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(#75) The Five Hidden Thermal Design Failures · Mechanical Engineering Made Simple

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  Welcome back, design junkies, to mechanical engineering made
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  simple. And welcome to a deep dive that
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  I think is for anyone who's ever been just completely blindsided
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  by a thermal system that refuses to cool down.
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  Oh, we've all been there. You follow the rules from the
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  textbook, right? You add more fins, you switch to
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  copper, you run the SIM. And you think I've nailed this?
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  And then you build it, you power it up.
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  And the temperature drops by, what, a few degrees when you
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  really needed thirty? It is absolutely madding.
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  It's so frustrating, and it's because thermal management is,
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  you know, it's a game of these invisible resistances.
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  If you optimize the wrong one, you're just wasting time and
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  money. So that's our mission today.
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  We're going to isolate 5 fundamental recurring reasons
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  why these thermal designs just stall out.
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  We want to help you stop chasing those tiny games.
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  And instead focus on the core physics that actually dictates
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  the system temperature. We're going to look at
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  everything from microchips to these massive industrial heat
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  exchangers. OK, so our blueprint is to find
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  the five invisible walls that Heat just can't seem to get
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  through. This is about helping you stop
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  just throwing copper at a problem and start optimizing the
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  right part of the system. Let's start with, I think the
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  most intuitive one, but also the most misunderstood.
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  The trap of just assuming more surface area is always better.
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  But isn't that the golden rule of convection?
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  I mean if I want to get more heat into the air, I need more
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  area for the air to touch. Why doesn't doubling the fins
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  give me double the performance? Because you hit a point of
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  diminishing returns and it's governed by two main things, the
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  efficiency of the fin itself and then the the fluid mechanics of
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  the air flowing over it. OK, let's break that down.
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  Start with fin efficiency. Right, so we use the term fin
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  efficiency, we call it ETA to measure this.
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  If a fin is too long or say, too thin, the heat just can't make
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  it all the way to the end. So the tip of the fin is much
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  cooler than the base. Exactly, and by the time you get
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  to the tip, the temperature difference between the fin and
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  the air is so small that it's barely transferring any heat at
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  all. So you've just got this
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  expensive piece of metal sitting out there doing nothing.
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  It's basically just mass. It's wasted mass.
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  It's a perfect way to put it. For a well designed fin, you're
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  looking for an efficiency and ETA of somewhere between say .5
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  and .7 and if it's. Lower than .5.
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  The heat isn't getting out there.
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  You need to make your fins shorter or maybe thicker.
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  You're just not using the material effectively.
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  OK so I optimize my fin geometry.
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  I hit that .5 to .7 range. Have solved the material side,
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  but you said there's a second problem.
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  The airflow becomes the bottleneck.
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  That's where the boundary layer takes over.
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  I mean, even if you had infinite surface area, if the air can't
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  physically get there to pick up the heat, you've got nothing.
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  The heat is trapped. Yeah, you see this with really
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  tightly cacked circuit boards. The air just feels stagnant.
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  Precisely. If you look at vertical plates
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  cooled by natural convection, which is super common in
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  electronics, there's this fascinating thing that happens
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  if the boards are too close. The boundary layers from each
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  board merge together. They do, they merge and they
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  literally choke the flow path. The air can't get through to
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  carry the heat away and your overall heat transfer just
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  plummets. So there has to be an optimal
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  spacing. There is, and it's all about
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  optimizing for the fluid dynamics.
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  There's an actual mathematical correlation for it.
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  For for symmetric isothermal plates, this optimal spacing or
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  B opt is 2.714 times P to the power of 1/4.
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  That's incredibly specific, but the point is, it's not just some
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  academic number. Getting that spacing right can
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  be the difference between a working design and a failure.
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  It really can. It's a fundamental redesign, not
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  just a marginal gain, OK. That leads perfectly into the
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  second failure point, the hidden barrier contact resistance.
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  Because you can have the best heat sink in the world, but if
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  the heat can't get into it. Then all that work is for
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  nothing, and contact resistance is, I think, the most insidious
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  one because it's microscopic. We think of 2 flat metal
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  surfaces and we assume they're perfectly touching.
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  But they're not. They're only touching at these
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  tiny little peaks, these disparities.
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  Right. Only a tiny fraction of the area
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  is actually making solid to solid contact.
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  The rest is just a gap, usually filled with air, which is a
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  great insulator. So the heat has to squeeze
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  through those tiny contact points.
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  Exactly that, joint resistance. Our sub J is super complex.
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  If you ignore radiation for a second it's basically 2 paths in
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  parallel. You have the heat going through
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  the micro contacts and then you have heat trying to get through
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  the gas in the micro gaps. And this is where we use thermal
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  interface materials, right? The thermal grease or the pads?
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  But it sounds like even they are fighting a losing battle against
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  the surfaces themselves. They are the resistance of the
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  Tim itself. Our sub Tim depends on its
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  thickness and conductivity. Sure, but it also critically
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  includes the contact resistance R sub Co, which is dominated by
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  the surface roughness of your two parts.
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  Let's call them Sigma 1 and Sigma 2.
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  Hold on. So if I buy the world's most
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  expensive thermal grease, but I put it between two really rough,
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  poorly machine surfaces. The roughness kills the
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  performance absolutely, because those rough surfaces create
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  bigger gaps, which means you need a thicker layer of grease
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  to fill them, and that just increases the resistance.
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  So spending time on a better surface finish might be way more
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  valuable than spending money on a slightly better Tim.
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  Often yes. Think about industrial stuff
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  like air coolers with high fin tubes.
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  If you just press fit the tubes into the plates, you have to
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  assume there's going to be a huge unpredictable contact
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  resistance. But if you braise them.
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  If you braise them, you create a metallurgical bond.
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  It's fused. The contact resistance basically
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  goes to 0. It's all about the interface
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  mechanics, not just the material.
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  Which brings us to failure #3 and this one is a classic.
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  Why did switching my material from aluminum to copper barely
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  change the temperature? Yes, a great material
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  switcheroo. This is all about system
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  resistance dominance. You've just successfully
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  optimized the wrong link in the chain.
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  You. Have to think of it like a
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  circuit, a series of resistors. Exactly, heat has to flow from
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  the source through the solid into the coolant.
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  In a big heat exchanger you might have like 5 resistances in
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  that chain. What are they?
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  You've got the hot side convection, then hot side
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  fouling, then the conduction through the wall itself, then
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  cold side fouling, and finally cold side convection.
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  And the material choice, the copper or aluminum, that only
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  effects one of those five, the solid wall conduction.
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  And if that one link is only, say, 5% of the total resistance
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  in the system, you could use a material with infinite
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  conductivity and you'd still only see a 5% improvement.
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  The problem is somewhere else. It's being dominated by
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  convection or what's fouling. Fouling is huge in industrial
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  settings. It's just chunk, scale, rust,
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  sludge, whatever building up on the surfaces and forming an
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  insulating layer. Like putting a tiny little
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  velvet jacket on your heat exchanger.
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  A very effective insulating velvet jacket.
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  The tubular exchanger Manufacturers Association TIMA
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  even publishes fowling factors. For something like heavy fuel
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  oil. That fowling layer can easily be
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  the single biggest resistance in the whole system.
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  Your choice of metal becomes totally irrelevant.
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  Wow. And you mentioned something
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  about complex electronics too, and it's a Tropic conductivity.
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  Right in a printed circuit board, it's a composite of
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  copper and Fr 4. The heat might flow really well
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  sideways through the copper planes.
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  But terribly downwards through the fiberglass substrate.
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  It's like a racetrack in One Direction and molasses in the
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  other. You can't just use one bulk
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  conductivity number for the whole board in your analysis.
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  You have to model the layers or you'll get completely wrong.
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  OK, so that covers the steady state world.
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  Our 4th failure point is about timing.
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  How do I estimate heat up or cool down time?
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  Why does my steady state thinking fail me here?
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  Because predicting the final temperature is a totally
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  different problem from predicting how long it takes to
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  get there. That's transient analysis.
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  It's critical for anything with pulsed power.
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  Microprocessors, lasers, things that turn on and off really
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  hast. And the tool everyone reaches
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  for first is the lumped capacity solution.
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  Where do we go wrong with that? Well, lunch capacity is
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  beautifully simple. It just says the rate of
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  temperature change DT over DT is the heating rate Q divided by
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  the mass times the specific heat C sub P.
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  It assumes the entire object is at 1 uniform temperature at all
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  times. And that's the trap.
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  That assumption is only valid if the object has really high
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  thermal conductivity, so heat can spread through it almost
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  instantly. So if you use it on something
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  with low conductivity, like a big chunk of plastic.
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  The surface temperature will skyrocket while the inside side
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  is still cool. The models core assumption is
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  violated and you will dramatically underestimate the
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  peak temperature during that heat up phase.
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  And for something complex like a chip package, it's not even one
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  smooth curve, is it? Not at all.
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  There are actually 4 distinct phases.
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  First the chip period where the heat is just inside the tiny
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  silicon dye, then an intermediate period where the
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  dye bond and encapsulate get involved, then a quasi steady
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  period where the whole package starts to heat up, and finally
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  you reach steady state. So for pulse power, you have to
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  model those early stages correctly.
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  You do. You can't use a simple model and
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  expect an accurate answer for those very fast transients.
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  Which leaves our fifth and final failure point, radiation.
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  I think we all tend to ignore this unless something is
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  literally glowing red hot. So when does it matter at lower
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  temperatures? You're right, the classic
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  thinking is that radiation depends on the 4th power of
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  absolute temperature. You know the heat transfer rate
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  Q sub R is proportional to T1 to the 4th minus T2 to the 4th.
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  So it dominates at high temps. Right, if my controller is at 50
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  Celsius in a 20° room, I'm thinking convection is doing all
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  the work. And that is a big surprise.
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  Here's the aha moment for small temperature differences, like on
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  the order of 10 Kelvin, the effective radiation heat
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  transfer coefficient. There's a coefficient for it.
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  Yeah, we call it H sub R For an ideal black surface, that
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  coefficient is approximately equal to the heat transfer
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  coefficient for natural convection in air.
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  Wait a minute, you're saying that at near room temperatures,
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  radiation can be responsible for half of the total heat transfer?
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  It's a 5050 partner with natural convection.
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  In many common passive cooling scenario, yes, that completely
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  changes the calculation and it means you suddenly have to care
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  a lot about surface properties, specifically emissivity or
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  epsilon. Which is just a measure of how
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  well a surface radiates heat compared to a perfect black
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  body. Exactly.
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  So if you take your shiny aluminum heat sink and you paint
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  it matte black with a high emissivity coating, you can
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  potentially double its performance without changing the
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  airflow at all. But the flip side is what
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  happens over time. That's the other trap, surface
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  aging. In the real world, surfaces
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  oxidize, They get dirty. That pristine polished aluminum
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  from your CAD model might after six months, have a completely
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  different emissivity. It acts like a different
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  material. Thermally speaking.
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  You have to design for the real aged surface.
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  This has been a total teardown of the common failure modes.
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  So to recap, adding surface area fails because of fluid
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  mechanics. Switching materials fails
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  because another resistance like convection or contact is the
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  real bottleneck. Transient estimates fail because
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  we misuse simple models, and radiation is a silent 5050
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  partner to natural convection even when things aren't hot.
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  The big lesson here is that it's all about managing a chain of
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  resistances. It is.
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  Stop asking how do I make this heat sink better?
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  And start asking which of these five resistances is the single
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  biggest bottleneck in my system right now?
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  That's the question, and that leads to one final, maybe
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  provocative thought. We've been talking about
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  managing these resistances, which is really about managing
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  thermodynamic inefficiency. But what if we use that
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  inefficiency as our actual design guide?
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  So look beyond just making the temperature lower.
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  Exactly. I'd challenge you to look into
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  something called Entropy Generation Minimization, or EGM.
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  OK, that sounds pretty advanced. It is, but the goal is elegant.
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  It guides you to the optimal physical design, the dimensions,
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  the shapes, the materials by directly linking thermodynamic
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  non ideality like temperature differences and pressure loss to
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  the physical system itself. So it's not just how hot is it,
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  but also how much energy am I wasting to pump this fluid?
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  It's a total system view. It forces a holistic view.
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  You're not just minimizing temperature, you're minimizing
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  the total entropy generated by all the irreversible processes
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  in your system. By doing that, it guides you to
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  the true balanced optimum, not just the one that's least bad in
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  one category. That's a really powerful
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  framework. Thank you for guiding us through
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  all these invisible forces that can really sabotage a design.
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  My pleasure. Until next time, keep digging
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  deep.