynamics of a IC

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JoshuaWhite5522

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After some discussion in another thread (https://www.homebrewtalk.com/f51/dual-coil-chiller-101156/), I came across a question that requires someone with a bigger brain than me. With an imersion chilleris there a point where the distance the water has traveld through the copper tube no longer produces any added cooling effect? I'm just wondering because I'm about to build an IC and whats the point of getting one thats 50ft of copper when it won't cool any more efficently than one that is 20ft of copper. If it makes any different I boil in a coverted sanke, typically 10 to 12 gallons.
 
I think you would see a difference between 20 and 50 feet of coil. The amount of difference will depend on the temperature of the cooling water.

Not sure if that helps...
 
No doubt the water temp plays a large role, but I've still seen the cold ground water of the Pacific NW come out nice and hot from a 50ft coil. I suppose you would have to consider that as the wort cools the cold water will reach further into the coild befor reaching the same temp as the wort.
 
It's not so much length as surface area, and longer is the easiest way to get more surface area. Flowrate is also important, so if you have low water pressure, and a lot of pressure drop (long coil of small diameter tubing), your cooling ability would actually diminish. It's hard to express the differences scientifically because of all the variables, but 50 ft of larger diameter copper will significantly increase your cooling time over 20-25 ft. I also have pretty cool water here in OR (probably very similar to yours), and I can chill 11 gallons from boil to pitching temp in 10-15 minutes with my 50' 1/2" ID chiller year round.
 
The cooling water temp plays a big part for the reason seen with a rapid temp drop that dramatically slows as everyone tries to get down the last 20 or so degrees. All of the various scientific formulas related to heat transfer show that the temp differential is a prime factor in heat transfer - not the actual temp of either the hot or cold substance. The heat transfer rate from wort to chiller tube at the start of the coil is much greater than the heat transfer rate at the end of the coil because the temp differential between wort and chiller tube is decreasing along the length of the tube. It would take elaborate scientific tests to determine the most efficient length. Suffice to follow anecdotal evidence. But, the question remains - would two 25' coils with independent cooling flows be more efficient than one 50' coil?
 
That’s true I didn't even consider flow rate, and yes it does appear that there are too many variables. I suppose one could find out the best (most efficient) length if they could keep water pressure as a constant, but I'm not interested in building several chillers of different lengths to fit my particular set up.

I would have to think that the two coil set up would have to work better if you fed them for independent sources, that way the temp differential would be greater at two points in the kettle. So could the best solution be to save the inner coils to be fed off a bucket of ice water after the outer coil is providing diminishing returns?
 
Here is what I wrote on the other related thread -

My plan is to use a $18 garden pump from Harbor Freight. Sit it in a bucket and connect to my not-yet-built dual chiller (that will have two parallel water circuits). Use a garden hose to keep the bucket full and start the pump. When the wort temp drop slows down significantly, start dumping ice into the bucket. When the chiller discharge gets down to garden hose temp, divert the discharge into the bucket and turn off the garden hose. Continue dumping ice until wort temp is where I want it.
 
Efficiency is hard to figure, but you might be able to figure out other factors.

Like cost might be a factor, also wort displacement might be an issue. If you are maxing out your boil kettle and you try to shove 50' 1/2" of copper in the kettle for the last 15 minutes of boil (to sanitize) you could may have some spillage.

(I've always wanted to use the word spillage :D ). My IC is only 12' of 1/2" and it works great... I don't get 10-15 minute speeds though. To improve the performance I wait until the cooling water cools down and I catch it in a tub... I put my kettle in the tub so I get IC cooling and a cold bath cooling (inside and outside the kettle) at once.
 
Efficiency is hard to figure, but you might be able to figure out other factors.

Like cost might be a factor, also wort displacement might be an issue. If you are maxing out your boil kettle and you try to shove 50' 1/2" of copper in the kettle for the last 15 minutes of boil (to sanitize) you could may have some spillage.

Agree. The science is interesting, but definitely over my head. I figure to build a chiller based on a flexible combination of my limited knowledge, reasonable sounding anecdotal evidence cited by others, within my budget, good money value, job size-matched with expansion capability, and doable within my limited skills. From all indications, what I plan will work and I am sure I can modify in different ways and it will still work.
 
Agree. The science is interesting, but definitely over my head. I figure to build a chiller based on a flexible combination of my limited knowledge, reasonable sounding anecdotal evidence cited by others, within my budget, good money value, job size-matched with expansion capability, and doable within my limited skills. From all indications, what I plan will work and I am sure I can modify in different ways and it will still work.

Sounds... complex. :cool:
 
The question isn't as complicated to answer as it might initially appear. Whether additional tubing length results in faster cooling is reducible to a much easier empirical question: Using a 20' cooler, is the exit water cooler than the wort? If it is, additional length will give faster cooling.

In practice, the exit water on a 20' cooler is going to be cooler than the wort (at least after the initial few minutes) by at least a few degrees. The real question is not whether additional length will result in faster cooling (it definitely will), but whether it will result in a big enough improvement in cooling rate to justify the expense and effort (as alluded to above).

As everyone else has mentioned, this depends strongly on the particular details of your setup, but it's still easy enough to answer. Simply take a 20' coil, measure the exit water temperature and compare it to the wort temperature. If it's quite significantly cooler, more length would help. Of course, if you're using the bathtub method, this experiment is a bit tough to perform.

For what it's worth, if I were you I'd go with the 20', unless you're planning to make batches larger than 5 gallons or have some reason to suspect you're going to have trouble cooling. 20' is fine for everyone else with 5 gallons, and it will almost certainly be fine for you.
 
WOW, that answer and method of deduction is so simply prefect. I will be doing batches of approximately 10 gallons so i think I'll end up going with a longer coil anyway. I love the info that comes up in these threads. HBT wins a gold star again.
 
if the exit water of the chiller is hotter than the wort temperature, you have violated the laws of thermodynamics.
 
Not quite (there is friction between the water and pipe, and within the water itself, although it's miniscule), but yes, effectively. You've misunderstood, though: the question isn't about whether it's cooler or hotter, but whether it's cooler or equal. And it's always going to be at least marginally cooler (again, thermodynamics) so the question is really (as I said above) about how much cooler it is.
 
Not quite (there is friction between the water and pipe, and within the water itself, although it's miniscule), but yes, effectively. You've misunderstood, though: the question isn't about whether it's cooler or hotter, but whether it's cooler or equal. And it's always going to be at least marginally cooler (again, thermodynamics) so the question is really (as I said above) about how much cooler it is.


This is a true statement. What annoys me right now is it seems like I would have been able to solve a problem like this when I was in my Thermal Fluid Dynamics class, but I am drawing a complete blank when I think of how I would go about setting up this problem. I keep tossing around words that I remember from the class like laminar and turbulent flow, as well as thinking that you could set up a model equation and differentiate to find the min/max's which would allow you to determine an optimium length. However I don't get far when actually trying to do it. The above description by ni seems like the most appropriate way to consider the issue. I do wish I wasn't so long out of college (only a few years) so I would have a chance at remembering how to approach a question like this.
 
Doesn't it all boil down to what temp the source water is?

All other variables (including the boil temp of the wort) are predictable. The volume of the wort is important, but that scales up and down predictably too.

What temp is your source water? You can guesstimate your length requirement by evaluating your source temp. The colder your source the more you can save on length, and visa versa, if you live south of the Mason-Dixon line you might need more copper in the pot.
 
The question isn't as complicated to answer as it might initially appear. Whether additional tubing length results in faster cooling is reducible to a much easier empirical question: Using a 20' cooler, is the exit water cooler than the wort? If it is, additional length will give faster cooling.

In practice, the exit water on a 20' cooler is going to be cooler than the wort (at least after the initial few minutes) by at least a few degrees. The real question is not whether additional length will result in faster cooling (it definitely will), but whether it will result in a big enough improvement in cooling rate to justify the expense and effort (as alluded to above).

Yes, exactly.
 
Doesn't it all boil down to what temp the source water is?

All other variables (including the boil temp of the wort) are predictable.

Close. For the most part, the source water temp is a known value coming out the tap. But that source water temp increases while passing through the chiller and the wort temp drops. The temp differential (TD) between chiller water and wort water is directly proportional to the heat transfer rate (HTR) between the two. The greater the TD, the greater the HTR and the faster the wort temp drops - which is the goal. The smaller the TD, the lower the HTR, and as chiller water temp increases and wort temp decreases, the wort temp drop is going slower and slower. The question then becomes a comparision between heat transfer efficiency and cost. As ni* indicates, as long as the chiller discharge temp is lower than wort temp, some heat transfer is occurring. 100' of coil would probably still allow for that heat transfer at the end, but the cost would be prohibitive and the heat transfer rate toward the end of such a long run would be low. I stick with my idea that two 25' coils will work better than a single 50' coil (or similar setup) because each coil will maintain a higher temp differential throughout its run. At the start of each 25' run, chiller water is as low as source water. Anecdotal evidence is that a 25' run discharge is pretty hot. With a 50' run, chiller water is as low as source water at the start and after 25 feet that temp is again, "pretty hot". (Sorry, but I haven't actually done measurements.) If that second 25' run was using water at source temp like a dual coil setup, the heat transfer rate would be higher because the temp differential is higher. But a dual coil setup adds financial and labor cost that some may find prohibitive.
 
the simple answer is that it's all about surface area. More = faster cooling, provided you're able to flow enough coolant water over it to absorb the heat.


There are other factors, but mainly it comes down to surface area and coolant capacity.
 
the simple answer is that it's all about surface area. More = faster cooling, provided you're able to flow enough coolant water over it to absorb the heat.


There are other factors, but mainly it comes down to surface area and coolant capacity.

I disagree that it is "all about surface area" but acknowledge that surface area is a factor. It's just that the price of copper and ability to work with larger copper tubing limits just what the average person can do to increase surface area. But the average person can work to ensure the greatest temp difference between the wort and chiller water. A Google search for heat transfer rates shows numerous formulas based on the particular application, and a common exponent in these formulas is the temperature differential. The general experience of homebrewers is that the wort temp drop from boil down to 100 or so occurs relatively quickly as compared to the drop from 100 down to 70. This is simply because temp differential between 212 degree wort and 70 degree tapwater is greater than that between 100 degree wort and 70 degree tapwater.
 
Wow, I just had a flashback to my days as a chemical engineering student. I now know why I got into sales and marketing instead fo staying on the technical side of the chemical business.
 
I didn't read all the way through, so if this is redundant, sorry.

Heat transfer is greater when the temp difference is high. So, to make a simple point, 212º water in a pot, with a 70º coil immersed, regardless of length, there is a big difference in temp. As the cooler water travels through the coils, it heats up, while the surrounding water cools. So, as the water temp drops, and the coil heats up, heat transfer is slowed.

Which brings me to my preferred method of cooling: a Counter Flow Chiller (CFC). I've been getting temps going into the fermenter right at ground water temp with my CFC. My well water is right around 60º right now. I have to throttle back my coolant flow just to keep temps at pitching temp. 60º water entering at the out flow of the wort, traveling the 25' of hose, and out the other end, does wonders.

YMMV, but I'd suggest building a CFC. Bobby_M has a good one on here, search for it.
 
I can totally appreciate the idea of a CFC to maintain the highest temp differential throughout the flow process. I just figured a dual coil immersion chiller was easier for me and still brought 5 gallons down in under 14 minutes.
 
Here's what a little theoretical investigation revealed - it's all about flow volume through the chiller (gallons per minute) - at least under the assumptions I made, which, of course are a gross simplification of reality.

The heat flow into the chiller is a quantity which declines as we proceed along the chiller from entry to exit. I'm pretty sure this is an exponential decrease with length (I'm pretty sure I'm right because using the exponential equations to figure the average heat loss yields the same results as using the well known "log mean temperature difference" equation (LMTD). So the equation for heat loss per unit length of chiller is of the form: h=h0*exp(-ax) where x is the distance from the chiller input to the point where the heat loss is calculated. h0 is the heat loss per unit length at the chiller entry; h is proportional to the temp. difference between wort and chiller water at the point in the chiller where h is calculated.

Chiller dynamics.jpg

On the above graph, the x axis is distance along the chiller from the entry - 10 units could be, for example 50 feet. The y-axis is the heat loss per unit length (arbitrary units) at each point along the chiller and is directly proportional to the temperature difference at that point.

The black curve extending to 10 on the x-axis represents a chiller 10 units long with a given flow (some number of gallons per minute) through it. The total heat flow into the chiller is the area under the curve. Curve equation is 100*exp(-x/5), so the area under it is the integral from 0 to 10 of that function which is (-100/.2)*exp(-x/5) evaluated from 0 to 10 which is 500*(1-exp(-10/5)) = 432.332 arbitrary units.

If the chiller tube is split into two parallel pieces of half the length, then the cross sectional area of both tubes together is double that of the single tube. If the tubes are filled with water in all cases, and if the total water flow into the chiller is the same with the parallel tubes as for the single long tube, then the flow rate through the parallel tubes must be only half as fast as the rate through the single tube, causing the water in each tube to heat up more rapidly than in the faster flowing single tube; therefore the temperature difference and heat flow drops off more rapidly with the shorter, slower flowing tubes. So we can model the heat transfer for one of the short tubes by h=h0*exp(-2ax) (the magenta curve) and the sum of both short tubes is 2*ho*exp(-2ax), or inserting arbitrary units = 200*exp(-x/2.5) (the red curve). The total heat being transferred at any given time is given by the area under the red curve from 0 to 5. This area is THE SAME as the area under the black curve from 0 to 10 ! Mathematically, the curve equation is 200*exp(-x/2.5), so the area under it is the integral from 0 to 5 of that function which is (-200/.4)*exp(-x/2.5) evaluated from 0 to 5 which is 500*(1-exp(-10/5)) = 432.332 arbitrary units.

In reality, you can probably get more total flow with two parallel tubes than with a single long tube because the resistance to flow will be less. I have made the assumption that the tubes are always completely filled, and of course I have no way to predict the details of the fluid flow (laminar, turbulent) and various other complicating factors. It's still interesting, nonetheless that the heat flow into the chiller under these assumptions seems to just depend on the total rate of chiller water flow. Even though the parallel tubes start out by absorbing a lot more heat, the water in them heats up very quickly because the water flow through them is slow, thus lowering the temperature difference quickly.
 
That's a pretty sweet explanation, Deaf.

I have to admit it's not intuitive, as i would guess that the 2 parallel chillers would be faster. The "intuitiveness" of this may relate to the likely faster flow you'd get in reality, as you point out.

I'll have to think about your equations a bit more (and your assumption of exponential decline), but at first glance this seems reasonable in the theoretical (though perhaps not the practical) sense.
 
From the practical side I just went from 20 to 40 feet of coil and on a 6 gallon boil I can go from 212 to 130F in under 3 minutes and to 70F is 7=8 minutes total on the output temp is still cooler than I would like but I don't want to add any more weight or cost. Input temp is between 38 and 40 F because I have a small IC in an ice bath.
 
You can approach this by modeling the chiller as a pair of channels in contact with one another. A length, dx, of the contact area is assumed to have an area per unit length of A so that the area in contact is A*dx, and a thermal conductivity G so that the heat flow between the two channels in time dt is
dq = (Tw(x) - Tc(x))A*G*dx*dt where Tw(x) is the temperature of the wort and Tc(x) is the temperature of the coolant as a function of distance, x, along the chiller. If the flow rate of coolant is Fc then in time dt an amount of coolant Fc*dt with mass pc*Fc*dt will flow past x where pc is the density and be subject to temperature rise dTx = dq/(pc*Fc*Cc*dt) = (Tw(x) - Tc(x))A*G*dx*dt/(p*Fc*Cw*dt) where Cc is the specific heat of the coolant. Thus dTc/dx = (Tw(x) - Tc(x))A*G/(pc*Fc*Cc) . Similar reasoning gives another equation for the rate of temperature loss in the wort as you move along the chiller
dTw/dx = (Tw(x) - Tc(x))A*G*/(pw*Fw*Cw)

Subtracting these two gives the equation

dTw/dx - dTc/dx = [(Tw(x) - Tc(x))]*(A*G)*[1/(pw*Fw*Cw) - 1/(pc*Fc*Cc)]

Thus d(Tw(x) - Tx(x))/dx = a*[Tw(x) - Tc(x)]

and it's clear that the solution will be exponential in form i.e. the temperature difference along the chiller is an exponentially decreasing function of x (assuming that the origin is where the beer enters and the coolant comes out). I'll leave the rest to the curious as it gets into some rather tiresome algebra.

This should be enough to illustrate that:
1. Enhanced cooling depends on the length of the chiller but the returns are exponentially diminishing with length.
2. The faster the coolant flow the more efficient (with 100% efficiency being defined as the wort leaving the chiller at the same temperature at which the coolant enters) the chiller. More broadly, the larger flow rate of coolant thermal mass, the more efficient the cooler.
3. The slower the wort flow rate, the more efficient the cooling will be. Again, the broader statement is the less the thermal mass passing through the wort channel per unit time, the better the efficiency. Thus a wort of high specific gravity will not be cooled as effectively as one of lower specific gravity.
4. The thermal conductivity (A*G) between the channels is the major driver in performance. Increasing G (as by putting fins on the wort tube in a coaxial design) always works. Increasing A may not be so effective because, where the flows are laminar, the wort in the center of the channel is insulated from the walls where the heat exchange takes place. One way around this is to be sure that the flows are rapid enough that they are turbulent. Fins not only help heat transfer but they can break up laminar flow and benefit in that way too.

It's probably clear, given particular length, A, and G that the faster you run coolant, the colder the wort will be but that you will consume more coolant. It's also probably clear that the slower you run the wort the cooler it will be but that as the process will take longer more coolant will be required. One can trade time, efficiency and coolant consumption but to do so requires thorough knowledge of the chiller. One can make measurements on a chiller to determine its A and G (or at least A*G) and thus model its cooling capabilities but one must be careful in doing this as the effective G changes as the flow transitions from laminar to turbulent.
 
Without the benefit of all the math and formulas I add my observation. I use 50' of ½" copper tube Immersion chiller. I had the opportunity to brew with a guy that uses a 25' IC. This was a situation where we had to share a hose for chilling. The hose had a "Y" so that we could share a single hose. The other guy began chilling about 15 minutes before I finished my boil. When I started chilling we were using the exact same ground water. We had to finish at the same time because other people needed to use the hose to start their chill. Even though I started 15 minutes later I was chilled to a lower temperature at the end.
 
Yes, but the same model should serve for one in which wort and coolant flow in the same direction (not that one would want to operate a chiller that way).
Quite true.

I was thinking of immersion chillers earlier in the thread. The big difference between an IC and a CFC (in terms of heat dynamics) is that in the IC, a lack of wort movement means that you'll have cooler-than-average wort right next to the chiller, reducing the temperature gradient and slowing heat transfer.
 
One way to measure the total cooling effect could be to measure your flow (clocking a certain volume would be the easiest way) and compare the temperature of incoming and outgoing cooling water.

Heat capacity of water, time spent in tube by the water, and temperature difference (before and after) should result give you a number to, uhm, enjoy and reflect upon.

Lets say you have have a flow of 1L per minute, ingoing temp 15°C and outgoing 50°C

effect: (1000/60)*4.18*35 = ~2438 W
first term is grams per second (flow), the second is joule per gram and Kelvin, the last is the difference in temperature.
(to use imperial units you'd need some more numbers in there to compensate for fahrenheits and what not.)

Energy capacity can't really be modified, but the others can be changed. You could blast a ridiculous amount of water through the cooler with only a slight difference in temperature and still cool it more than a lower flow with a higher temperature difference.

It'll be different for different wort temperatures, so measure both and plot some sweet graphs of your cooling effect over time and/or wort temperature. :rockin:

disclaimer: Can't guarantee that this is correct.
It's still interesting, nonetheless that the heat flow into the chiller under these assumptions seems to just depend on the total rate of chiller water flow. Even though the parallel tubes start out by absorbing a lot more heat, the water in them heats up very quickly because the water flow through them is slow, thus lowering the temperature difference quickly.

But isn't lowering the temperature difference the point of cooling?
The smaller the difference is, the more heat has been absorbed by the water.
 
Dude, that's a darn good point!

That's by far the easiest way to figure out and compare efficiencies of different coolers....thanks for sharing.
 
But isn't lowering the temperature difference the point of cooling?
The smaller the difference is, the more heat has been absorbed by the water.

The object is to remove as much heat as possible quickly. Once the water in the chiller heats up so that there is not much temp. difference wrt the wort, there's not much heat energy being absorbed by the chiller water. Ideally, you'd want to have such a fast flow rate that the chiller water would hardly heat up at all, maintaining a very large temperature difference (and heat transfer) between the wort and the chiller water. At the other extreme, assume you only have a trickle of water through the chiller - the water heats up quickly and removes all the heat it is capable of, but then there is no more heat removed until more cool water comes through.
 
The object is to remove as much heat as possible quickly. Once the water in the chiller heats up so that there is not much temp. difference wrt the wort, there's not much heat energy being absorbed by the chiller water. Ideally, you'd want to have such a fast flow rate that the chiller water would hardly heat up at all, maintaining a very large temperature difference (and heat transfer) between the wort and the chiller water. At the other extreme, assume you only have a trickle of water through the chiller - the water heats up quickly and removes all the heat it is capable of, but then there is no more heat removed until more cool water comes through.

Ye, the point isn't to maximize the heat transferred to each unit of cooling water, but to maximize the heat transferred from the wort.
I kinda lost that somewhere while reading the thread. :eek:

Do you have any thoughts on the rest of my post above?
 
There are 4 basic factors involved, temperature difference between fluids, resistance of heat flow through tubing, surface area, and turbulence or movement of liquid over tubing. If you have large differential, surface area, low thermal resistance but no fluid movement over outside of tubing not much happens, stir the wort and things change dramatically. Parallel tubing immersion chillers will exploit higher temperature differential over shorter run, but if there is no stirring not much improvement over continuous tubing run of same length.
The plate heat exchangers work well in spite of high thermal resistance of stainless steel by creating turbulent flow on both sides of the heat exchange plates, and thin plates. Counter flow chillers offer similar results with constant flow over both surfaces and counter circulating coolant.
 
Motivated by this thread I dug out and posted (to www.wetnewf.org) my old notes on counterflow chillers. The bottom line is that each chiller's geometry, materials, length... give it a characteristic "capacity" or "size". This is a number expressed in units of flow rate e.g. gallons per hour. This capacity can be determined by establishing counter flowing "wort" (water for this determination) and coolant and then measuring the "efficiency" which is the difference between inlet and outlet wort temperature divided by inlet wort temperature minus inlet coolant temperature. Thus if outlet wort temperature is equal to inlet coolant temperature the chiller has done the best it possibly can and the efficiency is 100%. The efficiency and wort and coolant flow rates are sufficient to determine the capacity, Q. The performance of the chiller depends on the wort and coolant flows normalized by Q and the notes have a graph for various levels of efficiency. If coolant flow is equal to Q and wort flow to Q/5 the chiller will be 99% efficient. If wort flow is doubled for the same coolant flow efficiency drops to about 85%.

Unfortunately, to utilize any of this you'll have to wade through quite a bit of algebra but at least you don't need to understand it at any more depth than is necessary to appreciate what the graph is telling you.

The big caveat here is that as flow transitions from laminar to turbulent, Q is going to change and the model does not account for that. If you measure Q in the turbulent region then you can use the model in the turbulent region but not in the laminar and vice versa. To further stir the pot on this issue note that wort could be laminar which coolant is turbulent and there are 3 other combinations.
 
Ye, the point isn't to maximize the heat transferred to each unit of cooling water, but to maximize the heat transferred from the wort.
I kinda lost that somewhere while reading the thread. :eek:

Do you have any thoughts on the rest of my post above?

From your equation, you could determine the heat transfer with a given flow rate and temperature difference. Also, it is obvious that you could increase the heat transfer by increasing the flow rate or by increasing the temperature difference. The only way to increase the temperature difference is to either decrease the flow rate, or to increase the heat transfer coefficient of the chiller; i.e., more surface area, larger diameter, longer coil. Decreasing the flow rate will increase the amount of heat transferred per unit volume of water through the chiller, but will decrease the heat transferred per unit of time.
One way to look at this is to use the Log Mean Temperature Difference equation, or LMTD:

http://en.wikipedia.org/wiki/Log_mean_temperature_difference

Admittedly, this is more of a cross-flow situation, so a correction factor might be needed to account for that, but ignoring that for the moment, let's say we have a chiller with a certain transfer coefficient and we have a certain flow rate and temperature difference. Let's look at a single point in time where, for example, the wort temp. is 85º C, chiller water enters at 15ºC and leaves at 50ºC (also assume the wort is circulating around the outside of the chiller coils so the temperature of the wort in contact with the coils is everywhere 85ºC. So the LMTD or temperature driving force is:

(delta Ta - delta Tb)/ln(delta Ta/delta Tb) = ((85-15) - (85-50))/ln(70/35) =
35/ln(2) = 50.5ºC.

Now assume we double the flow rate, and assume for the moment that the heat transferred per unit time remained the same. If this were true, the temperature change in the chiller water would be half as great, or 17.5ºC instead of 35ºC and the chiller water would exit at 32.5ºC. This would mean the LMTD is ((85-15)-(85-32.5))/ln(70/52.5) = 17.5ºC/ln(1.33) = 60.8ºC. So there would be a greater temperature driving force in this case, which contradicts the assumption that the heat transfer is equal if we double the flow rate - in fact, the heat transfer would go up. So even though the water doesn't heat up as much with the faster flow, there is still more heat removed per unit time.
 
One way to look at this is to use the Log Mean Temperature Difference equation, or LMTD:
http://en.wikipedia.org/wiki/Log_mean_temperature_difference

Ooh, I remember that badboy from a course on interior climate about a year ago. (which nosed a bit on heat exchangers)

But I believe we more or less wrote the same, although you had a good explanation as to why it is that way
"You could blast a ridiculous amount of water through the cooler with only a slight difference in temperature and still cool it more than a lower flow with a higher temperature difference."

To clarify, the temperature difference referred to is between water going in and out of cooler. Not the one between coolant and wort.

More specifically what I was wondering was if you had any thoughts about making those measurements mentioned above and comparing the results?
I started to try and elaborate here but I lost track, not sure what you'd get out of comparing that in the end. But jaginger seemed to like the idea.
 
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