heat-sink-design

name	heat-sink-design
description	Heat sink design — fin geometry (rectangular/pin/corrugated), convection coefficient, thermal resistance network, forced/natural convection, pressure drop, material selection (Al/Cu), heat pipe integration, TIM selection, JEDEC standards, electronics cooling.
metadata	{"priority":7,"promptSignals":{"phrases":["heat sink design","fin heat sink","thermal resistance heat sink","electronics cooling","heat sink natural convection","forced convection heat sink"],"minScore":3}}

Heat Sink Design — Complete Skill

Thermal Resistance Network

Junction-to-ambient thermal resistance: R_ja = R_jc + R_cs + R_sa [°C/W; R_jc = junction-to-case; R_cs = case-to-sink; R_sa = sink-to-ambient]

Junction temperature: T_j = T_ambient + Q × R_ja [°C; Q = power dissipated [W]] Maximum junction temperature: set by device spec (e.g., T_j_max = 125°C for silicon; 150°C for SiC) Derating: operate at T_j ≤ 0.8 × T_j_max (reduces failure rate)

Thermal interface material (TIM) resistance R_cs: R_cs = t_TIM / (k_TIM × A_contact) [°C/W; t_TIM = bond line thickness; k_TIM = TIM conductivity; A = contact area] Bond line thickness (BLT): 50–150 μm under clamping pressure TIM options:

• Thermal grease (Dowsil TC-5026): k = 2–3 W/(m·K); BLT = 50–100 μm; reusable
• Phase change material: k = 3–6 W/(m·K); BLT = 75–125 μm; solid at room T, liquid at operating T
• Indium foil: k = 81 W/(m·K); BLT = 125–250 μm; very low resistance; expensive
• Thermal pad (Bergquist GP3000): k = 3 W/(m·K); BLT = 0.5–2 mm; easy assembly; higher resistance

R_cs typical values: Thermal grease: R_cs = 0.01–0.05 °C/W (25 × 25 mm package) Thermal pad: R_cs = 0.05–0.2 °C/W

Fin Geometry

Rectangular (Plate) Fins

Fin efficiency: η_fin = tanh(mH) / (mH) [dimensionless; H = fin height; m = √(h_conv × P / (k_fin × A_c))] P = fin perimeter; A_c = fin cross-section area; h_conv = convection coefficient; k_fin = fin material conductivity

For thin rectangular fin: m = √(2h_conv / (k_fin × t)) [t = fin thickness] η_fin decreases with increasing H and decreasing k_fin

Overall surface efficiency: η_o = 1 - (N_fins × A_fin × (1 - η_fin)) / A_total [N_fins = number of fins; A_total = base + all fin areas]

Total thermal resistance: R_sa = 1 / (η_o × h_conv × A_total) [°C/W]

Key dimensions: Fin pitch S: distance between fins; S = 2–5 mm (forced convection); S = 8–15 mm (natural convection) Fin height H: 15–50 mm typical; limited by pressure drop and manufacturing Fin thickness t: 0.5–2 mm (aluminum); structural and manufacturing limit

Pin Fins

Cylindrical pin fin array: h_conv per pin: depends on staggered vs. inline arrangement; Nu_D = C × Re_D^m × Pr^(1/3) (correlation) Higher h_conv per pin area but lower total area vs. plate fins (for same volume) Advantage: isotropic flow direction; good for omnidirectional air flow (natural convection) Pin diameter: 1–4 mm; height: 10–30 mm

Corrugated (Folded) Fins

High surface area density: surface area density > 2,000 m²/m³ (plate fins: 200–800 m²/m³) Used in: aircraft electronics, automotive intercoolers, high-performance CPUs Very thin fins (0.1–0.4 mm); manufacturing by stamping + brazing Low flow resistance: many flow channels with short hydraulic diameter

Convection Coefficient Calculation

Forced Convection (Internal Channel Flow)

Channel Nusselt number (laminar flow, Re < 2,300): Nu = 3.66 (uniform temperature) or Nu = 4.36 (uniform heat flux) — parallel plate

For developing flow (short channels): Nu = 7.54 + 0.03 × (D_h / L × Re × Pr) / (1 + 0.016 × (D_h / L × Re × Pr)^(2/3)) [Gnielinski; more accurate]

Turbulent (Re > 10,000): Nu = 0.023 × Re^0.8 × Pr^(0.4 for heating; 0.3 for cooling) [Dittus-Boelter] Or: Nu = (f/8 × (Re - 1000) × Pr) / (1 + 12.7 × √(f/8) × (Pr^(2/3) - 1)) [Gnielinski; more accurate]

Heat transfer coefficient: h_conv = Nu × k_fluid / D_h [W/(m²·K); D_h = hydraulic diameter = 4A_c/P_wetted]

Air properties at 50°C: k = 0.0285 W/(m·K); μ = 1.96×10⁻⁵ Pa·s; Pr = 0.71; ρ = 1.09 kg/m³

Natural Convection

Vertical plate (Churchill-Chu correlation): Nu_L = {0.825 + 0.387 × Ra_L^(1/6) / [1 + (0.492/Pr)^(9/16)]^(8/27)}² Ra_L = g × β × ΔT × L³ / (ν × α) [β = 1/T_film for ideal gas; L = plate height; ν = kinematic viscosity; α = thermal diffusivity]

Simplified formula for air at 50°C ΔT: h_conv_natural ≈ 1.42 × (ΔT/L)^0.25 [W/(m²·K); ΔT = surface-ambient [°C]; L = fin height [m]] Typical: h ≈ 5–10 W/(m²·K) for natural convection (much lower than forced: 50–500 W/(m²·K))

Pressure Drop in Heat Sink

Pressure drop through fin channels: ΔP = f × (L / D_h) × (ρ × v²/2) + K_entrance × (ρ × v²/2) + K_exit × (ρ × v²/2) K_entrance ≈ 0.5 (sudden contraction); K_exit ≈ 1.0 (sudden expansion) f × Re = 96 (parallel plates, laminar); f × Re = 56 (square channels)

Fan selection: Operating point: fan curve P = f(Q) intersects system resistance curve P = K × Q² P_system = ΔP through heat sink + duct losses

Fan laws: Q ∝ N; P ∝ N²; W ∝ N³ (for similar fan at different speeds)

Material Selection

Material	k [W/(m·K)]	ρ [kg/m³]	Cost
Aluminum 6063	200	2,700	Low
Aluminum 6061	167	2,700	Low
Copper	385	8,900	High (4× Al)
Graphite foam	40–150	250	Medium
Vapor chamber	10,000–20,000 eff.	2,000	High

Aluminum (Al 6063-T5): dominant for heat sinks; k = 200 W/(m·K); extruded; excellent cost/performance Copper: 2× better k than Al; used where weight is less critical (automotive ECU, power electronics) Vapor chamber: passive two-phase device; spreads heat over large area; effective k >> 1,000 W/(m·K); for spot heat sources

Heat Pipe Integration

Heat pipe principle: wick-assisted capillary pumping of evaporation-condensation cycle; k_eff = 10,000–100,000 W/(m·K) (much higher than any solid) Diameter: 3–10 mm (sintered wick or axial groove); bending radius ≥ 3D

Maximum heat transport (capillary limit): Q_max = A_w × k_eff × ΔT_max / L [simplified; actual depends on wick structure and fluid] 6 mm heat pipe, water fill, L = 150 mm: Q_max ≈ 30–80 W per pipe

Design: embed heat pipe in Al heat sink base → spreads heat from source over entire fin array; reduces spreading resistance

JEDEC Standards

JEDEC JESD51: standardized methods for junction-to-ambient thermal resistance measurement

• JESD51-2: natural convection conditions for θja measurement
• JESD51-6: forced convection conditions θja (junction-to-ambient): single number; combines junction-to-case, case-to-board, board-to-ambient — not sufficient for system design θjb (junction-to-board): better metric for surface-mounted components in PCB assemblies Ψjt (junction-to-top): measures thermal gradient to top of package; used with external heat sink design

Design Optimization

For given Q and T_j constraint: Required R_sa = (T_j - T_ambient) / Q - R_jc - R_cs R_sa determines: fin area, fin count, fin height, air flow rate needed

Optimization trade-off: More fins (smaller pitch): ↑ area → ↑ Q per ΔT; but ↑ pressure drop → ↓ flow rate → ↑ R_sa (counterproductive) Optimal fin pitch: maximize Q / (η_o × h × A × ΔP) — complex optimization; use CFD or correlations

Standards

Standard	Scope
JEDEC JESD51	Thermal resistance measurement methodology
JEDEC JESD51-2	Natural convection thermal measurement
JEDEC JESD51-6	Forced convection thermal measurement
IPC-7093	Design and assembly guidelines for SMT
MIL-HDBK-251	Reliability derating for electronics (thermal)

Output

Provide: power dissipation Q [W] and maximum T_j [°C], thermal budget allocation (R_jc + R_cs + R_sa + R_ambient = ΔT/Q), required R_sa [°C/W], fin geometry (type, number, height H [mm], thickness t [mm], pitch S [mm]), fin material and k [W/(m·K)], fin efficiency η_fin [%], overall surface efficiency η_o [%], convection coefficient h [W/(m²·K)] (forced or natural), air velocity [m/s] or flow rate [CFM/m³/h], pressure drop ΔP [Pa], total thermal resistance R_sa_actual [°C/W], T_j_predicted [°C] vs. T_j_max, and applicable standard (JEDEC JESD51-2/6, MIL-HDBK-251).