Rough estimate of thermal resistance of steel plate ?

[MathWizard]

For ages I've been thinking of making a scalable, high power electronic load, for testing computer SMPS, so for example a 12V rail at 50Amps. I've seen good design's on here, and have most the parts sitting around, but no heatsinks remotely good enough.

But I have six 12" * 12" *0.25" mild steel plates,  (30.48mm and 6.35mm). Their thermal conductivity is about 45(W/K*m). They weigh 4.5kg each. (so not practical but they just sit on the basement floor anyways)

I've been looking up free convection of a plate surface, and made it to Nusselt numbers, and I'm just getting bogged down. I can't find the short-cut eqn I used ages ago to get a rough thermal resistance heatsink-ambient.

I'm not going drilling through 1/4" steel, so I'd probably just make a plate/TIM-mosfet-TIM/plate sandwich just to hold them together, that changes the equations a lot too.

How much power could I dump into a single plate and keep it under 60C?

[bob91343]

You need to know the thermal capacity of the plate and the thermal resistance of your interface to it.  If the heat is applied to a small area, the size of the plate becomes less important.

[T3sl4co1l]

So, as a radiator?  Probably not too terrible.

I recall evaluating this, and the hot spot (effective active area) goes as the ratio of lateral conductivity to specific convection rate (assuming a linear W / (m^2 K) figure).  The solution involves a Bessel function (assuming a circular heat source in the middle, and a circular boundary to the plate -- hence the radial symmetry, and the appearance of this function not being too surprising), but we don't need to evaluate it to get the aspect ratio.

The number is pretty reasonable, like for typical PCB (2oz pours) the effective radius is 5cm or so, so I think I had done that right.  Though it's been long enough I don't recall all the setup or the exact formula anymore, just that it's reasonable in the way you'd expect...

So, substitute whatever the average conductivity of that PCB is, with your steel plate (material and thickness), and scale the radius accordingly.

Anyways, the K/W then follows from the effective area.  Mind, the source (hotspot) temperature varies with its radius, ultimately going inverse with it (since, you put 100W into a pinpoint and it's going to turn to plasma, after all).  So it does assume a big enough spot to start with.  (Values are pretty reasonable for conventional size semiconductors, not much surprise there.)

60C is a pretty low ask though.  A hundred watts maybe?  An aluminum heatsink will definitely be more compact (and cheaper, if you didn't have the plates already that is), and a fan will help greatly.  (Mind, the fan increases convection coefficient, thus shrinking the hotspot, and so too the active area -- dissipation still goes up quickly with airflow at first, as the boundary layer shrinks, but eventually the rate slows as the hotspot shrinks.  I think.)

Tim

[MathWizard]

Ok thanks, I'm looking at a few pages, and I've seen the characteristic length being Volume/Area=L, or L/4, or A/perimeter for a horizontal plate , so in this case is it just the 0.25inches? or you're saying it's L ?

http://people.csail.mit.edu/jaffer/SimRoof/Convection/#Natural%20Convection

https://www.engineersedge.com/thermodynamics/convective_heat_transfer.htm
So I have to find the convective heat transfer coefficient.

I checked my 1st year physics book expecting something, but they barely mention this aspect of thermodynamics. I look forward to trying Poisson's eqn and all that stuff, but not tonight.


Now I should also just hook up a BJT or mosfet and put a known power into the steel plate, and see what it can take.

I have x20 IRFZ44N, which are cheap but they also rated for high current and 175C junction temp.

[T3sl4co1l]

Oh.  You're going to get a far more accurate result from those -- which look to be empirical.  Their L is a completely different thing.

My goal (in working that particular problem) was just to get a wave-of-the-hand figure.  At typical temp rise and assuming a 150 C in^2/W dissipation figure (yeah, I know, I only memorized the bastard unit version, for whatever reason), it's probably within 20% or something -- good enough for design purposes, or at least checking how feasible something is, if not the exact dimensions required.

Tim

[SeanB]

Simplest way to make the dummy load is to use big resistors to handle most of the power, leaving only a small amount to have fine control. For short term testing nothing beats a length of heavy steel wire wound into a coil, and immersed into a bucket of water.  A few tap points brazed to it to allow selection of current ranges will be simple, and so long as the bucket still has water covering the coil it will stay at constant resistance. Used that as generator test load, though the steel load was an old bedspread with strap webbing, which had a cut in the short sides to allow insertion of a large SRBP separator, and leads bolted on to the long sides of the frame. Still had the legs, and would pass around 2000A, depending if you put on the extra heavy steel springs, that would clip to the angle iron frame as extra power resistors. Run to red heat if you left it running for an hour or so.

12V 50A load easy to go buy a dozen 12V 50W halogen downlighters, and a dozen sockets for them, and mount the sockets on a few strips of aluminium, so you current selection is determined by how many lamps you plug in.

[Kleinstein]

I have x20 IRFZ44N, which are cheap but they also rated for high current and 175C junction temp.

The IRFZ44 has a relatively limit SOA. They may still be OK for low voltaages like < 15 V, e.g. for battery testing, but rather poor for >= 30 V.  Changes are there is not DC curve in most datasheets - though IR now belongs to Infineon and the Infineon data-sheets are at least often quite accurate with the SOA, so you may be lucky.
Current sharing with multiple MOSFETs is not good and usually every FET would need it's own control loop. Many low power FETs are not very attractive. For a relatively cheap MOSFET for linear use I would more look at something like IRFP250 or IRFP460 - so FETs for a much higher voltage, even if only 30 V are used. The larger TO247 case also makes cooling easier and about 2 times the practical power compared to TO220.

For the heat sink a fan can help a lot, so for more than some 50-100 W I would definitely look for a fan. The heat sink can than be much smaller in area - though thermal conductivity gets more important, but with less material. 

[NiHaoMike]

If you have a large 12V input power inverter, you can use it along with a heating appliance as a test load.

[mc172]

I'm not going drilling through 1/4" steel, so I'd probably just make a plate/TIM-mosfet-TIM/plate sandwich just to hold them together, that changes the equations a lot too.

Why make it so difficult? It's not hard to drill through 1/4" steel plate, especially with a small diameter drill like an M3 tapping drill. It would take you max. 10 seconds per hole with a pistol drill, if that.

[Siwastaja]

Look at data of standard panel radiators, you know those things that circulate water to heat up your house.

Despite the name, most of the heating effect of a "radiator" comes from natural convection. Radiation isn't insignificant, though.

There are types with flat surface for easy cleaning in hospitals, etc. Look at 1-leaf simple models ("10" type), the surface are is similar to that of a simple steel sheet. Manufacturers give tables or formulas to calculate heat output at given average panel temperature and ambient temperature. It's nonlinear.

[Siwastaja]

Why make it so difficult? It's not hard to drill through 1/4" steel plate, especially with a small diameter drill like an M3 tapping drill. It would take you max. 10 seconds per hole with a pistol drill, if that.

Yeah I agree, if having hard time drilling through 1/4" steel, that is a sign of poor quality drill bits. Just almost any HSS drill bit does the job but there are "fake" drill bits on the market with wrong dimensions or substandard alloy.

Do use cutting oil, though.

[Conrad Hoffman]

Steel makes a truly dreadful heatsink, barely better than nothing. Don't waste your time. Find some aluminum or copper sheet to build a sink.

[mag_therm]

Steel Heatsink !
I converted a model for an Aluminum Heatsink.
This is a simple 2D steady state thermal model of one steel plate 300 by 300 by 6mm.
View is edgewise into page, with a line of heat sources running into the page.
Steel K = 45 Watt/metre.Kelvin
A high thermal conductivity plastic body surrounds the heat source and  is in contact with the steel, with guessed K = 60
The heat source total  is 190 Watt total.

The boundaries of the steel plate:
Emissivity = 0.7 ,    to 20 Celsius
Convection = 30 Watt/Metre_squared.Kelvin ,   to 20 Celsius

Two scrots of the solution, one scrot shows most of the plate, the other is with the heat source magnified.
https://app.box.com/s/rhnb5y8omjt3gfkdwf56ltoogi4ejtuh
https://app.box.com/s/rtbyptihe9g7lnpvsht6glcjsapes86v

[Conrad Hoffman]

Cool- I like Quickfield. I think those plots show the problem. The heat isn't conducting well to the outside; you could make the plate smaller and it would work about the same! Long ago I mounted a TO-220 voltage regulator on a large steel chassis. I was amazed at the resulting hot spot and the inability to get heat out of the device. I think I ended up putting an aluminum spreader on it.

[coppercone2]

Steel makes a truly dreadful heatsink, barely better than nothing. Don't waste your time. Find some aluminum or copper sheet to build a sink.

I wonder what kind of corrosion problems can happen with steel+whatever the heat sink tab is

I think its a bad idea

[T3sl4co1l]

The IRFZ44 has a relatively limit SOA. They may still be OK for low voltaages like < 15 V, e.g. for battery testing, but rather poor for >= 30 V.  Changes are there is not DC curve in most datasheets - though IR now belongs to Infineon and the Infineon data-sheets are at least often quite accurate with the SOA, so you may be lucky.

A shame they don't usually have DC SOA, even for these old parts.  The ST cross does, however -- for whatever that's worth:
https://4donline.ihs.com/images/VipMasterIC/IC/SGST/SGSTD014/SGSTD014-905.pdf?hkey=FB3F1F3F2A09A989A6BF9D772C3B8264

I would personally be shocked if they didn't handle full DC SOA.  Always test it, to be sure, but also it's not like you have a lot to loose, they're still cheap.

Current sharing with multiple MOSFETs is not good and usually every FET would need it's own control loop. Many low power FETs are not very attractive. For a relatively cheap MOSFET for linear use I would more look at something like IRFP250 or IRFP460 - so FETs for a much higher voltage, even if only 30 V are used. The larger TO247 case also makes cooling easier and about 2 times the practical power compared to TO220.

That, or a lot of source degeneration.  If you can afford a few volts as the minimum drop (at full current), that's easy.  If you need low dropout, it's gotta be an op-amp per.

FWIW -- give or take heatsinking hardware of course -- TO-220s are actually the cheapest per watt at low voltages.  I looked at this a little while ago and found PHP33NQ20T,127 to be the cheapest.  TO-247s weren't anywhere close (~3x price to start).  That said, if you have a cheap, ready supply of (legit) IRFP260s or whatever, absolutely, nothing wrong with that.

BJTs may be attractive too (you need ones with extended SOA to cover these voltages, but such is definitely available), though I'm not sure about cost/watt at lower voltages.  I have looked into higher voltages before:
https://www.eevblog.com/forum/projects/why-are-mosfets-used-as-pass-elements-in-linear-power-supplies/msg3531820/#msg3531820
The biggest problem with BJTs is the high current density, meaning, you don't get much die area for even like 10A capacity, so the power dissipation is like 50W even with water cooling.  Well, a 10A die should do more like 100W fine, but that's also not going to be the cheapest BJT I mean...

Tim

[IanB]

For ages I've been thinking of making a scalable, high power electronic load, for testing computer SMPS, so for example a 12V rail at 50Amps. I've seen good design's on here, and have most the parts sitting around, but no heatsinks remotely good enough.

But I have six 12" * 12" *0.25" mild steel plates,  (30.48mm and 6.35mm). Their thermal conductivity is about 45(W/K*m). They weigh 4.5kg each. (so not practical but they just sit on the basement floor anyways)

I've been looking up free convection of a plate surface, and made it to Nusselt numbers, and I'm just getting bogged down. I can't find the short-cut eqn I used ages ago to get a rough thermal resistance heatsink-ambient.

I'm not going drilling through 1/4" steel, so I'd probably just make a plate/TIM-mosfet-TIM/plate sandwich just to hold them together, that changes the equations a lot too.

How much power could I dump into a single plate and keep it under 60C?

This is the kind of thing where you would use rules of thumb and some experiments to fine tune the design.

First off, as Conrad mentioned, steel is very poor conductor of heat, which means if you make one end of the plate hot, it will take a very long time for the rest of the plate to heat up. To verify this, just place a stainless steel teaspoon in a hot cup of coffee or tea, and notice how cool the handle remains. Do the same with an aluminum or silver spoon and you will drop it very quickly.

So you will want to use aluminum or copper for your heat sink.

For the convective coefficient, you can mess around with Nusselt numbers and Grashof numbers, but honestly, you can just look up a ballpark number in an engineering toolbox/quick reference. There are too many variables to get an exact number from a calculation. For a vertical surface in free air, the surface coefficient will be somewhere around 5 W/m²-K. Adding a fan will make a big difference.

[MathWizard]

Yeah this "project" will mainly be for computer PSU's......which reminds me, to test this I'll have to hook up 1 of them to get any amount of current, nothing else I own comes anywhere close to their power/current rating.

Investing in some more power resistors, and lights for load tests is on my list of things to get.

On a proto-board I put 4 mosfets, each with 4x 0.1R source resistors in parallel. And copied a quick and easy op-amp driver/current controller. Works ok in spice.

Just to test the heatsinking of the steel, I'd try up to 10-20W/mosfet, that should be pretty safe, and not take forever to heatup the plate, or cook them at 1st.

However, even that is getting up around 25A total, so I really better add lots of extra cabling to this, and solder the PSU's cables (old PSU) right onto the board, or even add some connector of an old motherboard, until I get some proper hardware for this.

What does a good heatsink with fans cost for dumping 500-1000W ? I'm not going to be testing PSUs very often, so I don't really need a permanent setup, I could put part of the plates in a bucket of water too.

[mag_therm]

I think static water cooling is a workable idea at those power levels.

For cooling the capacitors and busbars of my home brew inverters I have a small 12V pump with 1/4 inch plastic hoses and recirculate to a laundry bucket filled with water.
For testing the old 16 Ohm guitar amplifiers I used this (below)  contraption, it is a 1 kW resistor immersed in a 1 litre Ball Jar.
https://app.box.com/s/3l3c9vzxej13c7yayyprs2pjflk5zaf0
Refer for example to Backer Hotwatt tubular stainless steel resistors.
One litre of water will take 294 kW.second to heat to 70C.
From your testing time and typical power level, you can work out how many litre.
In such a static water cooling system for permanent use, don't use glass containers,
and make it so the water can be drained and changed safely and easily.

[MathWizard]

Ok I finally learned DC analysis for MOSFET's/IGFET's. So before I learn the AC models, I'm wondering what I should be going for with my load tester for high wattage computer PSU's. I'm using IRFZ44N, so with at least 12V rail, if not +/-12V for OP07. This thing will be modular, and I'll scale it up, and use real connectors, and real brand name parts. With 12V at 80A rating of some of my PSU's, I'm worried I'll make a welder.


I want a good DC load tester and a good variable load tester, to mimic a real computer.

I can use lot's of switches if the 2 don't circuit can't be made without them. 

I've done Laplace transforms and 2nd order ODE's but I've never really done the chapters where u put them together. I know the basics of feed-back loops but I have a few chapters worth of that to do yet I'm sure.

I'm been looking at various schematics, including retail schematics, and since I haven't finished the above, I'm not making the control boards yet.

But what about this? for instance as a way to limit the max current to 5A from a single IRFz44N, with say 40mR sense resistor, that's around a gate voltage of 4.9V ignoring rd (or 4.75 and LTS had the other) . So purely based off DC considerations, if I choose a gate resistor divider that can limit the max gate voltage, is that a resonable way to limit max current, and if it works w/ AC considerations ? Why not ?

[T3sl4co1l]

Sure, and you can have multiple safeguards, nothing wrong with that.  So, setting Vg(max) say by voltage divider or op-amp supply voltage (output saturation), is one option; depending on Rs, Vgs(th), temperature, etc., you get a crude limit that way.

This is only practical for active use (like, easy paralleling), if you can afford the relatively high drop on Rs -- if you want a low dropout, stick with a small Rs and op-amp per FET.

Mind ground offset voltages between modules.  Probably the input should be differential, so you have a global signal GND reference, through which little or no current flows, and a shared power ground which may accumulate some 10s mV of offset.

And then put whatever you like in front of the current sink, say if you want a CR, CV, CP characteristic instead of CC; CV needs an error amp, CR needs a resistor divider, CP needs a multiplier and error amp.  (Probably, you'd solve 0-2 of those in hardware, and do the last one with an MCU, say.  Which has the bonus of being able to monitor/log operation, say to a serial console.)

Tim

[MathWizard]

And then put whatever you like in front of the current sink, say if you want a CR, CV, CP characteristic instead of CC; CV needs an error amp, CR needs a resistor divider, CP needs a multiplier and error amp.  (Probably, you'd solve 0-2 of those in hardware, and do the last one with an MCU, say.  Which has the bonus of being able to monitor/log operation, say to a serial console.)

Tim

Ok thanks, yeah I should not rush this, no need. The main retail model I've been looking at is the Array 37xx, thanks to Kerry Wong
http://www.kerrywong.com/2018/11/05/teardown-of-an-array-3711a-300w-dc-electronic-load/

They have a 12 or 16bit DAC I think for controlling down to 1 mV/1mA. That design is for up to 360V, I haven't considered/tried any real difference that makes in LTspice, I just tried 12V DUT so far, I'm not planning for more than 60V with these mosfets.

So far I was playing with the gain of the current sensing op-amp, to raise it's o/p a little, in order to make the differential ref/Isen op-amp go max +V-rail near my current limit of say 5A /mosfet as a test.

So for DC in a basic neg. feedback amp A/(1+BA), thats raising B. Looking at the AC sim, I see that area's of the circuit go to +20dB for the original gains around 1MHz say, then drops off again. Raising B to achieve a max  current limit makes it go down around 15dB. I'm not sure if that's good or bad, for preventing unwanted osc, but then also wanting to control it simulate a PC switching at whatever freq. I've heard of the "Barkhauseen" loop gain.

Scullcom electronics also has a nice well thought out design, for digital control from the start. I'm still thinking I'll just try some 7555 PWM type control for something besides DC control. Or my Sig gen as the input.
http://www.scullcom.uk/design-build-an-electronic-dc-load-part-1/

I have the TL082's, I want to try with 4 mosfet's and LM358 for now, see if it works up to 20A