A VFD (variable frequency drive) in a sealed electrical cabinet. It tripped on over-temperature every hot afternoon. The cabinet was 600×800×300 mm, sealed, with the VFD dissipating 120 W. The customer thought the VFD was defective. It was — for the environment it was in. The cabinet had no cooling. This is the thermal calculation I do now for every sealed enclosure.
The thermal resistance chain
Heat flows from the VFD to ambient through a chain of thermal resistances:
T_rise = P × (R_jc + R_cs + R_sa)
Where:
- R_jc — junction to case (from the VFD datasheet, typically 0.5 °C/W)
- R_cs — case to sink (thermal interface material, ~0.1 °C/W)
- R_sa — sink to ambient (the heat sink or cabinet wall)
The VFD’s max junction temperature is 125°C. Ambient is 40°C (summer afternoon in the cabinet). Allowable rise: 85°C. For P = 120 W, allowable R_total = 85/120 = 0.71 °C/W. R_jc + R_cs = 0.6, so R_sa must be under 0.11 °C/W.
The cabinet as a heat sink
A sealed steel cabinet dissipates heat through its walls by natural convection. The thermal resistance of a bare steel cabinet is roughly:
R_sa ≈ 1 / (h × A)
Where h is the convection coefficient (natural convection ≈ 5-10 W/m²·K) and A is the surface area. For a 600×800×300 mm cabinet, total surface area is about 2 × (0.6×0.8 + 0.6×0.3 + 0.8×0.3) = 2 × (0.48 + 0.18 + 0.24) = 1.8 m². R_sa = 1 / (8 × 1.8) = 0.07 °C/W. Wait — that’s under 0.11. The cabinet should handle it. Why did it overheat?
Because the VFD wasn’t mounted to the cabinet wall. It was mounted on a mounting plate inside the cabinet, 100 mm from the wall. The heat had to convect from the VFD to the inside air, then from the inside air to the cabinet wall. That’s an additional thermal resistance (air gap inside). R_air ≈ 1 / (5 × A_vfd) = 1 / (5 × 0.05) = 4 °C/W. That kills it. Total R_sa = 4 + 0.07 = 4.07 °C/W. T_rise = 120 × 4.07 = 488°C. Obviously unrealistic — the VFD would be at 528°C. In practice, the VFD heats the inside air, the inside air heats the cabinet wall, and the wall can’t shed heat fast enough. The cabinet interior reaches 70°C, the VFD reaches 90°C, and it trips at 85°C.
What actually fixes it
| Solution | Added thermal resistance | Cost |
|---|---|---|
| Mount VFD to cabinet wall (thermal pad) | Removes air gap, R drops to ~0.15 | Cheap |
| Add a fan inside (forced convection) | h increases to 25 W/m²·K, R drops | $50 |
| Add a filtered exhaust fan | Pulls outside air through cabinet, direct cooling | $150 |
| Add a heat exchanger (air-to-air) | Sealed cabinet, transfers heat across a plate | $500 |
| Add an AC unit | Active cooling, controls cabinet temperature | $1,000+ |
What I did
I mounted the VFD directly to the cabinet wall with a thermal pad. The VFD’s heat goes through the wall to outside air. The air gap resistance was eliminated. R_sa dropped to about 0.15 °C/W. T_rise = 120 × (0.6 + 0.15) = 90°C. The VFD runs at 40 + 90 = 130°C — still too hot. So I also added an exhaust fan (120 mm, 50 CFM) on the cabinet top. It pulls outside air in through a filtered vent at the bottom. The inside air stays close to ambient. The VFD now runs at 55°C. It doesn’t trip.
The total cost was $50 for the fan. The AC unit would have been $1,000. Mounting the VFD to the wall was free (just a longer bolt and thermal pad). The combination solved it.
The quick rule I use
For a sealed cabinet with no active cooling, the rule of thumb is 10 W per square meter of cabinet surface. If the dissipation exceeds that, you need a fan or heat exchanger. For 120 W and 1.8 m², that’s 67 W/m² — way over the 10 W/m² threshold. A fan was required. The cabinet that overheated wasn’t undersized for its volume; it was undersized for the heat with no airflow.
The number I check: heat dissipation divided by cabinet surface area. If it’s over 10 W/m² for a sealed cabinet, add a fan. Mount heat-generating components (VFDs, power supplies) directly to the cabinet wall with a thermal pad. Don’t rely on natural convection in a sealed box for anything over 50 W. The VFD that tripped wasn’t defective — it was in a box that couldn’t breathe.
