## Wednesday, September 28, 2011

### Hidden Problems in Heat Transfer

I get a pretty large number of trade magazine, but one that I am always excited to see is "Electronics Cooling". As you would expect, the magazine is largely oriented towards heat transfer in electronics applications, a problem that I am rarely concerned with, but there is at least one article per issue that addresses heat transfer in general, and often in very enlightening ways. This month is a terrific example with the article "Does Your Correlation Have an Imposed Slope?".

This article (combined with the editorial at the front of the issue really take engineers to task for relying excessively on those darling dimensionless numbers. For those not familiar with dimensionless numbers, these are grouping of variables that are dimensionless. The most commonly used one is the Reynolds number which is ρVL/μ, where ρ is the density of the fluid, V is the velocity of the fluid, L is an appropriate length from the test setup and μ is the viscosity of the fluid. When running fluid mechanics test, you don't need to explore the impact of all these variables over their full ranges, you only need to explore the Reynolds number of its full range and you're covered for all situations. Quite a time saver, eh? You can see why engineers love them so much.

The dimensionless numbers in heat transfer are numerous and I won't get into any of them today. Their large number would be expected since there are 4 modes of heat transfer (conduction, forced convection, natural convection and radiation). As the article points out, the numbers by themselves are not a problem. The issue arises when multiple dimensionless numbers are used in heat transfer correlations, and when the same parameters are used in multiple numbers. One example given is when the Nusselt number, Nu, is correlated to the Rayleigh number, Ra, as
Nu = C Ran
Looking at the parameters that make up these numbers, you find:
q L/(ΔT k) = C [g ΒρcpΔT L3 / k ν ]n
where ΔT (temperature difference), L (length) and k (thermal conductivity) are on both sides of the equation. This then leads to situations were random numbers can show correlations and the article gives a specific example of this.

Correlating dimensionless numbers with each other leads in other situations to an increase in the errors associated with the correlations, something that I remember well from my undergraduate days. I dug out my old heat transfer book and sure enough, I see correlations with 2, 3 or even 4 dimensionless numbers in the same equation. I am quite sure that my professor never warned us of these issues, despite their existence first being described back in 1963!

"Electronics Cooling" is free - you can get a subscription at the bottom of the first page I linked to above. If you work with heat transfer (and unless you work exclusively all day long with room temperature equipment and chemicals, you do work with heat transfer), do yourself a favor and get a subscription.

Heat Transfer Coefficient said...

Hello Dude,

Nice post! Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. It is classified into various mechanisms, such as heat conduction, convection, thermal radiation and phase-change transfer. Thanks a lot.....

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Clive Jones said...

Whether its paracetamol for a headache or an occasional sachet of cold remedy, we all self medicate every now and then. But if you suspected you had high blood pressure and heart problems, would you still self-diagnose or would you go to an expert? A process plant is like a human body and each element of it has to be addressed holistically in order to ensure that it doesn’t fail, creating problems on the rest of the line.

The area of the plant that I see being self-medicated most regularly is thermal fluid in heat transfer applications. Manufacturers are unaware of the risks they take by ignoring thermal fluid degradation and by sampling oils incorrectly, without the input of specialists.

If oil samples are not collected while the fluid is hot and circulating, artificially high flash point values will be returned. As a result, an unsafe situation could be presented as a safe one. The plant manager would underestimate the health and safety risks and maintenance would not be conducted appropriately.

Based on this kind of incorrect diagnosis, the equivalent of life threatening cholesterol levels could be regarded as nothing more than a headache – and treated with drugs from the bathroom cabinet. Decreased energy efficiency, unmanageable flash points and increased risks of explosions are a few of the dangers resulting from erroneous sampling and testing.

Testing of thermal fluids should always be conducted using hot sampling techniques and samples should be submitted to an independent laboratory. Only by doing this can manufacturers ever have sufficient assurance that the state of their thermal fluids has been correctly diagnosed and can be accurately treated.

Best regards,
Clive Jones
Managing director at Global Heat Transfer