Steady-State Heat Conduction — Fourier Law & FEM
Fourier's law, thermal conductivity, FEM formulation, boundary conditions (fixed temperature, heat flux, insulation), and contact conductance.
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Quick Explainer
What is the thermal equivalent of a stiffness matrix in heat conduction FEM?
The conductivity matrix [K] plays the same role as structural stiffness. Its entries depend on thermal conductivity and element geometry. Solving [K]{T}={f} gives nodal temperatures, then Fourier's law gives heat flux from temperature gradients — directly analogous to strain and stress from displacement.
How do contact thermal resistance and gap conductance work in assembly models?
Real surfaces contact only at asperities — actual contact area is a fraction of nominal area. Contact thermal resistance models this as a thermal resistance at the interface, depending on roughness, contact pressure, and interstitial material. Incorrect interface conductance is a common large source of error in electronics thermal models.