Thermal inertia

Bodies with relatively large mass and heat capacity typically exhibit slower temperature responses. However heat capacity alone cannot accurately quantify thermal inertia. Measurements of it further depend on how heat flows are distributed inside and outside a body, in accordance with system boundary conditions.

Whether thermal inertia is an intensive or extensive quantity depends upon context. Some authors have identified it as an intensive material property, for example in association with thermal effusivity. It has also been evaluated as an extensive quantity based upon the measured or simulated spatial-temporal behavior of a system during transient heat transfers. A time constant is then sometimes appropriately used as a simple parametrization for thermal inertia of a selected component or subsystem.

Description

A thermodynamic system containing one or more components with large heat capacity indicates that dynamic, or transient, effects must be considered when measuring or modelling system behavior. Steady-state calculations, many of which produce valid estimates of heat flows and temperatures when reaching an equilibrium, nevertheless yield no information on the transition path towards such stable or metastable conditions. Nowadays the spatial-temporal behavior of complex systems can be precisely evaluated with detailed numerical simulation. In some cases a lumped system analysis can estimate a thermal time constant.

A larger heat capacity ${\displaystyle C}$ for a component generally means a longer time to reach equilibrium. The transition rate also occurs in conjunction with the component's internal ${\displaystyle U_i}$ and environmental ${\displaystyle U_e}$ heat transfer coefficients, as referenced over an interface area ${\displaystyle A}$. The time constant ${\displaystyle \tau }$ for an estimated exponential transition of the component's temperature will adjust as ${\displaystyle C/(A\cdot U_e)}$ under conditions which obey Newton's law of cooling; and when characterized by a ratio ${\displaystyle U_e/U_i,}$ or Biot number, much less than one.

Analogies of thermal inertia to the temporal behaviors observed in other disciplines of engineering and physics can sometimes be used with caution. In building performance simulation, thermal inertia is also known as the thermal flywheel effect, and the heat capacity of a structure's mass (sometimes called the thermal mass) can produce a delay between diurnal heat flow and temperature which is similar to the delay between current and voltage in an AC-driven RC circuit. Thermal inertia is less directly comparable to the mass-and-velocity term used in mechanics, where inertia restricts the acceleration of an object. In a similar way, thermal inertia can be a measure of heat capacity of a mass, and of the velocity of the thermal pulse which controls the surface temperature of a body.