Project 15 · AME 431
Flight Computer Heat Sink Design
AME 431 · Heat Transfer · University of Southern California
Course
AME 431 — Heat Transfer
Project
Flight Computer Heat Sink
Team
Suvorov · Jackle · Glover · Yamaguchi
Heat Load
Q = 1,200 W
Selected Design
Al 700 µm · η = 97.33%
Designed and optimized a fin-array heat sink to cool a flight computer dissipating 1,200 W, using nitrogen gas at −20 °C as the coolant. Four candidate designs (aluminum and copper at two thicknesses each) were analyzed for fin efficiency, pressure drop, weight, and cost. The selected design — 700 µm aluminum, 22 fins — achieves 97.33% fin efficiency at a system weight of only 90 g and a cost-efficiency ratio of 46.3% per dollar, outperforming all copper alternatives on value.
Design Constraints & Mass Flow Calculation
The flight computer generates a continuous heat load of 1,200 W that must be rejected entirely to a nitrogen gas coolant stream. The maximum allowable surface temperature is 60 °C and the inlet coolant temperature is −20 °C, establishing a temperature difference ΔT = 80 °C across which all heat transfer must occur. The first step is finding the minimum coolant mass flow rate needed to absorb the full load.
ṁ = 1200 W / (1003.92 J/kg·K × 80 K) = 0.0149 kg/s
cp(N₂ at −20 °C) = 1003.92 J/kg·K · Evaluated at inlet conditions
Fin Analysis — Forced Convection Through Channels
Each fin design was analyzed as a set of rectangular fin channels with forced convection. The workflow for each design: compute channel geometry → find flow velocity from continuity → calculate hydraulic diameter Dh → determine Reynolds number and flow regime → apply the appropriate Nusselt correlation → compute convection coefficient h → evaluate fin efficiency η and total heat transfer Q.
The detailed hand-calculation for Fin 1 (Al 350 µm) illustrates the full methodology, carried by Henry and Sean:
Ac = 0.05 × [(0.23 − 50×0.00035) / (50−1)] = 2.17 × 10⁻⁴ m²
V = ṁ / (ρ · Ac) = 0.0149 / (1.36 × 2.17×10⁻⁴) = 50.5 m/s
// Hydraulic diameter
Dh = 4Ac / P = 4 × 2.17×10⁻⁴ / (2×0.00434 + 2×0.05) = 7.98 × 10⁻³ m
// Reynolds number → turbulent
Re = V · Dh / μ = 50.5 × 7.98×10⁻³ / 1.54×10⁻⁵ = 26,172 (turbulent)
// Petukhov friction factor (smooth tube)
f = (0.790 ln Re − 1.64)⁻² = 0.0244
// Gnielinski Nusselt → convection coefficient
Nu = 65.8 → h = k · Nu / Dh = 0.0223 × 65.8 / 7.98×10⁻³ = 183.8 W/m²·K
// Pressure drop
ΔP = f · (L/Dh) · (ρV²/2) = 0.0244 × (0.47/7.98×10⁻³) × (½ × 1.36 × 50.5²) = 97 Pa
After iterating the fin count down from 50 to the optimal 33 fins, the actual heat rejection was Q = 875.95 W with a fin efficiency of η = 73.0% and a total weight of 0.74 kg.
Four-Design Trade Study
Four fin configurations were evaluated in parallel — two aluminum thicknesses and two copper thicknesses — each designed to the same heat load and boundary conditions. Performance metrics included pressure drop (system pumping penalty), fin efficiency, weight, and material cost.
| Design | Material | Thickness | No. Fins | ΔP (Pa) | η (%) | Weight (kg) | Cost ($) | η / $ |
|---|---|---|---|---|---|---|---|---|
| Fin 1 | Aluminum | 350 µm | 33 | 627.62 | 73.00 | 0.74 | 1.58 | 46.2% / $ |
| Fin 2 ✓ | Aluminum | 700 µm | 22 | 201.05 | 97.33 | 0.99 | 2.10 | 46.3% / $ |
| Fin 3 | Copper | 80 µm | 35 | 29.08 | 29.94 | 0.59 | 3.75 | 8.0% / $ |
| Fin 4 | Copper | 160 µm | 42 | 104.9 | 79.38 | 1.15 | 7.29 | 10.9% / $ |
Copper was eliminated on cost grounds — despite Fin 3's low pressure drop, its 29.94% efficiency is unacceptably poor and costs 2.4× more than the aluminum 350 µm option. Between the two aluminum designs, 700 µm aluminum edges out the 350 µm design on every key metric: higher efficiency (97.33% vs. 73.0%), lower pressure drop (201 vs. 628 Pa), and marginally better efficiency-per-dollar (46.3% vs. 46.2%/$).
Selected Configuration — Aluminum 700 µm
At 97.33% efficiency the fins are operating nearly isothermally — the fin tip temperature is within 2.7% of the base temperature — meaning almost the entire fin surface is actively contributing to heat transfer. The wider channel (10.2 mm vs. 6.8 mm for the 350 µm design) reduces flow velocity, lowers the friction factor, and cuts pressure drop by 68%. The thicker fin also raises the fin parameter m = √(h·P/k·Ac) favorably for efficiency.
AME 431 — Final Project Presentation
Flight Computer Heat Sink Design · Team Suvorov, Jackle, Glover, Yamaguchi · 16 slides