🎓 Lesson 18
D5
Conjugate Heat Transfer in Electronics Cooling
Conjugate heat transfer is how heat moves through both solid parts (like a computer chip) and the surrounding fluid (like air or coolant) at the same time, and how those two parts affect each other.
🎯 Learning Objectives
- ✓ Calculate interface heat flux and temperature gradients across solid–fluid boundaries using energy balance principles
- ✓ Design a finned heatsink geometry by applying conjugate boundary conditions and evaluating thermal resistance reduction
- ✓ Analyze transient thermal response of a power semiconductor under pulsed loading using CHT simulation inputs
- ✓ Explain the physical significance of the Biot and Nusselt numbers in determining coupling strength between conduction and convection
- ✓ Apply commercial CHT solver settings (mesh independence, convergence criteria, turbulence model selection) to validate an electronics cooling case against experimental data
📖 Why This Matters
In modern mining electronics—from downhole telemetry sensors to autonomous haul truck control units—reliability hinges on thermal management. Overheating causes premature failure in harsh environments (e.g., >60°C ambient, dust-laden airflow, vibration). Conjugate heat transfer isn’t just academic: it’s how engineers predict whether a 3 kW inverter in a remote drill rig will survive 12-hour shifts without derating. Skipping CHT leads to over-engineered (costly) or under-cooled (risky) systems—both unacceptable in safety-critical mining infrastructure.
📘 Core Principles
Conjugate heat transfer begins with recognizing that heat flows via conduction in solids and convection + conduction in fluids—but neither process occurs in isolation. The theory rests on three pillars: (1) conservation of energy applied separately to solid and fluid domains; (2) interface continuity—identical temperature and normal heat flux across boundaries; and (3) coupling via boundary conditions that evolve iteratively during solution. At low Reynolds numbers or high-conductivity solids, conduction dominates and coupling is weak; at high flow velocities or with low-conductivity encapsulants (e.g., epoxy potting), fluid dynamics strongly dictate solid temperatures. Real-world electronics packages introduce multi-scale challenges: micron-scale solder joints, millimeter-scale PCB traces, and centimeter-scale heatsinks—all requiring consistent mesh resolution and proper turbulence modeling (e.g., k-ω SST for near-wall flow).
📐 Interface Energy Balance & Overall Thermal Resistance
The core conjugate relationship is expressed through the interface energy balance: q''_cond = q''_conv = h(T_s − T_f), where conductive and convective fluxes must match. For system-level design, overall thermal resistance R_th,total = R_th,solid + R_th,interface + R_th,fluid combines contributions from conduction, contact, and convection. Accurate estimation requires iterative evaluation because h depends on flow field, which depends on surface temperature—and vice versa.
💡 Worked Example
Problem: A GaN-based motor drive module (size: 40 mm × 40 mm × 5 mm, k_solid = 80 W/m·K) is mounted on an aluminum heatsink (k_Al = 205 W/m·K) with thermal interface material (TIM, k_TIM = 3 W/m·K, thickness = 0.1 mm). Airflow over the heatsink provides h = 12 W/m²·K. Calculate R_th,total from junction to ambient, assuming uniform heat flux and neglecting radiation.
1.
Step 1: Compute conduction resistance of GaN die: R_cond,die = t / (k·A) = 0.005 m / (80 W/m·K × 0.0016 m²) = 0.039 K/W
2.
Step 2: Compute TIM resistance: R_TIM = 0.0001 m / (3 W/m·K × 0.0016 m²) = 0.021 K/W
3.
Step 3: Compute heatsink base-to-ambient convection resistance: R_conv = 1 / (h·A) = 1 / (12 W/m²·K × 0.0016 m²) = 52.1 K/W
4.
Step 4: Sum resistances: R_total = 0.039 + 0.021 + 52.1 ≈ 52.2 K/W
5.
Step 5: Note: This simplified sum assumes no spreading resistance or fin enhancement—real CHT simulation would reduce R_conv by >40% via fin optimization and flow redistribution.
Answer:
R_th,total ≈ 52.2 K/W, but CHT simulation with optimized fin array reduces effective R_conv to ~28 K/W—highlighting why decoupled estimates over-predict temperature rise by up to 35°C.
🏗️ Real-World Application
Sandvik’s AutoMine® Level 3 automation system uses FPGA-based edge controllers housed in IP67-rated enclosures mounted on underground LHD machines. Field failures revealed junction temperatures exceeding 115°C during continuous operation—even with rated airflow. A conjugate heat transfer CFD study (ANSYS IcePak + Mechanical) revealed two root causes: (1) recirculation zones behind enclosure fins reduced effective h by 60%, and (2) epoxy potting (k = 0.3 W/m·K) created a 12 K internal gradient not captured in standard 'junction-to-case' datasheets. Redesigning the fin geometry and switching to thermally conductive potting (k = 2.5 W/m·K) lowered peak junction temperature to 89°C—meeting IEC 60079-0 explosion-proof thermal class requirements.
📋 Case Connection
📋 Thermal Management System for EV Traction Inverter
Peak junction temps >175°C causing derating and reliability concerns
📋 Thermal Design of Satellite Payload Radiator for Lunar Orbit Mission
Extreme radiative environment: solar flux up to 1360 W/m², albedo up to 0.12, IR emission from hot regolith (~390 K)