the importance of heating/cooling your batteries

[auraslip]

Before plunging for the 72V 10Ah headway pack, check what the internal resistance and compare that to the 20Ah ping you have. Real experimental data would of course be best, so if some volunteer would measure their headway pack at say 20 or 30A that would be better than using manufacturer data. Then do the same with your ping.

Thanks, this is good advice. I gotta find out the specific heat capacity of lifepo4, and I'll do the simulations tomorrow

I'm really interested to see how far off the simulation with a ping and the actual temp readings!

 

[liveforphysics]

oops
forgot to divide the 3200 watts by 4c.

(((3200 watts / 4c)/40)**2)*.0008 = .32 watts per cell or 288 joules per cell. That's 12.8 watts - 11520 joules for the pack.

tf-35 = 11,520 / (5780 * 1.010)

1.9 celsius gain is like 37 celsius.

Damn that is a good battery.

What happens if it's a 20ah and we go for half an hour though?

(((3200 watts / 2c)/40)**2)*.0008 = 1.28 watts per cell or 768 joules per cell. That's 51.2 watts - 30,720 joules for the pack.

tf-35 = 30,720 / (5780 * 1.010)

That's a 5.26 celsius increase, and you'd be running at 40 celsius by the end.

No. Your math is wrong again. Your second example actually raises less than 1deg.

Your math is actually badly wrong in multiple places. First, you don't square power, or even look at it, you square current. Second, when you parallel cells, you either cut the resistance in half and model it as a single cell, or divide the current by 2, either way it works the same. There are 3 other mistakes as well, but I'm typing on my phone.

Last, its not seconds or watts that works for a thermal equation, its the combination of watts times seconds that gives joules, and joules divided by specific heat*mass can give the temp rise.

 

[northernmike]

The more >I< read about Lithium batteries, the more I realize that chemistry, above all else, determines available output.

That is the truthiest thing I've read here. All of this is dependent on the recipe and process used to make the battery.

By which I mean to say,

It might be better to buy batteries of a chemistry that does not require cooling.

 

[northernmike]

Sure, these old chemistry cells might be cheaper, and yes - the Tesla roadster pack uses a pile (haha, I pun) of them ... but as Luke pointed out, paralleling will significantly reduce that Ri value over the capacity of the pack, and more importantly, Tesla has to provide a WARRANTY on their product, it has to meet safety standards, and has to be somewhat predictable to build.

6800 pcs of 18650 to make a 53kwh pack ... they're not looking to return a few cells here and there to China after their customers have had them fail in traffic.

They also need to make sure a car left sitting in the desert sun for hours and hours won't be a risk of any kind. So, I understand cooling that pack.

An eBike or motorcycle affords a little more wiggle room. Your pack is likely a lot smaller, more accessible, and a whole lot less expensive.

I would rather save up for some better cells than spend my evenings attaching CPU fans, thermocouples, and more circuits to my project.

My computers don't even have fans... actually the new macbook Air doesn't seem to have even a single moving part inside...

(edit - corrected from "IR" to Ri, signifying "internal resistance" apologies)

 

[dogman dan]

The comment about parking in the sun in summer is significant. If your bike was parked in the Texas sun all day, AND the battery box was black, you could cook your battery to 150F easily. In my case, I have a nice shady place to park during work charging, and a nice cool 120F garage when I get home. So if you have to park charging in sun, paint that battery box white.

In winter, I have to insulate the pack on three sides to keep in enough heat to get good performance. Some heat is made discharging it, but in summer, I've never seen it get above ambient. But I don't know what the temps in the center of the pack are. It's only the size of a loaf of bread, so I doubt it's that hot. My pings are 15 or 20 ah, so the c rate doesn't heat em too much. Bigger c rates would of course heat em more. but in my opinion, worrying about heat on a ping bike size battery only applies if you have too much insulation around your battery in summer. Smothering the bms can cause cutouts or worse.

 

[grindz145]

Sure, these old chemistry cells might be cheaper, and yes - the Tesla roadster pack uses a pile (haha, I pun) of them ... but as Luke pointed out, paralleling will significantly reduce that IR value over the capacity of the pack, and more importantly, Tesla has to provide a WARRANTY on their product, it has to meet safety standards, and has to be somewhat predictable to build.

6800 pcs of 18650 to make a 53kwh pack ... they're not looking to return a few cells here and there to China after their customers have had them fail in traffic.

Dead on. When you lower the C rate the energy density does very different things at different temperatures. 18650 LiCo still has incredible energy density at the right C rate.

 

[auraslip]

Thanks again lfp. I fixed up the spread sheet and colorfied it.
Let me know what you think.
Still a lot of work to be done before it is really useful. IR increases with heat. So the hotter the battery gets, the less heat it makes. I'm not really sure how to model that. Then there is the issue of the battery radiating the heat gained off! Very complicated. Lots of factors. This article on heat modeling of lithium batteries in EVs will help. Mostly over my head though.
I've tried to start compiling IR of common batteries in the spread sheet. Feel free to add your own.

Here is a quick comparision between headway and nanotech lipo. It makes the headway look pretty poor.

72v10ah headway
amp draw 40
discharge time in minutes 15
c rate 4 c
heat generated per cell in watts 14.4
heat generated per cell in joules 12960
total heat in watts 345.6
total heat in joules 311040
heat gain in celsius 42.214983713355
ambient temp 35
Temp including ambient 77.214983713355

Nanotech lip pack 80 volts 10 ah

amp draw 40
discharge time in minutes 15
c rate 4 c
heat generated per cell in watts 0.32
heat generated per cell in joules 288
total heat in watts 12.8
total heat in joules 11520
heat gain in celsius 1.97334612353969
ambient temp in celsius 35
Temp including ambient 36.9733461235397

My opinion about heat management and cell shape is still always the same: the more cell shape surface per Watt you have the best it is!

That's why there is many controuversy about small vs bigger cell for EV construction... small cells represent much more work.. but the heat dissipation is better cause heat need to travel less thickness to be dissipated... That's why the Tesla choosed the 2.4Ah 18650 li-Co cells with PTC. 18650 offer more surface per Watt than anyothers...
The pouch cells like ping pack offer large surface but cels are too close to dissipate heat..

doctrobass

The comment about parking in the sun in summer is significant. If your bike was parked in the Texas sun all day, AND the battery box was black, you could cook your battery to 150F easily.

Yes, yes it is. It literally gets hot enough to cook eggs on the pavement. last summer I left my bike out side for half an hour, and the lcd screen on my cycle computer had turned pitch black. Luckily it free'd up when I got riding and the wind was moving over it.

Even if those lipo blocks were duct taped to your top tube, and not even heating up at all from discharge, the sun would still substantially heat them up. Might be better to keep them in an insulated box so the heat doesn't radiate in, and get plenty of air moving through it.

 

[liveforphysics]

Auraslip-

Somebody like Jeremy might go through and correct everything because he is super nice and patient.

Myself, I'm just going to make sure you know ALL your thermal calcs are wrong, for each and every example. Many wrong by a factor of 10x or more.


Also, it's Ri for battery internal resistance, not IR, which means Infra-red.

Also, Ri drops with temp not increases...


Lastly, trying to do thermodynamics examples to share with the world thinking they are accurate (or even in the ball-park) while having no foundation skills to do them or understanding what units you're trying to plug into formulas seems like something that as a really strong chance of just ending up adding to the giant pile of misleading and incorrect battery related BS all ready on the internet (which this forum and others are all ready jam-packed with.)

 

[northernmike]

Yes - I meant Ri. Apologies. Corrected in previous post.

 

[auraslip]

Somebody like Jeremy might go through and correct everything because he is super nice and patient.

Myself, I'm just going to make sure you know ALL your thermal calcs are wrong, for each and every example. Many wrong by a factor of 10x or more.

The spreadsheet outputs the exact same value as the previous calculation we did for the nanopacks. So were you wrong before?

Also, it's Ri for battery internal resistance, not IR, which means Infra-red.

Also, Ri drops with temp not increases...

Yeah, I got them both backwards on accident.

Lastly, trying to do thermodynamics examples to share with the world thinking they are accurate (or even in the ball-park) while having no foundation skills to do them or understanding what units you're trying to plug into formulas seems like something that as a really strong chance of just ending up adding to the giant pile of misleading and incorrect battery related BS all ready on the internet (which this forum and others are all ready jam-packed with.)

Yeah this is my first semester back in school after a lapse of 7 years, so my math isn't too strong. Luckily I don't mind people telling me I'm wrong. I know it would be pretty much impossible to get this tool accurate, but I think it could really help people understand the limitations of their batteries. I would think you would love it, since it shows off how awesome lipo can be.

 

[jag]

Myself, I'm just going to make sure you know ALL your thermal calcs are wrong, for each and every example. Many wrong by a factor of 10x or more.

LFP must have woken up on the wrong side today. Auraslip did more than 90% of the students (and faculty) at our university (and most other universities) would be capable of: Looking up various theory, trying to apply it. Just didn't get it quite right.

Lets say we want to draw 40 amps,

Heat produced is (I**2)R

Yes. Now we only need the internal resistance Ir of the batteries. Lets go back to your Ping and Headway example. The Ir of your current 48V20Ah Ping pack happens to be listed on ebikes.ca simulator as 0.20Ohm. Hence

P = 40^2*.2 = 320W

Now for the Headway pack I had some notes that a 72V10Ah pack would have Ir = 0.24Ohm. Warning: not sure how correct this is. I probably found it on the Internet, and hopefully computed it from discharge graphs at some similar current, but my notes are a couple of years old (and convinced me not to buy Headways at the time, so I never tried in reality) Someonw with actual headways could measure the Vdrop at 40A and tell us.

P=40^2*.24 = 384W

Both of these battery packs are waisting a lot of the chemical energy jsut heating themselves instead of powering your bike.

Now suppose you could be satisfied with just 30A, then things look much better (thanks to the nonlinear I^2 term being much smaller)

Ping
P = 30^2*.2 = 180W

Headways
P = 30^2*.24 = 216W

How much does that heat the pack?

The amount of heat energy (q) gained or lost by a substance is equal to the mass of the substance (m) multiplied by its specific heat capacity (Cg) multiplied by the change in temperature (final temperature - initial temperature)

q = m x Cg x (Tf - Ti)

Lipo has a specific heat capacity of 1010 j/kg/Celsius. Weight is 5780 gm.

No idea where you got the heat capacity from. Water is about 4kJ/C/kg. Anyhow, heating would be

Ping (10kg) @40A
\Delta T = 15min*60s*P/Cg/m = 15*60*320/1010/10 = 28C temperature rise above ambient

Headways (7kg) @40A
\Delta T = 15*60*608/1010/7 = 49 degrees above ambient

These are both a bit on the high side for temp rises.

Now in practice a pack gets cooled from the airflow, so heat rise would be slowed down. Still 30A would be more reasonable for continuous use than 40A for both these cell types. 40A peak at acceleration is no problem.

 

[liveforphysics]

Myself, I'm just going to make sure you know ALL your thermal calcs are wrong, for each and every example. Many wrong by a factor of 10x or more.

LFP must have woken up on the wrong side today. Auraslip did more than 90% of the students (and faculty) at our university (and most other universities) would be capable of: Looking up various theory, trying to apply it. Just didn't get it quite right.

So maybe write a thread called, "is this how to calculate a battery temp rise" rather than putting more incorrect stuff people inevitably will think is true on the intarwibs?

Lets say we want to draw 40 amps,

Heat produced is (I**2)R

Yes. Now we only need the internal resistance Ir of the batteries. Lets go back to your Ping and Headway example. The Ir It's still R sub i, even for Jag. Ri. Saying Ir means current through some resistive path, we are using our unit to represent a psudo resistance internal to the battery.of your current 48V20Ah Ping pack happens to be listed on ebikes.ca simulator as 0.20Ohm. Hence

P = 40^2*.2 = 320W



Now for the Headway pack I had some notes that a 72V10Ah pack would have Ir = 0.24Ohm. Warning: not sure how correct this is. I probably found it on the Internet, and hopefully computed it from discharge graphs at some similar current, but my notes are a couple of years old (and convinced me not to buy Headways at the time, so I never tried in reality) Someonw with actual headways could measure the Vdrop at 40A and tell us. for a 72v pack made from 22 cells, resistance should be in that ball-park if you have perfect interconnects, as the cells are around 10mohm each.

P=40^2*.24 = 384W

Both of these battery packs are waisting a lot of the chemical energy jsut heating themselves instead of powering your bike.

Now suppose you could be satisfied with just 30A, then things look much better (thanks to the nonlinear I^2 term being much smaller)

Ping
P = 30^2*.2 = 180W

Headways
P = 30^2*.24 = 216W

How much does that heat the pack?

The amount of heat energy (q) gained or lost by a substance is equal to the mass of the substance (m) multiplied by its specific heat capacity (Cg) multiplied by the change in temperature (final temperature - initial temperature)

q = m x Cg x (Tf - Ti)

Lipo has a specific heat capacity of 1010 j/kg/Celsius. Weight is 5780 gm.

No idea where you got the heat capacity from. It came from my thermal calcs on other pack designs, and I got it from a white paper on thermal modeling for LiPo pack cell cooling. Water is about 4kJ/C/kg. Anyhow, heating would be

Ping (10kg) @40A
\Delta T = 15min*60s*P/Cg/m = 15*60*320/1010/10 = 28C temperature rise above ambient

Headways (7kg) @40A
\Delta T = 15*60*608/1010/7 = 49 degrees above ambient

The problem here is ion movement becomes much less restricted as the cells start to heat, and resistance drops. This is why you see the voltage very often RAISE on low-C rate cells as they start to discharge, the Ri can be cut in half as the cells start to warm, so the modeling using room-temp Ri numbers doesn't work in practice as the cells start to warm. With LiPo it works because the delta-T is so small the Ri value stays close to constant. TexasPyro did some good Ri testing showing an A123 M1 cell having something like a 3-4x change in Ri depending on temps.

These are both a bit on the high side for temp rises.

Now in practice a pack gets cooled from the airflow, so heat rise would be slowed down. Still 30A would be more reasonable for continuous use than 40A for both these cell types. 40A peak at acceleration is no problem.

It's not this cut-n-dry for packs that will be making a big temp swing. LiPo is simple and realistic to model this way because the temps range stays so small. What is important to know, is that your goal should be to keep the cells warm if you want to be making good use of them, and just stay under the temp at which the electrolyte starts to break-down (which can range from beyond 100c clear down to below room temp (for a battery designed to operate in extreme cold).

 

[auraslip]

Jag thanks for the kind words! I was getting discouraged.

No idea where you got the heat capacity from.

It came from the pdf here. I just guessed for lifepo4.

The problem here is ion movement becomes much less restricted as the cells start to heat, and resistance drops. This is why you see the voltage very often RAISE on low-C rate cells as they start to discharge, the Ri can be cut in half as the cells start to warm, so the modeling using room-temp Ri numbers doesn't work in practice as the cells start to warm.

Yeah. This is why I said it would be hard or impossible to do this accurately.However, this paper shows how to model it very accurately. I just haven't been able to wrap my head around it yet. This sim is still in beta.

What is important to know, is that your goal should be to keep the cells warm if you want to be making good use of them, and just stay under the temp at which the electrolyte starts to break-down (which can range from beyond 100c clear down to below room temp (for a battery designed to operate in extreme cold).

Talk about misleading people. The only time you want to purposely warm your batteries is A) when the ambient temperature is cold enough to inhibit performance and B) when you want more performance out of a battery. Second off, 100c down to RT is even more misleading. We aren't talking about high temp or low temp batteries. Every study I've ever seen shows mark decrease in cycle life above 45C. Third off, electrolyte break down isn't the only thing bad that can happen at high temps.

So maybe write a thread called, "is this how to calculate a battery temp rise"

This thread is called the importance of cooling batteries. We need to find out how warm our packs are getting before we can decide how to protect them.

 

[liveforphysics]

You always want your batteries warmer, for all situations, max range, commuting cycles, racing, charging, etc. It is always a good thing if you are using the battery.

Just store them cold (and at nominal V) to avoid accelerated calendar life loss.


I could get no ill thermal effects from LiPo even at 400degF with a heat gun as far as a violent reaction. Headways did start to billow flame at 400degF after 10mins though, from the solvents boiling out.


The break down temp for a cell is entirely dependent on the solvent choices. The cathode and anode materials don't care. If you want a cell for high temp use, you can use solvents that handle 100c or more. The downside, is that they don't function at all at low temps. So you have to blend the low temp solvents with the high temp solvents to end up with something that works across the range you need. For example, an RC Lipo cell doesn't need to work well when its -5deg out, but people do still expect a laptop to operate when they bring it in frozen from their car, so they need a blend that can still function at low temps.

If you're making a battery to function in deep space, you might use a solvent that boils at room temp. If you're making a solvent for an F1 KERS system, you might pick a solvent that just gets optimal at 100degC, but falls on its face at room temp.

 

[auraslip]

However, for cells cycled at 50 and 55 8C after 200 cycles, the impedance of the negative electrode increases at higher rate than the impedance of the positive electrode. Both primary (Liþ) and secondary active material (LiCoO ) is lost during charging. Thus capacity fade for the cells cycled at elevated temperatures can be quantified as primary active material loss (Liþ), secondary active material (LiCoO / 2carbon) loss, and capacity loss due to a decrease in the rate capability of the cell with continued cycling. These losses will be quantified in the second part of this paper. The capacity fade for the cell cycled at 50 and 55 8C can be explained by taking into account the repeated film formation over the surface of anode that results in increased rate of lithium loss and the overall cell resistance at high temperatures.

http://www.che.sc.edu/faculty/white/2002CapacityFade%20ofsonPart%201%20RamadassHaranWhitePopov.pdf

It's not just electrolyte loss.

I could get no ill thermal effects from LiPo even at 400degF with a heat gun as far as a violent reaction. Headways did start to billow flame at 400degF after 10mins though, from the solvents boiling out.

To be clear I am not talking about cooling batteries to prevent venting of the solvents in gaseous form. I'm talking about cooling of batteries to prevent premature cycle fade that has been well documented in lithium batteries above 45C.

You always want your batteries warmer, for all situations, max range, commuting cycles, racing, charging, etc. It is always a good thing if you are using the battery.

This is true, by every metric a batter performs better at warmer temperatures. Except of course, when it comes to lifespan. Those in the north may be interested in warming batteries, but those of us in the south should be wary of the heat.

In regards to the spreadsheet. It should be easy to resample the temp and adjust the Ri accordingly. To be honest though, I don't know what where to start in regards to Ri changing with temp. One would assume that given two Ris taken at different temps you could extrapolate, but that is a pretty big assumption.

I'm taking a python class this semester, so maybe this would be a good first "practical" project.

 

[jag]

I'm taking a python class this semester, so maybe this would be a good first "practical" project.

Python is a decent language I've heard.

Lots of people use Matlab for scripting mathematical calculations and programs.
You can either download an open source version "octave"
http://www.gnu.org/software/octave/
Or buy the student version for $100 in your campus bookstore.

The read and learn from the free online books:
http://www.mathworks.com/moler/

 

[dogman dan]

Wow what a discussion. How many days over 113 F do you get in Texas? I get maybe one, and not every year. Might be more of a problem in Phoenix or Yuma. Gosh it would suck if a pingbattery used in those towns only lasted 3 years instead of 5. Ive been keeping mine in a pretty hot garage for three summers, but no signs yet it's failing.

I kinda doubt that it's a deal where everything is fine and then at 46 c wham! Chances are, the typical lifepo4 or lipo bike battery can take any temperature you can. So if you do live in Phoenix, bring the battery inside when your ride is done if you are worrying.

Interesting discussion, but not really worth worrying about to me. I bet you don't see really bad effects on your battery till the tires are melting off the bike.

 

[auraslip]

Gosh it would suck if a pingbattery used in those towns only lasted 3 years instead of 5.

lol, that is true. I don't think I'll WANT to be using my ping in 3 years.

How many days over 113 F do you get in Texas?
kinda doubt that it's a deal where everything is fine and then at 46 c wham!

The real issue is that these batteries heat up above ambient. For example when doctor bass tested the 10ah headway at 3.5c it heated up from 22c to 45c in 20 minutes. Now this was a single cell, suspended in that air and not contacting anything. With pouch cells it is totally different. Especially for the cells inside the pack. With no airflow or way to conduct heat out (since they are surrounded by hot cells) they'll just get hotter and hotter.

Combine that with being in a bag or case, and the hot sun. Now go on an hour ride at 1c (doctor bass saw a 10 celsius increase even at 1c!)

I'm not sure how it hot it gets, but It should be easy to test.

http://hobbycity.com/hobbyking/store/uh_viewItem.asp?idProduct=9744
I'm ordering one of these. I'll put it down in the middle of the ping, and see how warm it gets.
It cost $10, and it could totally be worth it.

 

[auraslip]

Gosh it would suck if a pingbattery used in those towns only lasted 3 years instead of 5.

lol, that is true. I don't think I'll WANT to be using my ping in 3 years.

How many days over 113 F do you get in Texas?
kinda doubt that it's a deal where everything is fine and then at 46 c wham!

The real issue is that these batteries heat up above ambient. For example when doctor bass tested the 10ah headway at 3.5c it heated up from 22c to 45c in 20 minutes. Now this was a single cell, suspended in that air and not contacting anything. With pouch cells it is totally different. Especially for the cells inside the pack. With no airflow or way to conduct heat out (since they are surrounded by hot cells) they'll just get hotter and hotter.

Combine that with being in a bag or case, and the hot sun. Now go on an hour ride at 1c (doctor bass saw a 10 celsius increase even at 1c!)

http://hobbycity.com/hobbyking/store/uh_viewItem.asp?idProduct=9744
I'm ordering one of these. I'll put it down in the middle of the ping, and see how warm it gets.
It cost $10, and it could totally be worth it.

 

[dogman dan]

Was that an increase from an ambient temp of 110f? Or an increase from ambient temp of something cooler, like 70f.

My pings, discharged at about 1-1.5 c never seem to get above 110. They get warm if it's cold, but don't start boiling if it's hot when I start. The hottest I ever see is slightly above body temp. True, I don't have a thermometer on it, but after long hard rides in the desert, they feel only slightly warm to the touch.

That includes the rides on the mountian, during motor heat destruction testing on 110 degree days. So those days I was pulling about 1200 watts, continuous, for miles out of a 15 ah ping. The battery gets warm, perks up and performs really nice, and never gets hot.

Stop fretting. It's an issue on a huge pack. On a small bicycle pack, you discharge it before it gets very hot.

 

[auraslip]

For example when doctor bass tested the 10ah headway at 3.5c it heated up from 22c to 45c in 20 minutes.

It was an increase from 71f to 113f.

 

[liveforphysics]

The battery gets warm, perks up and performs really nice, and never gets hot.

Stop fretting. It's an issue on a huge pack. On a small bicycle pack, you discharge it before it gets very hot.

Exactly.

And when you increase the discharge rates, the time interval drops with it. It's not like you can have more than 15minutes of 4C discharge, and its not like you can have more than 6minutes of 10c discharge or 3 minutes of 20C discharge etc.

So while Ri heating goes up at the square of current in a cell, the time interval goes decreases linearly, so you end up with a linear relationship between the thermal energy going into a pack vs the current rather than an x^2 relationship.

Further dampening thermal concerns, the function works backwards of something heading towards thermal run-a-way, as the hotter it gets, the less heat it produces.

 

[liveforphysics]

The real issue is that these batteries heat up above ambient. For example when doctor bass tested the 10ah headway at 3.5c it heated up from 22c to 45c in 20 minutes. Now this was a single cell, suspended in that air and not contacting anything. With pouch cells it is totally different. Especially for the cells inside the pack. With no airflow or way to conduct heat out (since they are surrounded by hot cells) they'll just get hotter and hotter.

Once again a misunderstood concept. You model a single cell, or model a pack, it makes no difference in the calculations you're doing, which are specific heat * mass * energy. If you have 1 lone cell, or 10,000cells all clustered together (round or pouch or whatever, it makes no difference) with no airflow between them or around them or whatever, the change in temp is the same if the C-rate is the same.

When you model a single cell heating under discharge in this way, you're all ready modeling it as if it's in a perfectly insulated situation. The concept of combining heat in this model is a fallacy, 1 cell or 100000 cells works out identically if the c-rate is the same.

 

[auraslip]

Once again a misunderstood concept. You model a single cell, or model a pack, it makes no difference in the calculations you're doing, which are specific heat * mass * energy. If you have 1 lone cell, or 10,000cells all clustered together (round or pouch or whatever, it makes no difference) with no airflow between them or around them or whatever, the change in temp is the same if the C-rate is the same.

When you model a single cell heating under discharge in this way, you're all ready modeling it as if it's in a perfectly insulated situation. The concept of combining heat in this model is a fallacy, 1 cell or 100000 cells works out identically if the c-rate is the same.

The portion you quoted was talking about an actual test and real world performance, and not the shitty simulations I've been working on.

I suspected what you are saying about the pack heating evenly in a theoretical closed system, and I'm glad you verified this.

It's not what I was talking about in the portion you quoted though.

Now this was a single cell, suspended in that air and not contacting anything. With pouch cells it is totally different. Especially for the cells inside the pack. With no airflow or way to conduct heat out (since they are surrounded by hot cells) they'll just get hotter and hotter.

The single cell in the test is allowed to radiate heat into the air around it. If in a pack, all the cells would heat equally. Yet because this isn't a closed system, the cells on the outside would be able to radiate heat into the air. However, the cells on the inside would not be able to dissipate heat at the same rate as the cells on the outside because they are in contact with the warmer cells and not the relatively cool air. I don't know all the laws of thermodynamics at play there, but it's pretty simple and logical.

 

[auraslip]

Also, I should note that, the very inaccurate spreadsheet, when set at the same parameters as doctorbass's test, was only 10 Celsius higher. Not a factor of 10x.

I started rewriting it to re-sample the pack temp 4 times during the discharge cycle, I just need to find some real world tests of Ri at differant temps or a way to model Ri based on temp.