Heat transfer is characterized by three mechanisms: conduction, convection, and radiation. In MEMS actuators and sensors heat transfer by conduction is usually the dominant mechanism. Conductive heat transfer is diffusive and is driven by a temperature gradient. Within a solid the heat transfer equations take the following form:

Here ρ is the density of the solid, Cp is its heat capacity, k is Boltzmann’s constant, T is the temperature, and Q is a term that includes heat sources and sinks. The Heat Transfer in Solids interface solves Equation 2-14, without additional coupling assumed.

Equation 2-14 is solved in the Joule Heating interface, along with the equations for electric current flow. In this case the volumetric heat source Q takes the value:

where J is the current density, and E is the electric field. The electric field component in the direction of the current flow expresses the voltage drop per unit length of material in the direction of flow. Since the current density gives the current per unit area through a surface with normal parallel to the direction of flow, the quantity Q is a power per unit volume, with dimensions W/m3. The Joule Heating interface includes heat transfer and electromagnetic fields; in addition, solid mechanics is required to model thermal actuators. The MEMS Module includes The Joule Heating and Thermal Expansion Interface interface for this purpose.