Intuition The one core ideaA working chip is constantly pouring heat into a tiny spot, and that heat must escape to the room or the chip cooks itself. Everything in this topic is about measuring how easily heat flows from the hot chip to the cool air — and making that flow easier.
Before you can read a single formula in the parent note, you need to know what heat is , what "flows" means for it, and what each letter on the page stands for. We build every one of them here, from nothing, in the order they depend on each other.
T Temperature is a single number that says how hot something is. In this topic we measure it in degrees Celsius (°C) , where water freezes at 0 and boils at 100.
Symbol: T Picture: a thermometer — a tall scale where the marker rises as things get hotter.Why we need it: a chip has a safe temperature limit (often ~100 °C). Everything we do is to keep T
Deep inside a CPU there is the hottest spot, called the junction (where the transistors actually switch). Its temperature gets its own symbol:
T j junction temperature (the hottest inner point of the chip)T ambi e n t ambient temperature (the room air around the machine)
The whole cooling job is a journey: heat starts hot at T j T ambi e n t
Figure s01 — The heat journey. The picture below traces one lump of heat: it is born hottest at the junction (T j T ambi e n t
Intuition Difference, not absoluteWhat makes heat move is not how hot something is, but how much hotter it is than its surroundings. A 90 °C chip in a 25 °C room feels a "push" of 65 degrees. That push has its own symbol next.
We just named two temperatures: T j T ambi e n t T hot T cold whichever two points you are comparing — in the main CPU example they are T j T ambi e n t
The symbol Δ the change in " or "the difference in ". So:
Δ T = T hot − T cold T hot T cold T hot = T j T cold = T ambi e n t Δ T = T j − T ambi e n t
Plain words: how many degrees hotter one place is than another.Picture: the height of the drop on the thermometer scale between the chip and the air.Why we need it: heat only flows when there is a difference. No difference (Δ T = 0
Intuition Sign convention — keepΔ T from hotter, so Δ T ≥ 0 Δ T into the chip (a heating case) — which never happens in normal cooling. So: always write Δ T = T hot − T cold
This is the single most reused quantity in the whole parent note, so lock it in.
Reveal Δ T = T hot − T cold T j − T ambi e n t gap that drives heat flow, always ≥ 0
Heat is a form of energy. But we rarely care about a lump of energy; we care about the rate it arrives — how much heat per second.
Definition Power and heat-flow ratePower P watts (W) . One watt = one joule of energy every second.
Symbol: P Q same quantity when they mean "heat flowing through a slab." P Q P Q P Picture: water pouring from a tap — the flow rate (litres per second), not the total pool.Sign/domain: P ≥ 0 produces heat, so the flow is always outward. A chip at rest makes P = 0 Why we need it: a CPU's TDP tells you how many watts of heat it dumps. That is the "flow" the cooler must carry away continuously.
Intuition The bucket picturePicture a bucket with a hole. Water pours in at rate P out through the hole (the cooling). If the hole is too small, water level (temperature) climbs until it overflows — overheating. Cooling design is just "make the hole big enough for the incoming P
Figure s02 — The bucket analogy. Water flows in from the top at rate P
Heat can only get from chip to air by three routes. You must recognise all three by name.
Definition Conduction, convection, radiation
Conduction — heat crawls through a solid by jostling neighbours. Picture: a metal spoon in hot tea; the handle warms even though it never touched the tea. This carries heat from chip into the heatsink. Convection — a moving fluid (air or water) scoops up heat and carries it away bodily. Picture: blowing on hot soup; the breeze hauls heat off the surface. This carries heat from heatsink into the room air. Radiation — heat leaves as invisible light (infrared). Picture: feeling warmth from a fire without touching it. Minor here (<5%) at chip temperatures.
For electronics: conduction then convection , in that order, is the main path.
Which mechanism moves heat through solid metal? Conduction.
Which mechanism needs moving air or liquid? Convection.
Which one dominates only in space or at very high temperatures? Radiation.
This is the idea the whole parent note is built on, so we earn it slowly.
We already have two quantities:
P Δ T
R t h P how many degrees hotter does the source get?" A path that heats up a lot for little power is a bad cooler; a path that stays cool is a good cooler. We need one number that captures this "difficulty of flow."
Definition Thermal resistanceThermal resistance R t h R t h = P Δ T [ W °C ] Δ T ≥ 0 P ≥ 0 ≥ 0
Picture: a narrow pipe. Squeeze more flow (P Δ T R t h Why this exact tool? Because it lets us predict temperature with simple arithmetic instead of solving physics every time. Rearranged, Δ T = P ⋅ R t h
Intuition Why "resistance" — the electricity analogyThis is a deliberate copy of Ohm's law from electricity, V = I ⋅ R
voltage V Δ T
current I P
electrical resistance R R t h the same trick works: resistances in series add up. That is why the parent note simply sums them.
Figure s03 — Resistances in series. Three resistances (chip, paste, heatsink) sit end to end. The single red arrow is the heat flowing straight through all three — since it must cross each in turn, their resistances simply add to one total between T j T ambi e n t
Common mistake Higher number ≠ betterBig R t h bad (hard for heat to escape, chip gets hot). A great cooler has a small R t h
The parent note's two formulas use extra letters. Each is a plain physical thing.
Definition The geometry and material letters
k thermal conductivity — how naturally a material passes heat. Copper k = 400 k = 205 k ≈ 0.025 A area — the size of the surface heat crosses, in square metres. Picture: the width of a doorway; wider lets more through.d thickness — how far heat must travel through a slab, in metres. Picture: how long the doorway tunnel is; longer is harder.h heat transfer coefficient — how well moving fluid carries heat off a surface (W/m²·K). Unlike k fast the air moves, not just what it is.
Intuition Why area and thickness pull opposite waysMore area A d
This formula is not pulled from nowhere — it is Fourier's Law of conduction rearranged, and it only holds under three simple assumptions.
Read R t h , co n d = k A d d k A
Intuition The invisible blanketRight at any surface, a paper-thin layer of air clings and barely moves. This boundary layer acts like an insulating blanket — heat has to conduct slowly across it before the breeze can carry it off. A fan's real job is to rip this blanket thin , letting heat escape faster. That is why h
Why does a fan improve cooling so dramatically? It thins the insulating boundary layer of stagnant air, raising h
Mechanisms conduction convection radiation
Material k area A thickness d
Series sum of resistances
Predict junction temperature
Design the cooling solution
Every arrow is a "you must know this first" link: you cannot understand R t h Δ T P k A d
Cover each answer and test yourself. If any one stumps you, re-read its section above.
What does T j Junction temperature — the hottest inner point of the chip; it hits the safety limit first.
Write Δ T Δ T = T j − T ambi e n t ≥ 0
What are the units of power P Watts; 1 watt = 1 joule of heat energy every second.
P Q Same quantity (watts of heat); the parent note uses Q P
Name the three heat-transfer mechanisms and which two dominate in a PC. Conduction, convection, radiation; conduction and convection dominate.
State the definition of thermal resistance R t h R t h = P Δ T
Is a large R t h Bad — it means big temperature rise per watt, i.e. poor cooling.
Why do thermal resistances in series add? Because it copies Ohm's law (V = I R
Derive R t h , co n d = d / ( k A ) Fourier: P = k A Δ T / d R t h = Δ T / P Δ T d / ( k A ) k
What three assumptions sit behind R t h , co n v = 1/ ( h A ) Constant h
Related: Heat dissipation and cooling solutions · Thermal Design Power (TDP) · Thermal throttling · Heat pipes · Reliability and MTBF
