liquid cooling 1

[fuggeos]

Hello everyone,

I have an application where some electronics with a known heat dissipation of 50 watts, will be fully immersed in oil with a known thermal conductivity, k, in w/m-K, to aid in cooling. This electronics will be housed in a closed cylindrical stainless steel housing. The housing will be immersed in seawater of known temperature.

Does anybody know what the relevant heat transfer equations to use, assuming housing OD of D, wall thickness of x and tube length of L, to determine the temperature inside the housing given an ambient outside seawater temperature?

All help appreciated.

fuggeos

 

[25362]

Instead of relying on sophisticated formulas that could be off by more than +/- 30%, wouldn't you agree that a small lab experiment with the same water, oil and electrical heating element will give you more reliable information that any alternative calculation ?

Anyhow, from old books, assuming the seawater will be somehow moving, or agitated, its degree of fouling and corrosion minimal, and assuming the oil (a silicone?) will not develop gases with time, the expected overall coefficient of heat transfer would be around 30 kcal/(h*m²*K). The main resistance would be on the (internal) oil side where natural convection would be dominant, like in oil-filled transformers. Let's not forget that U, the overall HTC would be lower than that of the oil side.

Having the heat load, Q=43 kcal/h, the surface A, m², and U, Kcal/(h*m²*K) you can estimate the oil temperature, ^oC, from Q=A*U*delta t.

This is a ballpark estimate. If, however, everything has already been designed and constructed, I think a lab-bench test would be the most practical approach. You then can try to have the cylinder eiter horizontal or vertical to verify the best condition for cooling.

I hope this is acceptable to you. Otherwise, you may get the relevant formulas from Perry VI chapter 15. I don't have access to Perry VII, it may have more updated formulas.

Good luck.

 

[25362]

Another thing one has to remember is that a packed oil (no gas) when being heated may develop very high pressures in the range of 10 atm/^oC. Thus, the pipe and the internal electronic device must be protected from any such pressure increase.

 

[cbiber]

25362, Can you give the detail behind your 10 atm/deg C number? Seems awfully high to me to be a general number.

I would agree that thermal expansion needs to be taken into account, and the system should be designed to handle the density change as a function of temperature.

fuggeos, the approach 25362 describes above can be found in any heat transfer text. One that actually uses SI units (like Watts, and the conductivity units you gave) is by Frank M. White, Heat and Mass Transfer.

 

[TD2K]

The pressures you can experience when a liquid filled system is heated has been discussed several times on the site. A reasonable rule of thumb is 40 to 100 psi per deg F (5 to 12 atm per deg C). It's a factor not only of the liquid compressibility but also how much the piping system 'stretches' due to a change in temperature. There are some mathcad programs that Butelja (hope that's the right spelling) had written to take the various effects into consideration.

A keyword search might find them still on site.

As for the theory, the density of a liquid is only slightly dependent on pressure but is much more sensitive to temperature. When you warm a liquid in a liquid filled system, the density would normally decrease but can't because the volume of the liquid (pretty much so) is essentially fixed. Thus, the pressure has to increase (and increase significantly) until the effect of the additional pressure on the liquid density is enough to offset the effect of temperature on the density. Not sure if that is totally clear.

 

[cbiber]

Yep, it's clear. As I thought. Just didn't see how that physics could be so simplified into a rule of thumb. I've run into other rules of thumb that weren't based on real physics, though the "flags" they raised were real.

 

[25362]

to cbiber, the ROT is that the pressure developed on heating a packed liquid is equal to the ratio between its cubic thermal expansion 1/V(dV/dT)_p and its isothermal compressibility 1/V(dV/dp)_T, disregarding the flexibility of the containing material.

The CRC Handbook gives a list of these values at ambient temperatures for some liquids in a table titled pressure and temperature dependence of liquid density. Thus, the range of pressures developed on heating is quite wide.

For water @ 20^oC, 4.5 atm/^oC; for glycerin @ 0^oC, 20.5 atm/^oC, for paraffinic-type hydrocarbon oils, about 10 atm/^oC; for mercury @ 20 ^oC, 453 atm/^oC.

It appears that the lower the temperature the higher the developed pressure in atm/^oC.

If you can get access to those tabulated values and do some ratios, you'll find interesting results for different liquids at different temperatures.

 

[cbiber]

Thanks! Learned something new!

 

[fuggeos]

Thank you all for the useful information. This forum is great!

As regards 23562'c comments, I agree that it's better to do a real lab test but unfortunately, the stainless steel pressure housing is yet to be built. We're a small company with a limited budget for R&D so we're looking at some ballpark figures to guide us in the design at this stage.

Anyway, we don't have to fill the pressure housing with oil. We figure that a 90% fill with oil will be sufficient to immerse all the heat-generating components ( power FETS and transistors) in oil.

As for thermal expansion, we have a figure for DC200 silicon oil, with about .001 cc/cc/K thermal coefficient of expansion, so that 90% figure with a maximum rise of 20 oK in temperature ( this we know for sure) will give .02 cc/cc.
That's about 2% of volume expansion, so our 90%fill is quite conservative.