Project 15  ·  AME 431

Flight Computer Heat Sink Design

AME 431 · Heat Transfer · University of Southern California

Forced Convection Extended Surfaces Fin Efficiency Turbulent Flow Pressure Drop Nusselt Number Material Comparison N₂ Coolant

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%

Final Design

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 · cp · ΔT    →    ṁ = Q̇ / (cp · ΔT)
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
ΔT (design)
80 °C
60°C surface − (−20°C) gas
Heat load
1,200 W
Flight computer dissipation
Coolant
N₂ gas
Evaluated at −20 °C inlet
ṁ required
0.0149 kg/s
Minimum to absorb 1,200 W

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:

// Channel geometry (50 fins, 0.47 m × 0.23 m base plate)
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 1Aluminum350 µm33627.6273.000.741.5846.2% / $
Fin 2 ✓ Aluminum 700 µm 22 201.05 97.33 0.99 2.10 46.3% / $
Fin 3Copper80 µm3529.0829.940.593.758.0% / $
Fin 4Copper160 µm42104.979.381.157.2910.9% / $

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

Material
Aluminum
Lower cost than copper
Fin thickness
700 µm
0.70 mm per fin
No. of fins
22 fins
21 cooling channels
Channel width
10.2 mm
0.0102 m spacing
Fin efficiency η
97.33%
Near-isothermal fins
Pressure drop
201 Pa
System pumping penalty
Total weight
90.1 g
0.0901 kg heat sink
Coolant cost
$1,030/day
N₂ at ṁ = 0.0149 kg/s

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

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