Laptop Fin Array CHT
Conjugate heat transfer validated against real sensor data
Predicted tau=589s vs measured 582s (+1.2%). Identified vapor chamber thermal mass as the dominant factor in the laptop's slow thermal response.
Key Results
The Problem
My Dell G16 laptop has a chassis temperature sensor (temp2) that shows a cool-down time constant of ~582 seconds. But a single cooling fin should only have tau ~ 89 seconds. Where’s the extra thermal inertia?
The answer: the vapor chamber, heat pipes, and base plates store far more heat than the fins themselves. Predicting the real cool-down requires simulating the entire solid assembly coupled with the air flow — conjugate heat transfer.
What I Did
1. Extracted geometry from a teardown video. I studied a teardown of the Dell G16 to identify the internal cooling architecture: fin dimensions, heat pipe routing, vapor chamber footprint (~60x80x4 mm), and materials (copper base, aluminum fins). No physical disassembly needed.
2. Dimensional analysis before touching the keyboard. Three numbers told me exactly what physics to expect:
- Re_H = 885 — laminar (Re_crit ~ 2300), so no turbulence model needed
- Bi ≪ 0.1 for all solid regions — each solid is internally isothermal, lumped capacitance valid
- L/D_h = 12.5 — developing flow, so entrance effects matter
3. Built a 4-region CHT model. In chtMultiRegionFoam:
- Copper base (2 mm, k=400 W/mK) — heat source representing the CPU die
- Vapor chamber (4 mm, k_eff=10,000 W/mK) — pseudo-isothermal spreader
- Aluminum fin (1 mm, k=205 W/mK) — conduction to the air interface
- Air channel (2 mm half-height) — forced convection
The interfaces use turbulentTemperatureCoupledBaffleMixed for temperature and heat flux continuity. PIMPLE with 5 outer correctors ensures convergence — I found that fewer correctors cause the coupling to under-converge and tau to diverge.
4. Calibrated fan velocity against the real sensor. The fan velocity is the main unknown. I swept U = 3.9 m/s and fit a power law:
tau = 1773 / U^0.846
At U = 3.68 m/s: tau = 589s — within 1.2% of the measured 582s.
The Result
The thermal mass breakdown explains everything:
| Component | Thermal mass | Fraction |
|---|---|---|
| Vapor chamber | ~30 J/K | 45% |
| Heatsink base | ~22.5 J/K | 34% |
| Heat pipes | ~7.7 J/K | 11% |
| Fin arrays | ~7.2 J/K | 10% |
| Total | ~67 J/K | 100% |
The vapor chamber alone holds 45% of the system’s thermal inertia. This is why a single-fin simulation (tau=89s) misses the mark by 6.5x — it only captures 10% of the thermal mass.
The lumped exponential fit has RMSE = 0.0006 K over the full 600s window, confirming the lumped model is physically valid.
Progressive Refinement
The project was structured as three fidelity levels, each one adding physics:
- Level 1: Single fin + air channel — correct convection, wrong thermal mass (tau=89s)
- Level 2: Add vapor chamber (3-region) — correct thermal mass direction, velocity sweep and mesh independence
- Level 3: Add copper base (4-region) — tau=589s at U=3.68 m/s, +1.2% vs measurement
Key Learnings
- A single-fin simulation gets the convection physics right but misses the thermal mass — tau=89s vs real tau=582s. Adding the full solid assembly corrects this.
- Bi ≪ 0.1 for all solid regions validates the lumped capacitance model — the entire solid assembly is effectively isothermal at any instant (delta_T = 0.002 K).
- Velocity calibration is the key degree of freedom: tau = 1773 / U^0.846 power law allows matching the measured sensor response.
- PIMPLE outer correctors must be at least 5 for multi-region CHT — with fewer, the solid-fluid coupling under-converges and tau blows up.