.FCSys.Subregions.Examples.ElectricalConduction

Information

This is an example of Ohm's law. The 1 cm × 1 mm × 1 mm subregion contains carbon (C⁺) and electrons. An electrical current of 50 mA (5 A/cm²) is delivered into the negative boundary and exits the positive boundary. Due to the finite mobility of the electrons a force is required to support the current; this maps directly to electrical potential. The example shows that the measured resistance is R = L/(A ρ μ) as expected, where ρ is electronic density and μ is electronic mobility.

The measured rate of heat generation (subregion.graphite.'e-'.Edot_DT) is equal to P = (zI)² R as expected, where zI = 50 mA is the electrical current. This heat is conducted through the carbon to the boundaries, which are held at 25 °C. The measured steady state temperature is T = T₀ + θ L P/(4 A) as expected, where T₀ = 25 °C is the boundary temperature and θ is the thermal resistance. The factor of one fourth is due to the boundary conditions; the conduction length is half of the total length and the heat is rejected to both sides. There is no thermal convection or radiation—only conduction to the sides.