| name | electronics-cooling |
| description | Electronics cooling — junction temperature, thermal resistance network, TIM selection, heat sink design, cold plates, thermoelectric coolers, forced air cooling, two-phase cooling. |
| metadata | {"priority":7,"promptSignals":{"phrases":["electronics cooling","junction temperature","thermal resistance","heat sink","TIM","cold plate","thermoelectric","CPU cooling","chip cooling"],"minScore":4}} |
Electronics Cooling — Complete Skill
Thermal Resistance Network
Junction-to-Ambient Path
T_j = T_a + P × R_θja
T_j = junction temperature [°C] — maximum limit
T_a = ambient temperature [°C]
P = power dissipated [W]
R_θja = total thermal resistance junction-to-ambient [°C/W]
Series resistance chain:
R_θja = R_θjc + R_θcs + R_θsa
R_θjc = junction-to-case (from datasheet)
R_θcs = case-to-heatsink (TIM + contact resistance)
R_θsa = sink-to-ambient (heat sink + fan)
Target: T_j < T_j,max (datasheet limit: MOSFET 150-175°C, IC typically 125°C, GaN 200°C)
Datasheet Parameters (JEDEC)
θ_JC: junction to case (bottom of package) — from datasheet
θ_JB: junction to board
θ_JA: junction to ambient (standard test conditions — NOT for design, test-only value)
Ψ_JT: junction to top-of-package psi (partial resistance, useful with external heatsink)
For heatsink attachment: T_j = T_a + P×(θ_JC + R_θCS + R_θSA)
Thermal Interface Materials (TIM)
TIM Types and Conductivity
| TIM Type | k [W/m·K] | R_θcs [cm²·K/W] | Rework | Application |
|---|
| Air gap (no TIM) | 0.025 | >>10 | — | Never use |
| Thermal grease (silicone) | 1-4 | 0.1-0.5 | Easy | CPU, power modules |
| Phase-change material | 3-7 | 0.1-0.4 | Moderate | Reflow soldering, BGA |
| Thermal pad (silicone) | 3-8 | 0.3-1.0 | Easy | LED, power resistors |
| Indium foil | 85 | 0.01-0.05 | Difficult | High performance, RF |
| Solder (SnBi) | 57 | 0.01-0.03 | Difficult | Flip-chip, COB |
| Diamond-filled epoxy | 10-15 | 0.05-0.15 | No rework | Permanent high power |
Bond line thickness (BLT): thinner = lower resistance; typical 50-150 μm for greases
R_TIM = BLT / (k_TIM × A_contact) + R_contact_resist (spreading + interface)
Heat Sink Analysis
Thermal Resistance (Natural Convection)
R_θsa = 1/(h × A_total × η_o)
η_o = overall surface efficiency (see fins skill)
h_natural ≈ 5-15 W/m²K (still air, vertical fin, depends on ΔT)
Forced convection (fan-cooled heat sink):
h_forced ≈ 30-150 W/m²K (depends on airflow velocity)
Q_air = 1.2 [kg/m³] × V̇ [m³/s] × c_p [1000 J/kgK] × ΔT_air
ΔT_air = P / (ρ × V̇ × c_p)
T_hs,out = T_a,in + ΔT_air (heat sink outlet temp = ambient rise)
R_θsa for finned heat sink (forced air):
R_θsa = ΔT_air + R_hs = P/(ρV̇c_p) + 1/(h×A_total×η_o)
Fan Curve and Operating Point
Fan curve: ΔP vs. V̇ (static pressure vs. volumetric flow)
System curve: ΔP = K × V̇² (pressure drop through heat sink)
Operating point: intersection of fan curve and system curve
Fan law: V̇ ∝ N, ΔP ∝ N², P_fan ∝ N³
Fan redundancy: 2N (full redundancy), N+1 (one spare) for critical systems
Cold Plate Design (Liquid Cooling)
Single-Phase Liquid
Q = ṁ × c_p × (T_out - T_in)
R_cold_plate = (T_surface - T_fluid_avg) / P
R_total = R_cp + R_TIM + R_JC
Microchannel cold plate:
h ≈ Nu × k_fluid / D_h
Nu ≈ 3.66 (laminar, constant T); 4.36 (laminar, constant q)
Re = ρ × V × D_h / μ < 2300 for laminar (microchannels usually laminar)
Pressure drop: ΔP = f × (L/D_h) × ½ρV² (Moody chart) + minor losses
Water performance: k=0.6 W/mK, c_p=4200 J/kgK, Pr=6.9 → high h capability
Typical cold plate R: 0.01-0.1 °C/W (200W chips → ΔT = 2-20°C)
Two-Phase Cooling (Phase Change)
Evaporative: liquid evaporates at chip → latent heat absorption
Much higher heat flux capacity than single-phase
Loop heat pipe: wick-assisted, passive, no pump
Vapor chamber: 2D heat pipe, spreads heat isotropically
Microchannel two-phase: highest heat flux capability (>1000 W/cm²)
Thermoelectric Cooler (Peltier)
Operation
DC current through Peltier element → one side cools, other side heats
Qc = α × Tc × I - ½I²R - K(Th-Tc) [cooling capacity]
α = Seebeck coefficient [V/K], R = electrical resistance, K = thermal conductance
COP: COP = Qc / P_input = Qc / (Qh - Qc)
Maximum COP (optimized I): COP_max ≈ ZTc²/(2√(1+ZT_avg)(Th-Tc)) - (Th-Tc)/2Tc
ZT = α²T/(ρk) = figure of merit (ZT ≈ 1 for Bi₂Te₃ at room temperature)
Limitations: low COP (0.3-0.7 for ΔT=20°C), requires rejecting Qc + P_input to ambient
Use for: spot cooling, cold below ambient, temperature control (laser stabilization)
NOT for: bulk electronics cooling (too inefficient)
System-Level Thermal Design
Thermal Budget Allocation
Total thermal resistance budget: R_budget = (T_j,max - T_a,max) / P
Typical desktop: T_j=100°C, T_a=40°C, P=100W → R_budget = 0.6°C/W
Allocate: R_JC=0.1, R_TIM=0.1, R_HS=0.4 → R_total=0.6 ✓
Power Map (Multi-Component)
Each component: T_j = T_a + P_i × R_ja,i [individual]
Shared heat sink: interaction between components (cross-talk)
Use thermal simulation (FloTHERM, ANSYS Icepak, 6SigmaET)
Thermal Design Power (TDP) vs. Peak Power
TDP = long-term sustainable power (used for cooling design)
Peak = transient power (limited by thermal capacitance of chip)
Thermal mass: Q = m × c_p × ΔT (absorbs short power spikes)
JEDEC JESD51: thermal transient testing → Zth (transient thermal impedance)
Cooling Method Selection Guide
| Power [W/cm²] | Method |
|---|
| < 1 | Natural convection, simple PCB |
| 1-5 | Heat sink + natural convection |
| 5-20 | Heat sink + forced air (fan) |
| 20-50 | Cold plate (liquid) or vapor chamber |
| 50-200 | Microchannel cold plate |
| 200-1000 | Two-phase microchannel, spray cooling |
| > 1000 | Jet impingement, advanced two-phase |
Output
Provide: T_junction [°C], R_θja breakdown (JC/TIM/SA), P_max for T_j,max [W], TIM recommendation (k, BLT), heat sink R_θsa required [°C/W], fan flow rate V̇ [m³/s], cold plate ΔT [°C].
