{"id":322,"date":"2012-07-28T20:25:29","date_gmt":"2012-07-29T01:25:29","guid":{"rendered":"http:\/\/tonykordyban.com\/?page_id=322"},"modified":"2014-04-13T20:27:54","modified_gmt":"2014-04-14T01:27:54","slug":"everything-you-know-is-wrong-november-2001","status":"publish","type":"page","link":"http:\/\/tonykordyban.com\/?page_id=322","title":{"rendered":"Everything You Know Is Wrong November 2001"},"content":{"rendered":"

Answers to those Doggone Thermal Design Questions<\/strong><\/p>\n

By Tony Kordyban<\/strong><\/p>\n

Copyright by Tony Kordyban 2001<\/p>\n

 <\/p>\n

Dear Thermal Answering Man,<\/em><\/p>\n

I did a thermal test at room temperature (around 21 deg C) and at 55% Relative Humidity (RH) and I got a component temperature of 49 deg C.\u00a0\u00a0 That seemed good because the component is rated for 85 deg C maximum.<\/em><\/p>\n

But what I really need to know is the component temperature when the ambient is 50 deg C and 23% RH.\u00a0 How do I extrapolate my test results to this condition?<\/em><\/p>\n

If the only change is from 21 to 50 deg C, then I would simply add the difference (50-21=29 deg C) to 49 deg C (29+49=78 deg C).\u00a0 I would then compare 78 deg C to the 85 deg C limit, and everything is still OK.\u00a0<\/em><\/p>\n

But how do I handle the moisture content change?\u00a0 By increasing the Specific Heat (Cp) value?\u00a0 By how much?\u00a0<\/em><\/p>\n

I expect that higher moisture incoming air would lead to better cooling. But is the effect negligible? Especially between 55% RH and 23% RH?\u00a0 <\/em>
\n\u00a0 Sweatin’ It Out in Watervliet<\/em><\/p>\n

 <\/p>\n

Dear Sweat,<\/p>\n

What an excellent question, which I swear I did not make up myself, this time.\u00a0 I have always just assumed that relative humidity didn’t affect air cooling of electronics very much, but I never sat down to verify whether that assumption holds water.\u00a0 The non-heat-transfer-understanding-type person thinks that high humidity makes things hotter, because we feel hotter when the humidity is high.\u00a0 But that is only because when the air is already full of water, our sweat can’t evaporate to cool us by absorbing the heat of vaporization from our skin.\u00a0 But unless your components have sweat glands, that has nothing to do with your question.<\/p>\n

Specific heat (Cp) changes with humidity, but I don’t think we care about that, unless all we want to know is the temperature rise of the air instead of the components.\u00a0 Where I think humidity affects convection is that the water vapor increases the density of the air.\u00a0 In general, the higher the density of the fluid, the better the convective heat transfer.\u00a0 The question is, how much better?\u00a0 To find out, I cracked open a textbook on convective heat transfer.\u00a0 Unfortunately, the answer is not as simple as one would like, for the purposes of a short, entertaining column like this.\u00a0 But here goes anyway.\u00a0 There are lots of empirical relationships for convective heat transfer, and they all have a form similar to this:<\/p>\n

Nu = C Rem<\/sup> Prn\u00a0<\/sup><\/strong><\/p>\n

where Nu is the Nusselt Number, Re is the Reynolds Number, and Pr is the Prandtl Number.\u00a0 I swore I’d never write an article using the Nusselt Number, but, darn it all to heck, there’s no way out of it this time.<\/p>\n

Let’s start by getting rid of the Prandtl Number.\u00a0 It is a property of the fluid, and since we are talking about air in both cases (as opposed to maybe comparing air to liquid sodium), Pr doesn’t change, so we can just ignore it completely, along with its little bothersome exponent “n”.\u00a0 (Maybe Pr does change a little with humidity, but let’s not get into that.)<\/p>\n

The Nusselt Number is a dimensionless form of the heat transfer coefficient (h), given by<\/p>\n

Nu = (h L)\/ k<\/strong><\/p>\n

where L is some length scale of the problem and k is the thermal conductivity of the fluid.<\/p>\n

The Reynolds Number is another dimensionless number defined as<\/p>\n

Re = (velocity x density x L) \/ viscosity<\/strong><\/p>\n

C, m and n are “constants” that change depending on the flow situation, such as whether it’s in a duct or over a flat plate or through\u00a0 pipe bundles, whether you have turbulent or laminar flow, constant flux or isothermal surfaces, and on and on.\u00a0 Every little situation has its own set of C, m and n.\u00a0 For our purposes, all we really need to care about is m, and you’ll soon see why.<\/p>\n

Why do we even need to bring up the Nusselt Number?\u00a0 You asked how component temperature varies with Relative Humidity.\u00a0 Here is how I will try to connect the dots:\u00a0 component temperature depends on the heat transfer coefficient, the heat transfer coefficient depends on Nu, Nu depends on Re, and Re depends on density, and finally, density depends on humidity.\u00a0 Got that?<\/p>\n

Now I’m going to speed up a little, because equations get boring real fast.\u00a0 Here is the basic equation for the temperature rise of your component above the ambient:<\/p>\n

temperature rise = Power \/ (h x Area)<\/strong><\/p>\n

Let’s divide the temperature rise at one relative humidity by the temperature rise at another,\u00a0 to get this:<\/p>\n

(temperature rise2 <\/sub>\/ temperature rise1<\/sub>) = (h1<\/sub> \/ h2<\/sub>)<\/strong><\/p>\n

Notice how conveniently the Power and Area cancel out.\u00a0 The same thing happens when we throw in the Nusselt Number expression for h.\u00a0 All the constants, the length scales, the velocities, the viscosities all cancel out, assuming that they don’t change with humidity.\u00a0 (This analysis only applies to fan cooling, not natural convection.\u00a0 I am assuming you have a fan cooled system, since you didn’t tell me.)\u00a0 The only thing left is the density, which we assume is not constant with humidity, and the exponent “m” that goes along with it.<\/p>\n

(temperature rise2 <\/sub>\/ temperature rise1<\/sub>) = (density1<\/sub> \/ density2<\/sub>)m<\/sup><\/strong><\/p>\n

What does this mean?\u00a0 It means, in general, as the density goes down, your temperature rise will go up.\u00a0 How strong this function is depends on the value of the exponent “m”.\u00a0 If m is a big number, the function is strong.\u00a0 If m is 1, then the temperature rise is inversely proportional to the density.\u00a0 If m is 2, then temperature will increase much faster.<\/p>\n

In the textbooks I checked, m ranges from 0.2 to 0.8.\u00a0 That means the function is weaker than being inversely proportional.\u00a0 Let’s assume the worst, that m = 0.8.\u00a0 If the density decreases by 50%, the temperature rise will increase only by 38%.<\/p>\n

Now we think we have a handle on how component temperature changes with density (if you believe any of that Nusselt Number\/ Reynolds Number stuff.)\u00a0 But how does air density change with Relative Humidity? \u00a0This part is not so simple either.\u00a0 There isn’t a simple equation.\u00a0 It is time for the big trick of the show — the Psychrometric Chart.<\/p>\n

When I was a college kid, all the engineers had a textbook with a fold-out, and not the full-color, airbrushed kind.\u00a0 Thermodynamics texts had a Psychrometric Chart in the back, that look like this:<\/p>\n

\"\"<\/a>

The Psychrometric Chart<\/p><\/div>\n

Since water vapor in air behaves very little like an ideal gas, we needed such a chart to find the properties of humid air.\u00a0 Don’t worry, you won’t have to learn to read such a monster — it has all been computerized for you.\u00a0 (Check out www.parkssoft.com\/ez_info.html <\/a>or www.linric.com\/webpsysi.htm<\/a> for examples.)\u00a0 From my faded and yellowed chart that I dug out of the appropriately damp basement, I find the water content of air in your two cases to be:<\/p>\n

\n\n\n\n\n\n
Case<\/td>\nTemperature<\/td>\nR.H.<\/td>\nkg H2<\/sub>O \/ kg dry air<\/td>\n<\/tr>\n
1<\/td>\n21<\/td>\n55%<\/td>\n0.0086<\/td>\n<\/tr>\n
2<\/td>\n50<\/td>\n23%<\/td>\n0.017<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

At 50C and 23% R.H. there is actually twice as much water in the air then at 21C and 55% R.H.\u00a0 So the air is denser at your higher ambient.\u00a0 Not what you expected, eh?\u00a0 (Me neither.)\u00a0 So the heat transfer will work a little better in Case 2 than in Case 1.\u00a0 How much better?<\/p>\n

There is also surprisingly little water in the air, so when it doubles, it doesn’t have much effect on the overall density of the air\/water mixture.\u00a0 The change in air density between Case 1 and Case 2 due to water vapor is about 0.8%.<\/p>\n

If you use the highest value of m to get the change in component temperature rise, you would get a reduction of about 0.6%.\u00a0 In your example the temperature rise was 28 degrees.\u00a0 The change due to humidity would be about 0.2 degrees C.<\/p>\n

So you can pretty much forget about the Relative Humidity.\u00a0 It is probably smaller than your experimental error.\u00a0 (As Van Johnson says, in my favorite line from Brigadoon, “It’s not the heat, it’s the humanity.”)<\/p>\n

But now that you brought up the subject, I can’t let you off the hook so easily.\u00a0 You were worried about humidity, but you didn’t even ask about the change in air temperature itself.<\/p>\n

[2012 Update: \u00a0alert readers sent in a correction after this article was first publsihed in 2001. \u00a0Adding water vapor to air actually reduces its density, because water vapor is less dense than dry air. \u00a0So the higher the Relative Humidity, the lower the density, the worse the convection, and the higher the component temperature. \u00a0The effect is still small enough to forget about, but we might as well get the physics right.]<\/p>\n

According to the Ideal Gas Law, when air temperature goes up from 21 deg C to 50 deg C (actually, from 294 to 323 K), its density goes down about 10%.\u00a0 That’s an order of magnitude bigger than the change due to humidity.\u00a0 Following my Nusselt Number argument, that could lead to an increase in component temperature rise as much as 7.8%, or about 2 degrees C, in your example.<\/p>\n

Forgot the Ideal Gas Law?\u00a0 Here is the version you need:<\/p>\n

(density2<\/sub> \/ density1<\/sub>) = (T1<\/sub> P2<\/sub>) \/ (T2<\/sub> P1<\/sub>)<\/strong><\/p>\n

where T is absolute temperature, and P is pressure.<\/p>\n

Pressure!\u00a0 You didn’t forget the pressure, did you?\u00a0 Did you record the barometric pressure at the time and location of your test?\u00a0 Density is directly proportional to the pressure, which can vary about 5% due just to changes in the weather.\u00a0 And, of course, it varies with altitude.\u00a0 What is the highest altitude at which your product is supposed to work?\u00a0 Better find out.\u00a0 That has the biggest affect on density of all these factors.\u00a0 For example, the density decreases by nearly 50% when you go from sea level to 13,000 ft.<\/p>\n

But, other than that, just go ahead and add the difference between your test ambient and 50 deg C to your component temperature.\u00a0 Feel any less sweaty yet?<\/p>\n

[Another 2012 update: \u00a0Another alert reader explained that I forgot to mention that the conductivity of air increases with temperature. \u00a0The increase in conductivity tends to cancel out the decrease in density, so that the convection itself does not change much as the ambient temperature goes up.]<\/p>\n

\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014<\/strong><\/p>\n

Dear Tony,<\/em><\/p>\n

That Nusselt Number stuff is very convincing.\u00a0 It’s always hard to argue with an equation that has fractional exponents.\u00a0 Is there any experimental evidence that says that component temperature increases with the fractional power of the air density?<\/em><\/p>\n

Skeptic from Missouri<\/em><\/p>\n

 <\/p>\n

Dear Skep,<\/p>\n

There are a few articles that give methods of correcting temperatures for different altitudes (which is the same thing as density.)\u00a0\u00a0 They give pretty much the same reasoning about Reynolds and Nusselt Numbers, with some other wrinkles thrown in.\u00a0 Some even give specific correction factors to predict component temperatures at different altitudes.\u00a0 But none are backed up by any experimental data, as far as I know.<\/p>\n

I have done a few simplistic tests on real circuit boards in altitude chambers.\u00a0 They seem to suggest that component temperature depends on more than just the change in density.\u00a0 All temperatures do increase as the density decreases.\u00a0 But many of the components did NOT increase as much as the Nusselt Number method would suggest, and I don’t know why.\u00a0 None increased MORE than the Nusselt Number method predicted.\u00a0 So the method is conservative, and, so far, it’s the only thing I have to work with.<\/p>\n

Sounds like a good research project for a university that has an electronics cooling program and an aeronautical engineering lab that might have a low pressure wind tunnel.\u00a0 Any body interested?\u00a0 I’ll kick in $75 from my research support budget.<\/p>\n

\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014<\/strong><\/p>\n

Isn\u2019t Everything He Knows Wrong, Too?<\/strong><\/p>\n

The straight dope on Tony Kordyban<\/em><\/strong><\/p>\n

\"\"<\/a>Tony Kordyban has been an engineer in the field of electronics cooling for different telecom and power supply companies (who can keep track when they change names so frequently?) for the last twenty years.\u00a0 Maybe that doesn\u2019t make him an expert in heat transfer theory, but it has certainly gained him a lot of experience in the ways NOT to\u00a0cool electronics.\u00a0 He does have some book-learnin\u2019, with a BS in Mechanical Engineering from the University of Detroit (motto:Detroit\u2014 no place for wimps) and a Masters in Mechanical Engineering from Stanford (motto: shouldn\u2019t Nobels count more than Rose Bowls?)<\/p>\n

In those twenty years Tony has come to the conclusion that a lot of the common practices of electronics cooling are full of baloney.\u00a0 He has run into so much nonsense in the field that he has found it easier to just assume \u201ceverything you know is wrong\u201d (from the comedy album by Firesign Theatre), and to question everything against the basic principles of heat transfer theory.<\/p>\n

Tony has been collecting case studies of the wrong way to cool electronics, using them to educate the cooling masses, applying humor as the sugar to help the medicine go down.\u00a0 These have been published recently by the ASME Press in a book called, \u201cHot Air Rises and Heat Sinks:\u00a0 Everything You Know About Cooling Electronics Is Wrong.\u201d\u00a0 It is available direct from ASME Press at 1-800-843-2763 or at their web site at\u00a0http:\/\/www.asme.org\/pubs\/asmepress<\/a>,\u00a0\u00a0<\/em><\/strong>Order Number 800741.<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Answers to those Doggone Thermal Design Questions By Tony Kordyban Copyright by Tony Kordyban 2001   Dear Thermal Answering Man, I did a thermal test at room temperature (around 21 deg C) and at 55% Relative Humidity (RH) and I got a component temperature of 49 deg C.\u00a0\u00a0 That seemed good because the component is […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-322","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/pages\/322","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/tonykordyban.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=322"}],"version-history":[{"count":3,"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/pages\/322\/revisions"}],"predecessor-version":[{"id":327,"href":"http:\/\/tonykordyban.com\/index.php?rest_route=\/wp\/v2\/pages\/322\/revisions\/327"}],"wp:attachment":[{"href":"http:\/\/tonykordyban.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=322"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}