Heat dissipation and cooling solutions

The physics of heat transfer

Heat moves from hot to cold through three mechanisms:

Conduction: heat flows through solid materials (chip → heatsink)
Convection: moving fluid (air/liquid) carries heat away (heatsink → environment)
Radiation: electromagnetic waves carry heat (minor at<100°C, dominates in space)

For electronics, conduction + convection dominate. Radiation contributes <5% at typical operating temperatures.

Formula Fourier's Law (conduction)

Heat flow through a material: $Q = \frac{k \cdot A \cdot \Delta T}{d}$

$Q$ = heat flow rate (watts)
$k$ = thermal conductivity (W/m·K) — material property
$A$ = cross-sectional area (m²)
$d$ = thickness (m)
$\Delta T$ = temperature difference across the material

Derivation from first principles: Heat diffuses down temperature gradients. In1D steady state, the heat flux (W/m²) is proportional to the temperature gradient: $q = -k \frac{dT}{dx}$ . For a slab of thickness $d$ with constant $k$ , integrate: $q = -k \frac{T_2 - T_1}{d} = k \frac{\Delta T}{d}$ Total heat flow is flux times area: $Q = q \cdot A = \frac{k \cdot A \cdot \Delta T}{d}$ .

What this tells us:

Double the area → double the heat flow (why heatsinks have fins)
Double the thickness → halve the heat flow (why thermal paste is thin)
High $k$ materials (copper: 400 W/m·K, aluminum: 205 W/m·K) move heat faster

Thermal resistance from Fourier's law: $R_{th,cond} = \frac{d}{k \cdot A}$

Formula Newton's Law of Cooling (convection)

Heat transfer to moving fluid: $Q = h \cdot A \cdot \Delta T$

$h$ = heat transfer coefficient (W/m²·K) — depends on fluid, velocity, geometry
$A$ = surface area
$\Delta T$ = surface temperature minus fluid temperature

Why this form? At the surface, a thin boundary layer of slow-moving fluid acts like insulation. Faster flow thins this layer, increasing $h$ . Unlike conduction, $h$ is not just material property—it depends on flow dynamics.

Typical values:

Natural convection (still air): $h \approx 5\text{–}10$ W/m²·K
Forced convection (fan, 2 m/s air): $h \approx 50\text{–}100$ W/m²·K
Liquid cooling (water): $h \approx 500\text{–}1000$ W/m²·K

Thermal resistance from convection: $R_{th,conv} = \frac{1}{h \cdot A}$

Total thermal resistance: resistances in series add. $R_{th,total} = R_{junction\text{-}case} + R_{case\text{-}heatsink} + R_{heatsink\text{-}ambient}$

Figure — Heat dissipation and cooling solutions

Worked example Example 1: CPU thermal path calculation

Given: CPU dissipates 150 W. Junction-to-case $R_{th} = 0.2$ °C/W (inside chip package), thermal paste $R_{th} = 0.1$ °C/W, heatsink-to-ambient $R_{th} = 0.3$ °C/W. Ambient air is 25°C. Find junction temperature.

Solution: Total resistance: $R_{th,total} = 0.2 + 0.1 + 0.3 = 0.6$ °C/W

Temperature rise: $\Delta T = P \cdot R_{th} = 150 \times 0.6 = 90$ °C

Junction temperature: $T_j = T_{ambient} + \Delta T = 25 + 90 = 115$ °C

Why each step?

Series resistances add because heat flows through each sequentially
Multiply by power to get temperature rise (Ohm's law analog: $V = I \cdot R$ )
Add ambient temperature because we measure relative to environment

Worked example Example 2: Heatsink fin design

Given: Need to dissipate 80 W with max 60°C rise. Ambient 30°C, so heatsink base can't exceed 90°C. Junction-to-heatsink base is already 0.25 °C/W. What heatsink thermal resistance do we need?

Solution: Temperature rise budget: $90 - 30 = 60$ °C

$R_{th,total} = \frac{\Delta T}{P} = \frac{60}{80} = 0.75$ °C/W

Heatsink resistance: $R_{th,hs} = 0.75 - 0.25 = 0.5$ °C/W

Why? The 0.25 °C/W is upstream (chip to heatsink base), leaving 0.5 °C/W budget for heatsink base to ambient. To achieve this:

Increase fin surface area (lower $R_{conv} = 1/(h \cdot A)$ )
Increase airflow (raise $h$ )
Use copper instead of aluminum (lower $R_{cond}$ in fins)

Cooling solution categories

1. Passive cooling (no moving parts)

Heatsinks conduct heat from the component to fins that increase surface area for natural convection.

Design elements:

Material: Copper ( $k = 400$ W/m·K) or aluminum ( $k = 205$ W/m·K). Copper is 2× better thermally but 3× heavier and costlier. Aluminum is standard; copper for extreme cases.
Fin geometry: Thin, tall fins maximize area but restrict airflow. Optimal spacing is ~2–3 mm for natural convection, ~1–2 mm for forced.
Surface finish: Black anodizing increases radiation (still minor), prevents oxidation

Pros: Silent, reliable (no fans to fail), low cost Cons: Limited to ~30–50 W without airflow, large/heavy for higher power

2. Active air cooling

Adds fans to force airflow, increasing $h$ from ~8 to ~60–100 W/m²·K.

Fan types:

Axial: standard case fans, move air parallel to shaft, high flow rate
Centrifugal (blower): move air radially, high static pressure for restricted spaces (laptops)

Performance factors:

CFM (cubic feet per minute): volumetric flow rate. Higher CFM = more air = more heat removal (if heatsink surface isn't saturated)
Static pressure: ability to push through resistance (dense heatsink fins). Measured in mmH₂O or Pa.
RPM vs noise: fan noise $\propto$ (RPM)⁵ approximately. Doubling speed increases noise ~32 dB. PWM (pulse width modulation) control allows variable speed.

Thermal interface materials (TIM): Between chip and heatsink, microscopic air gaps (terrible conductor: $k \approx 0.025$ W/m·K) dominate resistance. Thermal paste fills gaps:

Stock paste: $k \approx 3\text{–}5$ W/m·K, $R_{th} \approx 0.15$ °C/W (thin layer)
High-end paste: $k \approx 8\text{–}12$ W/m·K, $R_{th} \approx 0.05$ °C/W
Liquid metal: $k \approx 70$ W/m·K, $R_{th} \approx 0.01$ °C/W (conductive, risky if spilled)

Application: Thin layer (pea-sized drop or thin spread). Excess paste increases resistance by increasing thickness $d$ faster than it fills gaps.

3. Liquid cooling

Fluid (water, glycol mix) circulates through a cold plate on the chip, carries heat to a radiator cooled by fans.

Why water? Specific heat capacity $c_p = 4.18$ kJ/kg·K (4× air), density 1000 kg/m³ (800× air). Can carry far more heat per volume.

Components:

Cold plate: metal block with channels, mounted like heatsink. Water contact gives $h \approx 1000\text{–}1000$ W/m²·K vs air's 60.
Pump: circulates fluid. Flow rate ~1–2 L/min typical.
Radiator: heatsink for liquid. Multiple fans, large area.
Reservoir: expansion tank, fills loop

AIO (all-in-one): sealed unit, pre-filled, no maintenance. Custom loops allow better performance but require filling, leak risk.

Thermal performance: Liquid cooling's advantage is transport capacity, not surface heat transfer. The radiator still uses air convection (same $h$ ), but distributed over larger area away from the chip.

Total resistance: $R_{th} = R_{chip\text{-}water} + R_{water\text{-}radiator} + R_{radiator\text{-}air}$

Typically $R_{chip\text{-}water} \ll R_{radiator\text{-}air}$ due to high $h$ at cold plate. The radiator becomes the bottleneck, so large radiator area matters.

Pros: Handles 200–400+ W, quieter (larger, slower fans), flexible placement Cons: Cost ( $100–$ 400), complexity, pump/leak failure modes, slightly worse than top-tier air for<150 W loads

4. Exotic solutions

Phase-change cooling: Refrigerant evaporates at cold plate (absorbing latent heat), condenses at radiator. Like a refrigerator. Can reach sub-ambient temperatures (condensation risk). Used in extreme overclocking.

Direct-die cooling: Remove heatspreader, apply cooler directly to silicon. Eliminates one thermal resistance layer, gains ~10–15°C. Voids warranty.

Immersion cooling: Submerge entire system in dielectric fluid. Used in datacenters for density and efficiency. Not practical for consumer.

Recall Explain to a 12-year-old

Your computer's CPU is like a tiny oven that never turns off. It makes heat whenever it works, and it works all the time. If we don't take that heat away, the chip gets hotter and hotter until it breaks (or shuts itself off to avoid breaking).

So how do we get rid of heat? Three ways:

Conduction (like a metal spoon in hot soup): heat travels through solid stuff. We stick a big chunk of metal (a heatsink) on the CPU. Heat flows from the hot chip into the cooler metal.
Convection (like blowing on hot cocoa): moving air carries heat away. The heatsink has lots of thin metal "fins" to give the air more places to steal heat. A fan blows air past these fins, speding this up.
Radiation (like the sun warming your face): hot things glow invisible light that carries heat. This barely matters for computer chips because they're not that hot (compared to, say, a stove burner).

Think of it like this: the chip is a faucet dripping water (heat) into a bucket (the chip itself). If we don't drain the bucket, it overflows (overheats). The heatsink and fan are the drain—they let the water (heat) escape as fast as it comes in. A bigger drain (better cooler) means the bucket stays less full (chip stays cooler).

Some coolers use water instead of air! They pump water through a metal plate on the chip, water soaks up the heat, then it flows to a big radiator with fans (like a car radiator). Water is better at carrying heat than air, so this works for really hot chips.

Key formulas summary

Quantity	Formula	Units
Thermal resistance	$R_{th} = \frac{\Delta T}{P}$	°C/W or K/W
Conduction	$Q = \frac{k \cdot A \cdot \Delta T}{d}$	W
Conduction resistance	$R_{th} = \frac{d}{k \cdot A}$	°C/W
Convection	$Q = h \cdot A \cdot \Delta T$	W
Convection resistance	$R_{th} = \frac{1}{h \cdot A}$	°C/W
Junction temperature	$T_j = T_{amb} + P \cdot R_{th,total}$	°C

Connections

Thermal Design Power (TDP) — defines worst-case cooling requirements
CPU architecture and performance — higher clock = more power = more heat
Power supply efficiency — inefficiency becomes heat in PSU, needs cooling
Case airflow and positive/negative pressure — system-level cooling strategy
Thermal throttling — automatic slowdown when cooling fails
Overclocking — pushes power and heat beyond stock
Heat pipes — advanced heatsink tech using phase change
PCB thermal vias — conducting heat away from surface-mount components
Reliability and MTBF — high temperatures accelerate failure (Arrhenius equation)

#flashcards/hardware

What are the three mechanisms of heat transfer? :: Conduction (through solids), convection (via moving fluids), and radiation (electromagnetic waves). For electronics, conduction + convection dominate; radiation is <5% below 100°C.

Define thermal resistance and give its units :: Thermal resistance $R_{th}$ measures resistance to heat flow, calculated as $R_{th} = \Delta T / P$ , where $\Delta T$ is temperature difference and $P$ is power. Units: °C/W or K/W. Lower is better.

State Fourier's Law of conduction

Q = \frac{k \cdot A \cdot \Delta T}{d}

, where

Q

is heat flow (W),

k

is thermal conductivity,

A

is area,

d

is thickness,

\Delta T

is temperature difference. Heat flow increases with area and conductivity, decreases with thickness.

What is thermal conductivity of copper vs aluminum?

Copper: ~400 W/m·K, Aluminum: ~205 W/m·K. Copper conducts heat 2× better but is heavier and more expensive.

State Newton's Law of Cooling

Q = h \cdot A \cdot \Delta T

, where

h

is heat transfer coefficient (W/m²·K),

A

is surface area,

\Delta T

is temperature difference.

h

depends on fluid type and flow velocity.

Typical heat transfer coefficient for natural convection in air?

h \approx 5–10

W/m²·K (still air, no fan)

Typical heat transfer coefficient for forced air convection?

h \approx 50–100

W/m²·K (with fan, ~2 m/s airflow)

Typical heat transfer coefficient for water cooling?

h \approx 500–10000

W/m²·K (liquid has much higher

h

than air)

How do thermal resistances combine in series?

They add:

R_{th,total} = R_1 + R_2 + R_3 + ..

. Heat flows through each resistance sequentially, like electrical resistors in series.

Formula for thermal resistance from conduction

R_{th,cond} = \frac{d}{k \cdot A}

, where

d

is thickness,

k

is thermal conductivity,

A

is area. Thinner and larger area reduces resistance.

Formula for thermal resistance from convection

R_{th,conv} = \frac{1}{h \cdot A}

, where

h

is heat transfer coefficient,

A

is surface area. Larger area or higher

h

(faster flow) reduces resistance.

Why are heatsinks made with fins?

Fins increase surface area

A

, which reduces convection thermal resistance

R_{th} = 1/(h \cdot A)

. More area allows more heat transfer to air.

Why is thermal paste necessary?

Microscopic air gaps between chip and heatsink have terrible thermal conductivity (

k \approx 0.025

W/m·K). Thermal paste (

k \approx 3–12

W/m·K) fills gaps, lowering contact resistance.

What happens if you use too much thermal paste?

Excess paste increases thickness

d

. Since

R_{th} = d/(k \cdot A)

and paste has lower

k

than metal, thick paste layer adds resistance. Ideal is thin layer (~0.1 mm).

Why does a fan improve cooling so dramatically?

Fan increases airflow velocity, which increases heat transfer coefficient

h

from ~8 (natural convection) to ~60–100 (forced). This gives ~7–8× reduction in thermal resistance.

Compare thermal conductivity: air vs thermal paste vs copper :: Air: ~0.025 W/m·K (terrible insulator), thermal paste: 3–12 W/m·K (gap filler), copper: 400 W/m·K (excellent conductor). 16000× difference between air and copper!

Calculate junction temperature formula

T_j = T_{ambient} + P \cdot R_{th,total}

, where

P

is power dissipated,

R_{th,total}

is total thermal resistance from junction to ambient.

What is an AIO liquid cooler?

All-In-One: sealed liquid cooling system with cold plate, pump, radiator, and pre-filled coolant. No maintenance, easier than custom loop, more expensive than air.

Why does liquid cooling handle more power than air?

Water's high specific heat (4.18 kJ/kg·K) and density (1000 kg/m³) allow it to transport heat efficiently from chip to a larger radiator area. The cold plate also has much higher

h

(~1000–10000 vs 60 W/m²·K).

What is PWM fan control?

Pulse Width Modulation: varies fan speed by changing duty cycle of power signal. Allows dynamic speed adjustment for noise/cooling balance. Lower speed = quieter but less cooling.

What is a heat pipe and how does it work?

Sealed copper tube with wick and working fluid (water). Fluid evaporates at hot end (absorbing latent heat), vapor flows to cold end, condenses (releasing heat), liquid returns viawick. Very high effective thermal conductivity (~5000–2000 W/m·K).

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, yeh cooling ka core idea bahut simple hai — har electronic component jab kaam karta hai, toh energy ka thoda hissa heat mein convert hota hai. Yeh koi optional problem nahi hai, yeh physics ka rule hai. CPU jaisa chip jab billions of operations per second karta hai, toh ek chhoti si jagah par bahut zyada heat generate hota hai. Agar yeh heat nikala na jaaye, toh temperature badhta jaata hai aur chip ya toh apni speed kam kar deta hai (throttling) ya permanently kharab ho jaata hai. Bucket wala example yaad rakho — power andar aana matlab paani ka flow, aur cooling matlab bucket ka hole. Agar hole chhota hoga toh paani (temperature) overflow ho jaayega.

Ab intuition ka sabse important part hai thermal resistance ( $R_{th}$ ). Yeh bilkul electrical resistance jaisa hi hai — bas yeh batata hai ki heat ko flow karne mein kitni mushkil aa rahi hai. Formula simple hai: $R_{th} = \Delta T / P$ . Lower resistance matlab better cooling. Aur ek beautiful cheez yeh hai ki jaise electrical resistances series mein add hote hain, waise hi thermal resistances bhi add hote hain — chip se lekar heatsink se lekar air tak, har step ki resistance jodo aur total nikaalo. Heat transfer teen tareeke se hota hai — conduction (solid ke through, jaise chip se heatsink), convection (moving air ya liquid heat le jaata hai), aur radiation (jo electronics mein 5% se bhi kam matter karti hai). Isliye electronics mein hum mainly conduction aur convection pe focus karte hain.

Yeh cheez matter kyun karti hai? Kyunki jab tum koi bhi hardware design karte ho — laptop, phone, ya server — toh tumhe pehle se calculate karna padta hai ki junction temperature safe limit ke andar rahegi ya nahi. Example dekho: 150 W ka CPU, total resistance 0.6 °C/W, toh temperature rise 90°C — matlab ambient 25°C se junction 115°C tak pahunch jaata hai! Yeh sab isliyes important hai ki tum samajh sako ki bade heatsinks kyun banaye jaate hain (zyada area matlab zyada heat flow, Fourier's Law se), thermal paste thin kyun hoti hai, aur fans ya liquid cooling kyun lagti hai (kyunki forced convection aur liquid ka $h$ value bahut zyada hota hai). Yeh knowledge real-world engineering ka foundation hai.

The physics of heat transfer

Cooling solution categories

1. Passive cooling (no moving parts)

2. Active air cooling

3. Liquid cooling

4. Exotic solutions

Key formulas summary

Connections

Concept Map

Hinglish (regional understanding)

Hinglish (regional understanding)

Go deeper — visual, from zero

Test yourself — Power, Thermal & Reliability

Connections