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(#104) Why Thermal Calculations Fail in Reality · Mechanical Engineering Made Simple

• 0:00
  Welcome back to Mechanical Engineering Made Simple.
• 0:02
  Today we're doing a deep dive for a listener grappling with,
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  well, arguably the most frustrating question in
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  engineering Why is my system overheating when the
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  calculations say it shouldn't? Oh, absolutely.
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  It's that that deep chasm between theory and reality,
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  isn't it? It really is, and we've got a
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  fantastic stack of sources for this one.
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  We're covering everything from, you know, microscale thermal
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  properties and chip packages. All the way U to the mechanics
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  of these massive industrial heat exchangers.
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  Right. And our mission today is really
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  to understand why our perfect clean theoretical calculations
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  so often just collapse in the face of real world messiness.
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  OK, let's unpack this. We are tackling 5 key mysteries
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  that seem to plague every thermal designer.
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  Why are textbook constants are often wrong?
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  Why systems might meltdown at startup, and how to find that
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  single limiting factor the true thermal bottleneck in any
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  design? We're getting past the textbook
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  and into the actual science of system failure.
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  So we all know the routine you run the numbers.
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  You use the standard material properties, you plug in the
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  constants, and then you watch the prototype fail its thermal
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  stress test. You calculate a certain
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  temperature and the actual reading is 20° higher.
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  What did we miss? Well, the calculations are only
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  as good as the boundary conditions you define, and maybe
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  more importantly, they're only as good as the hidden thermal
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  resistance as you just assume away.
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  OK, that's where it gets really interesting.
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  When we talk about overall thermal resistance R sub T, we
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  often think of it as a simple series path.
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  You know hot fluid wall, All cold fluid, right?
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  But even for a basic heat exchanger, the heat has to fight
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  through as many as 5 resistances.
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  You've got convection on the hot side, conduction through the
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  wall, convection on the cold side.
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  And you're saying there's more? Yes, plus the fouling or build
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  up on both the hot and the cold surfaces.
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  And I imagine even simpler systems have their own hidden
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  complexities. They do take a microprocessor
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  package. The overall resistance R sub T
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  is the sum of the fundamental 1 dimensional resistance R1D and
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  this other thing called spreading resistance R sub
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  speed. Wait, what exactly is spreading
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  resistance for our listeners? Is that just the heat fanning
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  out from the source? Precisely.
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  If you have a tiny powerful heat source like a microchip, and
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  it's attached to a larger piece of metal like a heat sink base,
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  the heat has to spread out laterally to use the full
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  surface area of that heat sink. Our sub speed quantifies the
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  inefficiency of that lateral heat spread.
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  If you don't account for it, you think your heat sink is working
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  a lot harder than it actually is.
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  That makes perfect sense. So let's talk about the the
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  absolute king of overlooked dermal resistant.
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  Contact Resistance. Our sub Co Exactly.
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  This is so frequently underestimated, especially
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  mechanical joints that aren't, say, metallurgically bonded.
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  This is critical in industrial applications.
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  Just think about tubular heat exchangers.
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  I have one fluid flowing through a tube, another flowing outside.
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  If those tubes are simply expanded into the tube sheets.
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  Creating what's called an interference fit.
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  Right. If you do that, you absolutely
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  must anticipate significant bond or contact resistance.
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  That mechanical interference is great for a pressure seal, but
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  thermally it's just terrible. But if you braise them instead.
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  If those components are braised together, you're creating a true
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  metallurgical bond. Then for all practical purposes
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  you can neglect our subco entirely.
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  You have a continuous flow path for the heat.
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  If you don't braise, you're just relying on these microscopic
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  imperfect point contacts. So it sounds like what wrecks
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  are big macroscopic models. Is this friction at the
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  microscopic level? We assume 2 surfaces are
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  touching perfectly, but they're not.
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  They absolutely are not. For two rough non conforming
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  solids pressed together, the complex joint resistance R sub J
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  is actually 2 resistances working in parallel.
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  You have the actual metal to metal micro contact resistance.
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  RIIC. And you also have the micro gap
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  resistance RI nae. The micro gap is literally the
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  air or the fluid that's trapped between the rough peaks of the
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  two surfaces. And if you're operating in a
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  vacuum, say in a space application, those micro gaps
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  contain nothing. A vacuum contact, which means
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  that R my G value just skyrockets because there's no
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  Interstate official substance, no air, no grease to carry heat
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  across the gap. You're entirely dependent on
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  those few metal to metal contacts.
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  This is why engineers stress so much over minute surface
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  roughness standards. OK, so if our subco is so
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  critical, what's a classic real world scenario where an engineer
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  missed this and well paid for it?
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  The most common one I see is in thermal management for high
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  power LE DS or power electronics.
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  A designer specifies a certain thermal paste, you know the
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  interstitial substance for the joint between the component and
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  the heat sink. But then on the assembly line
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  they run out of the expensive stuff and swap it for a cheap
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  high viscosity gap filler with terrible thermal conductivity.
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  So the bond is fine mechanically, but the R sub code
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  just explodes. It explodes and the component
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  starts burning out prematurely. The calculation was perfect.
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  The assembly reality was completely flawed.
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  Now let's tackle that other classic problem.
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  Why does a prototype work erfectly in the lab but then
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  fail out in the field? This raises a really imortant
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  question. Are your test conditions
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  actually matching reality? The specs for high performance
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  chips, for instance, often assume something like a 45°C
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  ambient temperature. Which is hot, but it's a
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  controlled environment. Exactly.
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  But if the field environment where that equipment is
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  installed is hotter, say 60°C inside a tiny unventilated
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  telecom enclosure, your design immediately fails its thermal
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  requirement. And then of course things get
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  dirty over time, which was never an issue in the pristine lab
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  test. That is fouling.
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  It's the progressive accumulation of heat and
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  insulating substances on surfaces.
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  Fouling is an insidious thermal killer because it adds
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  resistance slowly over time. So if you design a heat
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  exchanger for a constant load, but forget to account for this
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  gradual insulation. You eventually lose performance.
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  It's guaranteed. The Tubular exchanger
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  Manufacturers Association TIMA provides guidelines for this.
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  They define specific fouling factors for common fluids.
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  Like what? Well, for heavy fuel oil, TIMA
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  says you have to factor in a resistance of 5.3 to 12.3.
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  If that resistance isn't built into your initial calculation,
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  field failure is just inevitable down the line.
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  We also need to think about bigger design flaws right?
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  Things that create pockets of insulating material like non
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  condensable gases. Indeed, this is a common and a
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  fascinating failure mode in large power plant surface
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  condensers, especially those with radial vapor flow into a
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  tube bundle. How does that work?
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  When steam condenses it shrinks and the non condensable air that
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  was initially dissolved in it just gets left behind.
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  If the design is poor, pockets of this gas form.
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  And those pockets act like insulation, blocking the steam
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  from reaching the cooling tubes. Exactly.
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  A good tube bundle layout has to be meticulous.
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  It requires that the pressure drop from the top of the bundle
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  all the way down to the air vent manifold is identical for all
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  possible vapor paths. That way you ensure A continuous
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  sweep of those gases out of the system.
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  OK, so we've covered the solid side resistances, both static
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  and fouling, but often the true variable we need to nail down is
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  on the fluid side, specifically that heat transfer coefficient
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  H. We know the textbook values are
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  fantasy, so how do we find the one we should actually use?
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  What's fascinating here is that we really need to move beyond
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  those simple correlations we all remember from school.
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  You know Nusselt equals C times Reynolds to the end times
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  Prantial to the M. Equals CER to the M Got it.
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  Real, right? Those are great for a basic
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  understanding, but they assume conditions that, well, they
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  rarely exist in the real world. You have to truly understand the
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  flow regime and the geometry. Right, because the textbook
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  Nusselt numbers like 3.66 for laminar flow in a round tube.
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  That only applies when the velocity and temperature
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  profiles are fully developed. Meaning the fluid has settled
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  into its final behavior pattern both mechanically and thermally.
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  But in reality, every process starts at an entrance, and that
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  entrance region changes everything.
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  So the heat transfer coefficient is higher at the start because
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  the fluid near the wall is still cold.
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  Much higher and that thermal development length X sub T is
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  the key. We so often miss in certain
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  thermally developing flows, especially when the Prandtl
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  number PR is much greater than one.
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  Which means the fluid thermal boundary layer is thin compared
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  to its velocity boundary layer. Right, in those cases that
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  thermal entrance length X sub T can be way greater than the
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  physical flow development length.
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  So the velocity profile might settle down quickly, but the
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  temperature profile keeps changing deep into the system.
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  Exactly. The fluid is moving at a stable
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  velocity, but it's still busy absorbing heat for a much longer
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  distance than you thought. If you ignore this entrance
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  region, you massively underestimate the heat transfer
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  coefficient you need for the device.
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  And how do we quantify that length?
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  We can approximate the thermal entrance length X sub T by
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  taking 10 to the -2 times the prantial number times the
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  hydraulic diameter D sub H times the Reynolds number re sub DH.
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  The big implication is that if you have a high prantle fluid
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  like oil, your thermal development zone is huge.
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  And the textbook coefficient just won't apply until much,
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  much farther downstream. Exactly.
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  And if you introduce phase change, say condensation or
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  boiling, those simple correlations don't just bend,
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  they completely break, right? In flow boiling and condensation
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  inside tubes, the heat transfer model has to account for the
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  flow pattern itself. Whether it's annular, stratified
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  slug or mist flow, the physics are wildly different.
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  And the predictive correlations are different for each one.
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  Wildly different. You might have a correlation
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  that's perfect for annular flow, where you have liquid in a ring
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  and vapor in the middle, but if your system briefly operates in
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  a slug flow regime where plugs of liquid block the tube.
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  That correlation is suddenly useless.
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  Totally useless. It's a detective game.
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  Just to choose the starting equation, you have to know your
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  flow pattern. Now for that classic mystery we
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  mentioned. Why does equipment spike in
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  temperature at startup and then just stabilize?
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  Feels like the system is getting used to the load.
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  What you're seeing are the effects of thermal mass and
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  transient behavior. It's transient versus steady
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  state blindness. If a solid has high thermal
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  conductivity and no external cooling, the initial temperature
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  rise rate is constant. We described that with a lump
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  capacity solution. Which relates the change in
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  temperature over time to the internal heating rate Q and the
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  mass specific heat product M * C sub P.
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  Correct. So the initial concentrated heat
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  input rapidly raises the temperature of the heat source
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  itself. That tiny high power element
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  before the larger surrounding structure, the thermal flywheel,
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  can respond and spread the heat out.
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  Thermal modeling of integrated circuit packages is actually
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  classified into four distinct time intervals after you apply
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  power. First is the early period, where
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  heating is confined entirely to the chip.
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  Second, the intermediate period where the dye bond and
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  encapsulate get involved. Third, the quasi steady period,
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  when the entire package begins responding and finally you reach
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  the steady state period. So that initial temperature
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  spike is confined to those early periods before the full thermal
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  mass of the package can even catch.
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  Up exactly, and the take away for our listener is that if your
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  temperature sensor is placed right next to the heat source,
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  you will capture that sharp, scary spike.
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  If it's far away on the casing, you might miss it entirely and
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  only see the gradual quasi steady rise.
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  Sensor placement determines which reality you measure.
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  And the startup change could also be fluid dynamics related
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  to, couldn't it? As things heat up, the fluid
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  properties change. Absolutely.
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  If the fluid in your heat exchanger starts cold, it's
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  viscosity is higher. That higher viscosity means
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  increased resistance to flow, which can decrease the flow rate
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  and the heat transfer coefficient leading to that
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  initial overheating. It all stabilizes as the control
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  system responds and the fluid temperature normalizes.
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  So it's this complex interplay between the components thermal
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  inertia and the fluid's properties changing dynamically.
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  It is so if we connect this to the bigger picture, successful
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  thermal management is often about just identifying the
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  weakest link, the thermal bottleneck in that entire
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  resistance chain. Right.
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  The total thermal resistance is the sum of all the individual
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  parts. Convection, conduction, fouling.
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  But which one is the problem? And this brings us to a crucial
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  design question. How do you know if conduction or
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  convection is the limiting factor?
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  And more importantly, when is adding fins completely
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  pointless? That's the $1,000,000 question
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  for a lot of engineers. It is.
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  Extended surfaces or fins are primarily effective only when
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  the convective heat transfer coefficient H is low.
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  Fins exist to dramatically increase the surface area when
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  the environment, the air or the fluid is just not good at
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  pulling heat away. But if the material side, the
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  internal conduction resistance L / K is already the bottleneck
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  because the thermal conductivity K of the material is poor.
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  Then adding fins is utterly pointless.
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  The heat can't even get efficiently from the base of the
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  fin out to its tip. So if you have a massive
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  aluminum radiator trying to cool something but the material is
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  bad, you have a conduction limited problem.
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  More fins just means more metal that the heat can't even reach.
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  Exactly. We measure this with something
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  called fin efficiency ETA. For an optimal design, you
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  usually want that efficiency to be between .5 and .7.
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  If your calculated efficiency is, say .2, that means 80% of
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  your fin surface is barely contributing.
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  You need to focus on the material conductivity, not
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  adding more surface. Area precisely.
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  And conversely, think about plate fin heat exchangers, where
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  one fluid, like a liquid, has a huge heat transfer coefficient
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  compared to the other, like air. In that case, it is entirely
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  permissible to have no extended surface in the core on the
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  liquid side. Why add metal when the fluid is
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  already doing an excellent job of pulling the heat away?
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  Exactly. The convection resistance is
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  negligible there, so the entire design focuses on boosting the
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  air side. So what does this all mean?
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  How do we use this knowledge to design better systems from the
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  very start? The ultimate goal should be
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  something called Entropy Generation Minimization, or EGM.
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  This is the philosophy that says you have to design systems that
• 14:27
  minimize waste and irreversibility.
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  This is different from a standard exergy analysis.
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  It is because EGM specifically forces you to adjust the
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  physical characteristics of the design, the geometry, the
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  materials, the finite dimensions to minimize that
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  irreversibility, not just rely on general thermodynamic
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  parameters. So EGM sounds like the process
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  of finding the optimal compromise between flow
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  resistance and heat transfer surface area.
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  It is precisely that balance. For systems cooled by forced
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  convection channels, like micro channels in a chip cooler, an
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  optimal channel size D exists. This is where EGM shines.
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  If D is too large, your total heat transfer surface area is
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  too small and the walls overheat.
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  But if D is too small, the flow resistance is incredibly high,
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  requiring huge pumping power and causing friction that can
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  overheat the entire volume. EGM helps you locate that sweet
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  spot. We started this deep dive with
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  five common points of failure in thermal design, and what we
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  found is that every problem really boils down to correcting
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  a flawed initial assumption. Right under Estimating contact
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  resistance, ignoring transient startup behavior, applying
• 15:34
  correlations outside their applicable flow regime.
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  Or just failing to factor in environmental variables like
• 15:39
  fouling. From that simple textbook
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  equation Q equals UA delta T to a robust real world design
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  requires recognizing that physical reality, like fouling
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  over time or the geometry of microscopic contacts always
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  introduces resistance that are ideal models neglect.
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  So successful mechanical engineering is minimizing the
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  destruction of extra G quantified as T naughty
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  multiplied by S Gen. that's introduced by all these real
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  world constraints. Exactly.
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  That sets us up for the future then.
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  Yeah. The highest heat flux is
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  forecasted for high performance computer chips back in 2006.
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  We're about 30.7 watts per centimeter squared.
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  Given the relentless trend toward miniaturization and power
• 16:20
  density today, how did the complexities of micro scale heat
• 16:23
  transfer, where effects are governed by electron and phonon
• 16:26
  interactions and continuum models, start to break down?
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  How does that challenge the basic principles we discussed
• 16:31
  today? It forces us to rethink
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  everything we thought we knew about thermal resistance.
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  That was a seriously deep dive into the world of thermal
• 16:38
  physics. Thank you for providing the
• 16:40
  sources for this exploration and you, our listener.
• 16:42
  If you haven't already, get over to our YouTube channel
• 16:45
  Mechanical Engineering Made Simple, where we post hands on
• 16:48
  how to videos, visual breakdowns, and practical
• 16:51
  engineering walkthroughs. You can actually use a family
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  that solves together, stays together.