This section presents the underlying theory of the Thermal capacitor option.

The heat flux q (SI unit: W/m2) in a material due to the temperature difference ΔT (SI unit: K) is:

where C (SI unit: J/K) is the thermal capacitance. The thermal capacitance is a measure of how much heat a body can store. It is defined as:

with V the volume (SI unit: m3), ρ the density (SI unit: kg/m3), Cp the heat capacity at constant pressure (SI unit: J/(kg·K)), and m the mass (SI unit: kg).

Under certain conditions, the temperature T of a solid body subjected to convective heat transfer on its boundaries may be considered as homogeneous, depending only on time, using the thermal capacitance:

This approximation, referred as the lumped thermal capacitance model (see Ref. 41), holds when h, C, and A are constant and the gradients of temperature within the body are expected to be smaller than the gradients of temperature between the body and the surrounding. It happens for example when the thermal contact between the solid and the fluid is poor, or when the solid is a good thermal conductor.

This is characterized by the Biot number Bi (dimensionless):

where L is a relevant length scale of the body, and k is its thermal conductivity.

The lumped thermal capacitance model is usually assumed to be valid when Bi < 0.1.