Temperature gradient, numbers needed

[cirthix]

Ok, I have someone who needs a temperature gradient from 32c to 15c in an aluminum block. Much to my disappointment, my boss took the easy way out and is using 9 150w resistors to heat the hot side and tapwater flowing through the other side (LOTS of water). HUGE WASTE of resources. I was thinking that if we cut up the block and put insulators between the chunks, we could use less heat to make the gradient.

Other bits of info:
There is no load on the block.

The block is about 2' by 2'

There is an 8x8 array of holes that go all the way through the block. they are 1" in diameter and about 3" apart, with a couple of extra inches on each side of the array to minimize edge effects.

The block is 4" thick

Maching insnt a problem, we've got a machine shop next door.

The hot side should be at 32c and the cold side at 15c

The block will be placed inside of a wooden box, so you can ginore any wind effects.

Ambient temperature is unfortunately probably higher than 15c, so peltiers at low voltage with some cpu heatsinks bolted to the block will probably work.

My idea is that we cut the block into slices, put insulators between them, bolt it all together, and have each strip be ~2c warmer than it's cooler neighbor.

My question to you guys is what insulating material, how thick, and how much heat needs to be put on the hot end? How much heat would need to be removed from the cold end?
Something like a strip of steel would be ideal.

UPDATE: we thought of a better way to reduce thermal conductivity: simply cut partially through the block to reduce the thickness of the aluminum. this will also make it simpler by keeping it all in one piece .

 

[DrPizza]

I've done similar problems in differential equations... It's been a long time though...


However, just off the top of my head...
1350 watts just to achieve 32c on one side??


And, water??? Again, off the top of my head, it seems like that's going to make it even more difficult.

And, forgive me, but why does someone need a 32 to 15 degree temperature gradient in a block of aluminum - yet you're allowed to machine all sorts of things on it?? Sounds a lot like homework.

Anyways, it seems that it'd be quicker and easier to arrive at a solution experimentally rather than through calculations. Use some heaters at one end and peltiers at the other.. vary the power until you reach the state that you want.

 

[CycloWizard]

Couple questions:

1. Do you need to keep the holes in the piece? If so, you will never get a constant thermal gradient. The holes are filled with air, which has a much lower thermal conductivity than aluminum, so they will transfer less heat and effectively create 'hot spots'.

2. What is the point of this? I can't think of any situation where this would be useful, but if you told me it might help me figure out what you're trying to do and help you solve the problem.

3. Why would you add insulators? The water is an effort to increase the rate of heat transfer, not decrease it. Adding insulators will always decrease it by lowering the effective thermal conductivity.

I'll be out of town for a conference until Wednesday, but when I get back I can solve this for you.

 

[DrPizza]

The only use I've thought of is an experiment to see what temperature bugs like to be at... Cover the top and see where the bugs go. I believe I saw a similar experiment done with cockroaches to see what their preferred temperature was. (and your range of temperatures seems to suggest something similar)

 

[DrPizza]

Also, you may want to make some accurate measurements....
if there's an 8x8 array of 1 inch holes that are 3 inches apart, plus a couple inches on each side of the array... I'm coming up with about 33"x33"

 

[cirthix]

yes, this is for someone who is doing research on microbes. the holes go all the way through the block and there is a light gradient from front to back and the temperature gradient from left to right.

clcylowizard, aluminum is a very good conductor of heat, adding insulators would slow down the flow from the hot side to the cold side, letting us use less heating on the hot side and less cooling on the cold side. we needed to run water through a tube in the block to cool the cold side. it's very hard to get rid of 1350w to a nice steady 15c otherwise.

drpizza, i can get more accurate numbers when i go back to work, those were just off the top of my head.

 

[Gibsons]

Maybe this wouldn't be an improvement, but two of these would make it really easy.
Text

 

[DrPizza]

Originally posted by: Gibsons
Maybe this wouldn't be an improvement, but two of these would make it really easy.
Text

I was thinking along the same lines... simply keep one edge at 33 and the other at 15 and let the aluminum do the rest. It won't be perfect, but probably as good as you're going to get with the holes cut through it.

 

[cirthix]

that's what is being done with the waterflow and the 8 resistors. i'm jut trying to get ti to be more effecient

 

[Gibsons]

Originally posted by: cirthix
that's what is being done with the waterflow and the 8 resistors. i'm jut trying to get ti to be more effecient

Well, using a recirculating water chiller on the cold side will at least not waste water.

Also, if you're looking to save energy by making the aluminum less conductive (by cutting and inserting some insulator) why not just switch to a somewhat less conductive metal?

 

[cirthix]

Originally posted by: Gibsons

Originally posted by: cirthix
that's what is being done with the waterflow and the 8 resistors. i'm jut trying to get ti to be more effecient

Well, using a recirculating water chiller on the cold side will at least not waste water.

Also, if you're looking to save energy by making the aluminum less conductive (by cutting and inserting some insulator) why not just switch to a somewhat less conductive metal?

because aluminum is very easy to machine and the block is already made

 

[CycloWizard]

Originally posted by: cirthix
clcylowizard, aluminum is a very good conductor of heat, adding insulators would slow down the flow from the hot side to the cold side, letting us use less heating on the hot side and less cooling on the cold side. we needed to run water through a tube in the block to cool the cold side. it's very hard to get rid of 1350w to a nice steady 15c otherwise.

Perhaps if you explained what you're doing a little more clearly, this wouldn't need to be said. I'm well aware that aluminum is a great heat conductor. However, I'm also aware that if you want a linear temperature gradient across a slab, you need a constant thermal conductivity. If you're going for a linear temperature gradient, as your problem statement suggests, then there is no reason to add insulation. Indeed, if my visualization of your problem is correct, then the profile is just about right. The temperatures at the center lines of the holes will be just about as follows:

Row #__Temp (°C)
1______31.1
2______26.8
3______22.5
4______18.2

If you're going for specific temperatures in each well row, then you might fine-tune it by adding insulation. However, given what you've told us so far, this is as good as I can give you. If you know some heat transfer stuff, then just use Fourier's Law. The presence of the holes will have some effect, but the effect is negligible in light of the fact that the wells can never have a uniform temperature. The magnitude of this nonuniformity around the holes is greater than the disturbance in the temperature field created by the presence of the holes.

 

[FrankSchwab]

OK, you need lots of water to get rid of the 1350 watts you're pumping into the hot side.

Let's think of it differently - how little heat do you need going into the hot side to not need any water on the cold side?

Remember, Al is a very good thermal conductor, it's just as good transporting heat from the hot side to the cold, as it is transporting cold from the cold side to the hot. There is an infinite curve of water flow vs. input power that meets your requirements - raise the heat input a bit, you need to raise the water flow a bit. Raise the water flow a bit, you need to raise the heat input a bit. Try going the other way - reduce the heat input a bit, you can reduce the water flow a bit. Keep doing this until the water is running at a trickle, and you're at the minimum solution.

I still like the previous suggestion of using a peltier on the cold side. It's then a slightly complex thermostat with a long settling time - measure the temperature on both sides, and use an SCR to control the power input to the resistors on the hot side, and a FET to control the power input to the peltiers on the cold side.

Good luck.

/frank

 

[jagec]

Originally posted by: FrankSchwab
I still like the previous suggestion of using a peltier on the cold side. It's then a slightly complex thermostat with a long settling time - measure the temperature on both sides, and use an SCR to control the power input to the resistors on the hot side, and a FET to control the power input to the peltiers on the cold side.

Good luck.

/frank

if you want to have fun you can actually use a heat pump to keep the cold side cold, and dump enough of the waste heat in at the hot side to keep it hot. It would take a lot of tweaking to get exactly the right size heat exchanger, but is the most efficient way of doing it.

 

[cirthix]

a linear gradient accross the whole block isnt needed. ideally, there would be no difference in temperature from one side of a hole to the other side of the same hole, so what is needed is a temerature curve that looks like a series of steps. the first row should be at 32c, the next at ~30, next at ~28 and so on untill the last hole is at 15.

here's a pic of what i mean
http://www.cryo-laboratory.com/upload/userfiles/cirthix/tempblock.GIF

 

[cirthix]

bump

 

[cirthix]

bump

 

[DrPizza]

Egads, the same temperature all the way around the hole? I'm stumped...

No I'm not.. but it would take a lot of machining... suppose where the holes are, you machined around them, essentially turning those holes into thin walled tubes sticking up through the block. (leaving enough aluminum to hold them in place). Then, fill those hollows with a liquid - water or oil or whatever. Circulate the water in each row such that it enters and exits each of these hollow areas in multiple places, to create enough circulation in those hollows to maintain a relatively consistent temperature in them.

This project sounds like a major pita!

 

[CycloWizard]

Originally posted by: cirthix
a linear gradient accross the whole block isnt needed. ideally, there would be no difference in temperature from one side of a hole to the other side of the same hole, so what is needed is a temerature curve that looks like a series of steps. the first row should be at 32c, the next at ~30, next at ~28 and so on untill the last hole is at 15.

here's a pic of what i mean
http://www.cryo-laboratory.com/upload/userfiles/cirthix/tempblock.GIF

I see what you're saying now. I'll take a look at it in more detail when I get a chance.

 

[cirthix]

Originally posted by: DrPizza
Egads, the same temperature all the way around the hole? I'm stumped...

No I'm not.. but it would take a lot of machining... suppose where the holes are, you machined around them, essentially turning those holes into thin walled tubes sticking up through the block. (leaving enough aluminum to hold them in place). Then, fill those hollows with a liquid - water or oil or whatever. Circulate the water in each row such that it enters and exits each of these hollow areas in multiple places, to create enough circulation in those hollows to maintain a relatively consistent temperature in them.

This project sounds like a major pita!

reality isnt ideal. there can be a small temperature difference from one side of the hole to another.

i just need to know how deep to cut the block and how many watts of heat to put on the hot side and how many to remove on the cold side.