Thermal Analysis

Good news — the workflow maps naturally from structural. You still mesh the geometry, assign material properties, apply boundary conditions, and solve a field equation. The difference is that your unknown field is temperature instead of displacement, and instead of stress you care about heat flux. The whole thing is governed by the energy balance equation: heat stored = heat conducted in + internal heat generated.

Absolutely. The general heat equation is: $$\rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + Q$$ Read it left to right: $\rho c_p \partial T/\partial t$ is the rate of thermal energy storage — density times specific heat times temperature rate of change. On the right, $\nabla \cdot (k \nabla T)$ is net heat flowing in by conduction. And $Q$ is internal heat generation — Joule heating from electrical current, chemical reactions, laser energy, whatever applies to your problem.

Exactly. When $\partial T/\partial t = 0$, you get $\nabla \cdot (k \nabla T) + Q = 0$ — Poisson's equation, a well-behaved linear PDE. For your electronics enclosure dissipating constant power, steady-state is usually the right starting point. You want to know: what is the worst-case chip temperature after the device has been running for hours?

Perfect example. Reflow soldering has a precise temperature ramp — preheat, soak, reflow peak, cool-down — and you need the full time history to confirm every solder joint reaches liquidus temperature without damaging surrounding components. Other classic transient cases: fire resistance of a structural beam, thermal shock in a turbine blade on engine startup, or a satellite cycling between sunlight and eclipse every 90 minutes. Whenever the time history itself matters, you go transient.

They're physically very different, and that affects how you model them. Conduction is heat diffusing through solid material via Fourier's law: $$\mathbf{q} = -k \nabla T$$ The heat flux vector points down the temperature gradient, scaled by conductivity $k$. This is always active inside a solid — no special setup needed beyond assigning $k$. Convection is heat exchanged at a surface with a moving fluid, approximated by Newton's cooling law: $$q = h(T_s - T_\infty)$$ Here $h$ is the convection coefficient in W/m²K. Getting $h$ right is the hardest part of most practical thermal models — it comes from empirical correlations, handbooks, or a coupled CFD run. Radiation is electromagnetic heat exchange: $$q = \varepsilon \sigma (T_s^4 - T_{\text{surr}}^4)$$ That $T^4$ dependence makes it strongly nonlinear. Radiation is negligible for a 60°C enclosure but completely dominates in furnaces, turbines, or spacecraft.

Conduction and convection — those are the two that dominate. Conduction carries heat from chip junction through the PCB, heat spreader, and chassis walls. Convection — either natural (buoyancy-driven) or forced air from a fan — removes it from the outer surface. Radiation from a metal box at 60–80°C can contribute maybe 5–15% of total heat removal depending on surface emissivity and geometry. Include it if you want a thorough result, but start without it to get your baseline.

It can be surprisingly nonlinear. Two main sources: first, temperature-dependent material properties. If $k(T)$ changes significantly across your temperature range — for steel from 20°C to 1000°C, conductivity can drop by 50% — then $k$ is a function of the unknown $T$ and you need Newton-Raphson iteration. Second, radiation: that $T^4$ term is inherently nonlinear and requires iterative linearization at every time step. Phase change is another nasty nonlinearity — the latent heat spike near the melting point needs very careful time step control to capture accurately.

That's sequential coupling — the most common approach. Run thermal, export the nodal temperature field, import it into the structural model as a body load, solve for thermal stresses. Works well when deformation doesn't affect temperatures. But truly coupled problems exist: Joule heating in a power bus bar where electrical resistance depends on temperature, which changes current distribution, which changes heating. Or conjugate heat transfer in CFD, where solid and fluid temperatures influence each other at every interface. Those require simultaneous solution — or at least tight iterative coupling between solvers.

The landscape really does span the whole CAE ecosystem. For general solid thermal and thermal-structural: Ansys Mechanical, Abaqus, MSC Nastran. For electronics cooling specifically: Ansys Icepak and Siemens Flotherm have purpose-built component libraries that make PCB and server thermal modeling much faster than a general FEA tool. For conjugate heat transfer with full CFD: OpenFOAM's chtMultiRegionFoam, Ansys Fluent, STAR-CCM+. And for spacecraft with complex radiation networks: Thermal Desktop or ESATAN-TMS, which specialize in view-factor computation for orbit thermal environments.

The view factor $F_{ij}$ is the fraction of radiation emitted from surface $i$ that geometrically arrives at surface $j$ — purely geometric, no material properties involved. Two large parallel plates facing each other: $F_{12} = 1$. A convex surface in free space: $F_{11} = 0$ (can't see itself). For complex 3D geometries like heat sink fins or spacecraft components, computing view factors requires numerical integration or Monte Carlo ray-tracing, which gets computationally expensive. That's why radiation is often the most CPU-intensive part of a thermal analysis despite appearing simple in equation form.

Always do a global energy balance first. If your model has 100 W of heat generation, and you integrate the total heat flux leaving through all boundary surfaces, you should get 100 W out. Any imbalance means a mistake in boundary conditions. Second, compare against simple analytical solutions — the 1D slab formula $Q = kA\Delta T / L$, or Newton's law for a lumped body. If your 3D FEA result is within a few percent of the simplified hand calculation for a geometry where that simplification is valid, you're on track. Only then refine the mesh and add complexity.

Yes, absolutely — especially for heat flux rather than temperature. Temperature converges relatively quickly with mesh refinement, but heat flux (the gradient of temperature) converges more slowly, just like stress converges more slowly than displacement in structural. Wherever you care most about heat flux accuracy — near a thermal contact, at the base of a fin, inside a narrow gap — that's where you need the finest mesh. A good habit: run three meshes with roughly 2× element count each time, and check that the peak heat flux or maximum temperature change is less than 5% between the last two. That's your mesh-converged solution.