Heat Transfer & Thermal Design

Heat leaves an automation component through conduction, convection, and radiation. MIT’s heat-transfer course emphasizes choosing a model that connects these modes to system behavior and design ¹.

For one-dimensional conduction through a layer,

For convection from a surface, \(\dot Q=hA(T_s-T_\infty)\). Both can be written as \(\dot Q=\Delta T/R_\theta\), letting thermal resistances combine like a network.

Worked enclosure estimate

Drives and power supplies dissipate 180 W inside an enclosure. If the effective enclosure-to-room thermal resistance is 0.18 K/W, steady temperature rise is

At a 30°C room, the predicted internal reference temperature is about 62°C—possibly unacceptable. Reducing loss, adding surface area, improving airflow, separating heat sources, or using a heat exchanger changes the resistance network. A fan rating alone does not prove component temperature; airflow paths and recirculation matter.

Transients and thermal mass

A body with thermal capacitance \(C_\theta=mc_p\) and resistance \(R_\theta\) has time constant \(\tau=R_\theta C_\theta\). Short power peaks may be absorbed with modest temperature rise, while repeated cycles accumulate toward a periodic steady state. Use the actual duty cycle, not only nameplate power.

Automation-specific traps

• Motor winding temperature can exceed case temperature.
• Slow motor speed may reduce self-cooling exactly when torque is high.
• Sealed enclosures protect against contamination but trap heat.
• Cable bundles, contact resistance, and undersized terminals create local hotspots.
• Pneumatic expansion can cool locally while the compressor rejects heat elsewhere.

Thermal verification plan

Define ambient range, load cycle, allowable temperatures, sensor locations, stabilization criterion, and shutdown limits. Compare thermocouple or embedded-sensor data with the model. If the model matches only after an unexplained “correction factor,” investigate contact resistance, emissivity, airflow, or uncounted losses before declaring success.

Practice

Create a thermal-resistance sketch for a motor drive or control enclosure. Calculate allowable total dissipation for a chosen maximum rise. Then identify the one parameter whose uncertainty most affects the result and design a safe low-energy experiment to measure it.