🎓 Lesson 4
D3
Heat Transfer Modeling for Battery Packs in Humid Drifts
Modeling how heat moves in and out of battery packs when they operate underground in warm, wet mine tunnels.
🎯 Learning Objectives
- ✓ Calculate convective heat transfer coefficients for battery enclosures under humid, low-velocity drift airflow (0.1–0.5 m/s)
- ✓ Analyze transient thermal response of a prismatic LiNiMnCoO₂ (NMC) module using lumped-capacitance and 1D conduction models with humidity-dependent air properties
- ✓ Design a passive–active hybrid thermal management strategy that maintains cell ΔT < 5°C across a 48-cell pack at 1.2C discharge in 35°C/90% RH ambient
- ✓ Explain the impact of condensation-induced thermal resistance and corrosion risk on long-term TMS reliability in humid drifts
- ✓ Apply ASHRAE Fundamentals Chapter 22 and ISO 16750-4 environmental test profiles to validate model boundary conditions
📖 Why This Matters
In deep underground mines—like those in the Sudbury Basin or Chilean copper operations—drifts often exceed 32°C and 85% RH year-round. Battery-electric mobile equipment (BEME), such as LHDs and haul trucks, must operate reliably without thermal runaway or accelerated aging. Unlike surface EVs, BEME battery packs face *dual stressors*: high ambient heat *and* moisture-laden air that degrades insulation, promotes condensation on cold surfaces (e.g., chilled coolant lines), and reduces convective cooling efficiency. Failure to model this coupling leads to premature pack failure, unplanned downtime, and safety incidents—making accurate humid-drift thermal modeling non-negotiable for BEME deployment.
📘 Core Principles
Thermal management in humid drifts requires extending classical heat transfer theory to include hygrothermal coupling. First, electrochemical heat generation (Joule + reaction enthalpy) sets the internal source term. Second, conduction through potting, busbars, and module frames governs intra-pack heat spreading. Third, convection is modified by humidity: moist air has higher specific heat (+12% at 90% RH vs dry air at 35°C) but lower density (−3.5%), reducing forced-air cooling efficacy; natural convection is further suppressed by stagnant, dense, humid air layers near enclosure walls. Fourth, latent effects emerge when local surface temperatures fall below dew point—causing condensation that increases thermal contact resistance and risks electrical tracking. Finally, material degradation (e.g., aluminum oxide growth, polymer hydrolysis) introduces time-varying boundary conditions absent in standard EV models.
📐 Humidity-Adjusted Convective Heat Transfer
Standard Newton’s law of cooling must be corrected for humid air properties to estimate realistic convection from battery enclosure surfaces. The adjusted coefficient h_hum accounts for variable density, viscosity, and specific heat using the psychrometric state. It is essential for sizing heatsinks and fan selection in low-velocity drift ventilation.
Humidity-Corrected Convection Coefficient
h_{hum} = \frac{Nu \cdot k_{hum}}{L}Convective heat transfer coefficient adjusted for moist air thermophysical properties to accurately size cooling surfaces in humid underground environments.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| h_{hum} | Humidity-corrected convection coefficient | W/m²·K | Effective heat transfer rate per unit area and temperature difference |
| Nu | Nusselt number | dimensionless | Ratio of convective to conductive heat transfer, computed via Ra-based correlations |
| k_{hum} | Thermal conductivity of humid air | W/m·K | Temperature- and RH-dependent property; e.g., 0.0271 W/m·K at 35°C/90% RH |
| L | Characteristic length | m | Typically height of vertical surface or hydraulic diameter of duct |
Typical Ranges:
Natural convection, vertical enclosure wall (0.5–1.0 m): 0.8 – 1.8 W/m²·K
Forced convection, low-velocity drift air (0.2–0.4 m/s): 3.5 – 8.0 W/m²·K
💡 Worked Example
Problem: A sealed battery enclosure (0.8 m × 0.6 m × 0.3 m) operates in a drift at 35°C dry-bulb, 90% RH, with natural convection airflow ~0.15 m/s. Estimate h_hum for the largest vertical surface (0.8 m × 0.6 m). Use correlation Nu = 0.59·Ra^{1/4} for laminar natural convection over a vertical plate.
1.
Step 1: Determine dew point = 32.4°C → surface temp likely >33°C to avoid condensation; assume Ts = 34°C → ΔT = −1 K (cooling *to* air).
2.
Step 2: Compute humid air properties at 35°C/90% RH: ρ = 1.142 kg/m³, μ = 1.92×10⁻⁵ Pa·s, k = 0.0271 W/m·K, cp = 1018 J/kg·K → α = 2.48×10⁻⁵ m²/s, β = 1/(35+273) = 0.00324 K⁻¹.
3.
Step 3: Ra = g·β·ΔT·L³/(α·ν) = (9.81)(0.00324)(1.0)(0.8)³ / [(2.48×10⁻⁵)(1.68×10⁻⁵)] ≈ 2.94×10⁷ → Nu = 0.59·(2.94×10⁷)^{0.25} ≈ 39.2 → h_hum = Nu·k/L = 39.2·0.0271/0.8 ≈ 1.33 W/m²·K.
4.
Step 4: Compare to dry-air h_dry ≈ 1.18 W/m²·K → humidity increases h by ~13%, but *only if no condensation occurs*. If surface cools below 32.4°C, h collapses due to film resistance.
Answer:
h_hum ≈ 1.33 W/m²·K — a modest gain, but critically dependent on maintaining surface temperature above dew point. Below dew point, effective h may drop below 0.5 W/m²·K due to water film resistance.
🏗️ Real-World Application
At Vale’s Onaping Depth Project (Ontario), a fleet of 45-tonne battery-electric LHDs experienced repeated 12–18 month pack life reductions versus warranty. Post-mortem analysis revealed localized condensation inside enclosures during shift-change cooldown, corroding busbar connections and increasing contact resistance. A revised thermal model—incorporating hourly drift RH/T profiles, enclosure wall thermal mass, and dew-point tracking—predicted condensation events with 92% accuracy. The solution combined: (1) insulated enclosure walls with vapor barrier, (2) controlled purge airflow (0.3 ACH) using filtered, desiccated air, and (3) minimum discharge power limit during first 15 min after cold start. Fleet-wide MTBF increased from 4,200 to 8,700 operating hours.
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