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Numerical Modeling of Water Blocks

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Well the graphs don't seem to be monotonic, but they do look like they might converge cofinally. Can you verify that Aesik? And does anyone have an explanation for why they are non-monotonic?

nihili
 
RO = R(subscript)theta,
we'll be seeing more of this symbol

Aesik,
I do presume that the temp you're describing is the bp (?)
several ways to slice this loaf
as a testing tinkerer, for sure I know that [reading the chart vertically]
increasing flow decreases the bp temps (though by nowhere near the amounts shown)

but in testing thickness as the independant variable, I got higher temps ALSO at 5gpm (my max) with thin bps

I'm in the midst of a transition to RTDs with a 0.001^C resolution, so I'll re-run the thicker ones again
- unfortunatly I can't drill the thin ones
-- I'll think on a method

be cool
 
BillA said:
RO = R(subscript)theta,
we'll be seeing more of this symbol

Out of curiosity, what do you guys use to write symbolic stuff? I typically use LaTeX, but I'm not sure how wideswpread it is outside of academia. I was just thinking we might find some common notational ground.

nihili
 
nihili said:


Out of curiosity, what do you guys use to write symbolic stuff? I typically use LaTeX, but I'm not sure how wideswpread it is outside of academia. I was just thinking we might find some common notational ground.

nihili

I could never get anyone outside of academia to even
start to use LaTeX. Those of us that have used it love
it, but I think it's a lost cause in the Real World. :eek:
 
latex ??
tisk, tisk nihili

I think the problem is figuring out what this forum software will accept
(I just use Word and import the stuff, but I've not tried to post it)

here: Rè
well it seems the subscript aspect was not recognized, also theta seems a bit large

be cool

EDIT: even stranger, the big theta changed into this accented e when posted
 
**EDIT** I didn't like this whole post do I
snipped it away.

What the Lee paper really seems to imply is that the
delta T across the plate will reach an asymptotic limit.
This is NOT the same as the total system convergence
limit. Since the spreading resistance is usually a small
part of the total thermal resistance, the ultimate HS
resistance mostly determines the temps.

What the graph seems to show is that after about
5 or 6mm thickness the contribution of spreading
resistance to the whole thermal resistance is at
a practical minumum.

Aesik, I still have to think about why your model predicts
changes in performance at much greater thicknesses
than this.
 
Last edited:
Thanks Hoot, I really appreciate your comments.

Nihili, in this 'ideal' model where ALL of the heat must be transferred into the fluid, they will never quite converge. If you were to test this in the real world and graph the emperical data, they would eventually converge because the heat would eventually be lost to parasitic sources once the base plate is so thick that the fluid has little to no effect. I am toying with the best way to model parasitic heat losses, but haven't put too much work into it just yet. They are not monotonic for reasons stated in my above post. It's the balance between effective cross sectional area vs. proximity to the convectional fluid.

BillA, the temperature is the temperaure of the block IMMEDIATELY above the CPU. And my values should seem higher than those you get while testing because my model is a very inefficient design. Just a long, straight tube. Not to mention that there are no parasitic heat losses built in. What's nice about using a design like this for modeling is that it more easily shows the extremes and effects of changes, which is the true goal of my exercises at the moment. Once I'm done messing with this model, I'll be working on how to add things that will more accurately reflect a real world block.

As far as symbolic stuff is concerned, when (if) I get serious about it i usually just write it in an equation editor and turn it into a graphic for posting. Most message boards are extremely stingy on what you can get away with in them. Haven't really messed with LaTeX lately. But if we could come up with a consensus, I think that would be great.
 
BTW, I must add a small disclaimer here, most of which can be inferred from my other posts. This model has a TON more work to be done to it. Right now it takes a very simplistic geometry with relatively simple boundary conditions. While it will mimic real world blocks to some extent and the numbers will be somewhat close, it cannot be used to perfectly model a 3D block. At this time it is best used as a tool to be able to understand how changing specific aspects of a system will effect the temperatures throughout the block.

Current variables that can be adjusted are:

Simple block geometry (circular or rectangular, straight channels)
Length of channel
Flow Rate
Input Power
Area of Input Power
Input Fluid temperature
Fluid Properties
Block Material Properties

Things I want and hopefully will be adding as variables:

More complex geometries
Effects of 'fins' and other geometries
Convective parasitic heat losses
Conductive parasitic heat losses
And more...

I'm sure I'm forgetting more things, but that's the main list. There are lots of little loose ends I need to clean up too. But once I got a decent working model, I really wanted to see some numbers (and so did others!) so after I finish the same graph above for aluminum, I'll be refining the model, then later start adding to it.
 
Wow, a lot of people here that know latex. I'd say even uncompiled latex is better than "RO".

Very interesting graph with the various flow rates. After you think about it enough it starts to make sense (it also helps if you don't read the key backwards.:rolleyes: )

Don't forget flow direction (not to rush you.)

Also, with respect to your list of variables, it looks like you could be hurting for cpu time. This is where using excel could be a big plus. If you set up the worksheet, i'm sure a bunch of people on this forum (including me) would be willing to crunch the numbers then return the results to you for compilation.
 
OK I have to clear something up. I nearly confused myself so
others might be confused, too. :)

On the Lee equation and the plots, what we are looking at
is spreading resistance. In Lee's model. for a given material
and geometry this spreading resistance converges monotonically
to a given value no mater what the heat sink C/W is.

This is NOT, however, more than a small part of the total
C/W for the system. The CPU temps are a function of
the total C/W. Clearly for a constant system C/W the
temps will converge on a given temp, but these temps
will all be different depending on the total thermal
resistance. Duh :D

So what can we get out of this? Well, for copper it looks
like you can just forget about spreading resistance after
about 5 or 6mm with nornal CPU die/HS base sizes.

For a WB the big gains should all come from turbulence
and flow rate for a given geometry.
 
Awesome!!:)

Aesik, what was the input power in this case? How
about the other parameters?

There is a whole lot to think about here. :)
 
This is a hodgepodge of thoughts, comments, and questions.

Aesik, when you say they won't converge in the real world do you mean:
A) The functions do not converge at any finite x.
B) The functions do not share a common limit.
C) The functions do not have finite limits.
D) The funtions do not have limits
I'm guessing you meant B), but since I erroneously asked about cofinal convergence, you might have meant A). Additionally, since all the functions appear to increase after an initial nonmonotonic segment, they might all aproach infinity, hence C). (If you choose C, I have questions about rates of increase that I'm holding in reserve.) I threw D) in mainly for completeness. It would be truly odd if the functions didn't have limits.

One interesting feature of the copper and aluminum graphs is that they suggest an answer to a question BillA asked previously about what is meant by tuning (designing) a block for low flow given that increasing the flow will improve block performance regardless of design (within certain limits of course). Given that the curves are nonmonotonic below about 150gph, optimising for low flow would mean, among other things, choosing a base plate thickness that was optimal for the target flow. Thus an aluminum base plate targeted at 70gph should be about 7mm. It's interesting that a copper block targeted at the same flow should be about twice as thick. Now of course running a higher flow in such a block will produce improved temps. But in terms of design, if you are designing a high flow block, you should use a thinner base plate. Lesson: Optimal design for a given flow rate is not the same as optimal flow rate for a given design.

Aesik, I'm guessing that all of the functions are nonmonotonic, but only because of an initial dip. Furthermore I'm guessing that as flow rate increases, the initial dip becomes smaller along both axes. The fact that no dip is apparent in your graphs of high flow rates could be explained by the dip occuring prior to x=1mm or by the dip being to small to see in your graphs. Is this right?

I'd love to see the graphs extended beyond 20mm and also below 50gph just to see if my intuitions about their shapes is correct? Is there anyway for you share the computational load? I'd be happy to put my machine to crunching numbers for you if it were possible. Unfortunately I am no more a programmer than I am an engineer, so this may be a laughable question.

Tecumseh, thanks for the explanation about the spreading resistance stuff. I had a nagging worry that we were missing something, but I was unable to put my finger on it.

Well that's enough for now,

nihili
 
Oh dear, I get more confused.
What is the R0(Rsubscript theta?)(C/W) for an average waterblock ?
From Billa's data* I suggest less than 0.1 (possibly approaching 0.001?) at any flow rate above 0.5gpm(30gph).
In this case, according to Lee(as presented by Tecumseh) the Thernal Resistance(C/W) and temperature should follow the high flow rate(300gph) model and rise with increasing thickness but Billa indicates(in this thread) thst his results show the opposite.

* Presented in this thread http://forum.oc-forums.com/vb/showthread.php?threadid=65078
 
Les

RO (Rsubscript theta) is NOT a valid term for wbs;
and I am not concerned with this statement being in contradiction with that of Seri Lee.
Rsubscript theta IS a valid term for the thermal resistance of the 'joint' between the die face and the wb bp face, normally stated as Rsubscript thetaJA by the EE people - hopefully one will jump in here and correct my inevitable errors.
(Yes, terms can be defined any-which-way; but this is causing confusion.)

C/W are the units, but note the lack of any dimenisonal characterization.
This is because of the very sloppy way in which this term has been improperly co-opted by OCers.
(as Aesik put it, it is a 'hack' term)

the C/W value for the TIM joint can be determined, and is indeed independant of the applied heat load, or the coolant flow rate;
BUT the value of 'C/W' so determined is valid ONLY for that specific instance of assembly.
--> There will be a new different TIM joint C/W EACH TIME THE TWO PIECES ARE ASSEMBLED

The Rsubscript theta of Lee is including the heat spreading resistance of the wb's bp AND the variable influence of the (air or liquid) coolant temp and/or flow rate;
a quite different thing than the EE definition.

Aesik is playing with the heat spreading resistance of a configuration; as it is affected by a change in the matls thermal conductivity, and changes in the flow rate.

My test data is a bit of a bast*rd that I've not yet understood/determined how to analyse as my TIM joint temp data include the (small) effects of copper's thermal conductivity, and also the (potentially ?) large effects of TWO thick TIM joints at each of the TCs that record the measurements.
[--> or can/should such be ignored ? anyone ?]
TIMjoint.jpg

(dwg by Apocalypse, not to scale)

But this setup does enable a die/bp temp measurement, and a die/coolant measurement;
which yield a (not yet understood) TIM joint C/W, and a (bast*rdized) wb 'C/W'

and several obvious derivatives

confused yet Les ? (I am < g >)

be cool
 
Tec: Graphs are same as before, just spiffied up and added aluminum.

nihili: You are correct; I meant B. The will not converge at a common value. They will also never quite reach a limit, because no matter how thick the block is, the fluid still has carry away the heat. This issue will be remedied when I add in the ability to have parasitic heat losses. Still brainstorming on how best to approach that situation.

You are also correct about the initial 'dip'. It doesn't show well for the higher flow rates because of the scale of the graph, but it is there. I'd have to re-do some things on my model in order to accurately go below 1mm thickness, but that wouldnt' be too hard to do. I've already cut the element size down to .00025m which only gives a thickness of 4 elements at 1mm. This really stretches the accuracy of the model. What I'll probably do is build a seperate model for 2mm thicknesses and under, and further reduce the element size. But because this gets beyond the realm of practicality for actually building a block, it will probably be on the back burner of my to-do list.

I worked quite a bit on making the model all inclusive so that I don't have to rely on a seperate spreadsheet to do all the initial bc calculations. I took out alot of the hard coded variables and made them alot easier to change. After a few more changes when I can get it to the point of almost being user friendly, I'll gladly make a copy of it available for those that wish to torture themselves by running the code ;) Still a ways off, but I really appreciate all the offers of helping with computational time (some have offered on this thread, others have contacted me by other means). I'm sure I'll take you all up on the offers, thanks.

One of the problems with using a spreadsheet is that the geometry is fixed for each situation. IE I can't change the geometry wrt the element size without making changes to individual cells in the spreadsheet. I'm seriously thinking about buckling down and writing Fortran code for it instead. The only problem with that is that you don't get the instant gratification of seeing spiffy graphs and other useful info.
 
Just a little more note on what Bill talked about wrt to C/W.

I know this won't be popular with most of the oc community, but in my opinion C/W needs to be tossed out the window. Completely and totally. Other than being a total hack way of comparing cooling systems, it does nothing but give a false sense accurate comparisons. Sure it's in the ballpark, but that's about it.

C/W takes 3 numbers and stuffs them together. What it doesn't take into account is the huge amount of variables that go into those 3 numbers. There are three major things that can cause variance and Bill already touched on them: the interfaces between the heat source and cooling device, the tc to cooling device, and the tc to die. All of these interfaces are going to have quite a bit of variance in thermal resistances. Another variable is that when a hole is drilled to place a tc in a block or hs, this is never going to be 100% consistent and will cause quite a bit of variance as well. If you think tolerance stackups can get ugly when machining mating parts, this is at least 10 times worse. You can quickly see how much variance there is by just cruising various websites and see the wildly varying results in C/W they get for the same HSFs.

Added to my list of to-do's for the numerical model is also how to model the TIM and allow for variance there. That shouldn't be too hard as I'll just have a side calculation that will calulate the resistance according to TIM material, thickness, etc. Damn, my list keeps getting longer!

Anyhow, as to a better solution than the current C/W? Well, I've thought about it from time to time and have some random ideas but honestly haven't had time to seriously sit down and bang out any kind of comprehensive thoughts to it. So for now, unless someone else comes up with something better, I think we are stuck with it.
 
Great Thread!!
Keep up the Good Work.

Which program are you using to create these results?
I'm inexperienced with programming and such but could I use Delphi 5 or AutoCad 2002 to produce similiar effects with these results?


Cheers,
Have a :beer: its on me!


Nick "Maximus Nickus"
 
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