Thermal & Thermo-Mechanical

Heat flows in, temperatures spread, parts expand — how hot, where, and what stress does the expansion cause?

1. What is it?

Steady thermal: heat sources and sinks balance out; you get the final temperature map. "Will this heatsink keep the chip under 85 °C?"
Transient thermal: temperature vs time after a switch-on or a step change. "How long until the centre of this block reaches 60 °C?"
Thermo-mechanical: the temperature field makes the part expand; constrained expansion = stress. "Will this bimetal joint warp or crack?"

2. When do I use it?

You have…	Use	Example
Steady heat source + sink	Steady thermal	Heatsink design
Switch-on, step change, time-varying	Transient thermal	Warm-up time
Temperature causes stress	Thermo-mechanical	Exhaust manifold
Convection/radiation losses	Surface BCs	Cooling fin

Use cases

Problem Type	Industry	Example
Heat exchanger design	Energy/Chemical	Tube sheet temperature distribution
Electronic cooling	Electronics	PCB thermal management
Thermal stress in piping	Power plants	Hot pipe expansion analysis
Casting solidification	Manufacturing	Mold temperature history
Cryogenic insulation	Aerospace	LNG tank thermal performance
Thermal barrier coating	Energy/Turbine	Temperature gradient across TBC

3. The flow

On macOS, author the solid in Design Studio (step 1), apply the hot/cold face pair on Conditions (suggested thermal setup), then Review → Mesh (keep the Hex8 solid) → Solve Thermal Steady-State or Thermo-Mechanical. See [Design Studio 7-stage pipeline](design-studio-pipeline.md).

Steady Thermal

Design — geometry
Boundary — material (thermal conductivity k) + prescribed temperatures + heat sources
Mesh — generate
Simulate → Thermal Steady
Results — temperature contour

Transient Thermal

Design — geometry
Boundary — material (k, ρ, cₚ) + initial temperature + heat sources + surface losses
Mesh — generate
Simulate → Thermal Transient → set time step and duration
Results — temperature vs time at each node

Thermo-Mechanical

Run thermal first (steady or transient)
Simulate → Thermo-Mechanical — uses temperature field as load
Results — stress from constrained expansion

4. Reading your results

Temperature contour

Color	Meaning
Blue	Cold
Red	Hot

Good: Max temperature is below your limit. Bad: Max temperature exceeds material rating.

Heat flux

Color	Meaning
Blue	Little heat flow
Red	High heat flow

Use it to: Find bottlenecks in your thermal path.

Thermo-mechanical stress

Color	Meaning
Blue	Low stress
Red	High stress (close to yielding)

Good: Stress from expansion is below yield. Bad: Constrained expansion causes cracking.

5. Boundaries of truth

What's validated

Case	Reference	Error
Steady 2D conduction	Analytical	< 1%
Higher-order (Tri6/Quad9)	Published	< 2%
Transient Crank-Nicolson	Published	< 2%
Thermo-mechanical staggered	Published	< 3%

What's NOT covered

Phase change — melting, solidification
Temperature-dependent material properties — constant properties only
Radiation view factors — simple linearized radiation only
Boiling/condensation — single-phase conduction/convection only
Very large temperature gradients — may need finer mesh

Common mistakes

Mistake	Fix
Missing thermal conductivity	Add k to material
No heat sink prescribed	Add at least one fixed temperature or convection
Time step too large in transient	Use smaller dt or let solver auto-scale
Forgetting ρ and cₚ in transient	Add density and specific heat
Coarse mesh at heat sources	Refine near sources and sinks