IEC 60890 - Heat Rise Calculations

[Dinoduck94]

TL;DR Summary

Where are the 'c', 'f', and 'k' constants derived?

When designing a panel, it is imperative that you keep the components inside at a temperature which they can operate optimally at; allowing the air temperature to go above this limit can cause component failure and fire.

To assist with calculating the air flow required to keep the components below their maximum operating temperature, the IEC 60890 Heat Rise Standard was produced.

Within the calculations, there is a table to reference, where you get your 'c', 'f' and 'k' constants, which depending on the dimensions, effective cooling surface area of the panel, where the enclosure is installed, and if there is ventilation or not.

My question, is where are these constants derived from?

'c' is noted as the Temperature distribution factor
'f' is mathematically produced from the dimensions of the enclosure - (height^1.35)/(Width x Depth)
'k' is noted as the Enclosure constant

They seem like arbitrary numbers, but they are pretty specific:
For example, if you calculate your 'f' factor to be '2.8' and your panel was installed to be a single enclosure with all sides available for cooling, then your 'c' factor is '1.3185' and your 'k' factor is '0.121'.

I like to get into the nitty-gritty side of mathematics, so I'd love to know how these numbers are derived.

Thanks

 

[Chestermiller]

It might help if you provided a diagram of the system.

 

[Dinoduck94]

It might help if you provided a diagram of the system.

Hi Chestermiller,
There isn't a diagram that I can produce.
The system is exactly as described above.

The maths involved with what I'm doing is as per the below;
You'll see that all the information that is needed, is easily available - however constants 'c' and 'k' are only retrieved by looking at a table in IEC 60890 - the standard doesn't explain where these constants are derived from and that is my question: where are they derived from?

$P$ = Heat dissipated by components (W)
$h$ = height of enclosure (m)
$w$ = width of enclosure (m)
$d$ = depth of enclosure (m)

$k$ = Enclosure Constant
$f$ = $\dfrac {h^{1.35}}{wd}$ (This assists with choosing the 'c' factor from the table)
$c$ = Temperature Distribution Factor

Temperature rise mid-way of enclosure in Kelvin ($t_{0.5}$)= $k . P^{0.715}$
Temperature rise at the top of enclosure in Kelvin ($t_{1.0}$) = $c . k . P^{0.715}$

Then you put $t_{1.0}$ into the below formula to calculate the required air flow to remove the excess heat in $m^3/s$:

You can manipulate $t_{1.0}$ to allow for a temperature window of 10°K, but removing 10°K from it before putting it in the below.

$C_{p}$ = specific heat capacity of air in the enclosure (J/K.kg)
$ρ$ = Density of the air (kg/m³)

$\dfrac {P}{C_{p} . ρ . t_{1.0}}$

or

$\dfrac {P}{C_{p} . ρ . t_{1.0}} . 3600$ for $m^3/h$

 

[Chestermiller]

Sorry. Even though I've had considerable experience with heat transfer, I'm unfamiliar with the derivation of this apparently empirical approach.

 

[Tom.G]

I just spent over an hour of on-line searching. The only descriptions I could find boiled down to' the values were derived from extensive testing,' and were verified 'by comparison with actual builds.'

So it sure looks like the 'under-lying math' never existed! It seems to be a hand-wavy and 'well these numbers work' approach.

Good luck!

Cheers,
Tom

 

[Dinoduck94]

I just spent over an hour of on-line searching. The only descriptions I could find boiled down to' the values were derived from extensive testing,' and were verified 'by comparison with actual builds.'

So it sure looks like the 'under-lying math' never existed! It seems to be a hand-wavy and 'well these numbers work' approach.

Good luck!

Cheers,
Tom

Thanks Tom! Such a shame!

 

[Dullard]

I think 'hand-wavy' may be a bit dismissive (no offense intended). I build a lot of electrical enclosures, and use calculators based on this method regularly. I can also do the (apparently) more respectable 'ground up' calculations - and I understand the effect of the required assumptions. This method makes simplifying assumptions and produces a reasonable 'miss on the safe side' result to determine enclosure ventilation/cooling requirements. The information required to produce 'better' results (mostly related to heat distribution, inside/outside convection, etc.) requires a modelling approach that may cost more than the equipment - if the required information can even be had. I believe that engineering (as opposed to physics) is (in part) the art of doing for $.05 what any knucklehead can do for $1.00. By 'doing,' I mean producing actual hardware. Unnecessary labor in unnecessary expense. This (important) aspect of engineering is sometimes under-respected. The best engineers that I know apply a mix of theoretical and empirical tools to reach an identified goal. Rant OFF

 

[Dinoduck94]

I think 'hand-wavy' may be a bit dismissive (no offense intended). I build a lot of electrical enclosures, and use calculators based on this method regularly. I can also do the (apparently) more respectable 'ground up' calculations - and I understand the effect of the required assumptions. This method makes simplifying assumptions and produces a reasonable 'miss on the safe side' result to determine enclosure ventilation/cooling requirements. The information required to produce 'better' results (mostly related to heat distribution, inside/outside convection, etc.) requires a modelling approach that may cost more than the equipment - if the required information can even be had. I believe that engineering (as opposed to physics) is (in part) the art of doing for $.05 what any knucklehead can do for $1.00. By 'doing,' I mean producing actual hardware. Unnecessary labor in unnecessary expense. This (important) aspect of engineering is sometimes under-respected. The best engineers that I know apply a mix of theoretical and empirical tools to reach an identified goal. Rant OFF

Hi Dullard,

Thanks for the response. Are you able to advise what these factors are assumptions of?
The descriptions of "k = Enclosure Constant" and "c = Temperature Distribution Constant" don't really provide an explanation to what it's truly representing.

Thanks!

 

[Dullard]

Duck-
I can't usefully de-construct the constants in this method - at least not easily. The thing to understand is that the thermal conductivity of an enclosure with known composition and dimensions is pretty straight-forward to calculate. The 'hard' part is evaluating the heat flow / temperature difference across a specific spot on the enclosure wall. Convection inside the enclosure depends mostly on the dimensions of the enclosure and the magnitude/distribution of the heat sources - it can produce a significant range of temperatures inside the enclosure, and (for me, at least) it is difficult to 'eyeball' a useful assumption based on the specifics of the enclosure. High (forced) air velocities help to narrow the uncertainties. The rate of heat removal at the outside of the enclosure also impacts the internal convection. I assume that the 'factors' use what you know (dimensions, mat'ls, power) and apply conservative assumptions for the convection-related uncertainties. I also assume that those assumptions are informed by lots of empirical results for enclosures designed to industry standards. Absent this method or a really fancy CFD model of the enclosure, the 'ground up' method would require an assumption of an 'average' wall differential temp - this method ultimately just makes that assumption for you.