Thermal inertia is a term commonly used to describe the observed delays in a body's temperature response duringheat transfers. The phenomenon exists because of a body's ability to both store and transport heat relative to its environment. Since the configuration of system components and modes of transport (e.g. conduction, convection, radiation, phase change) and energy storage (e.g. internal energy, enthalpy, latent heat) vary substantially between instances, there is no generally applicable mathematical expression ofclosed form for thermal inertia.^[1]

Bodies with relatively large mass andheat 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 systemboundary conditions.

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

Athermodynamic system containing one or more components with large heat capacity indicates that dynamic, or transient, effects must be considered when measuring ormodelling system behavior.Steady-state calculations, many of which produce valid estimates of heat flows and temperatures when reaching anequilibrium, nevertheless yield no information on the transition path towards such stable ormetastable conditions. Nowadays the spatial-temporal behavior of complex systems can be precisely evaluated with detailednumerical simulation. In some cases alumped system analysis can estimate athermal time constant.^{[2][3]: 627}

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 estimatedexponential transition of the component's temperature will adjust as${\displaystyle C/(A\cdot U_e)}$ under conditions which obeyNewton's law of cooling; and when characterized by a ratio${\displaystyle U_e/U_i,}$ orBiot number, much less than one.^{[4]: 19–26}

Analogies of thermal inertia to the temporal behaviors observed in other disciplines of engineering and physics can sometimes be used with caution.^[5] Inbuilding performance simulation, thermal inertia is also known as thethermal flywheel effect, and the heat capacity of a structure's mass (sometimes called thethermal mass) can produce a delay betweendiurnal heat flow and temperature which is similar to the delay between current and voltage in an AC-drivenRC circuit. Thermal inertia is less directly comparable to the mass-and-velocity term used inmechanics, 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 thermalpulse which controls the surface temperature of a body.^[1]

For a semi-infinite rigid body where heat transfer is dominated by the diffusive process of conduction only, the thermal inertia response at a surface can be approximated from the material'sthermal effusivity, also calledthermal responsivity${\displaystyle r}$. It is defined as the square root of the product of the material's bulkthermal conductivity andvolumetric heat capacity, where the latter is the product ofdensity andspecific heat capacity:^[6][7]

${\displaystyle r=\sqrt{k\rho c}}$

• ${\displaystyle k}$ is thermal conductivity, with unit W⋅m⁻¹⋅K⁻¹
• ${\displaystyle \rho }$ is density, with unit kg⋅m⁻³
• ${\displaystyle c}$ is specific heat capacity, with unit J⋅kg⁻¹⋅K⁻¹

Thermal effusivity has units of aheat transfer coefficient multiplied by square root of time:

• SI units of W⋅m⁻²⋅K⁻¹⋅s^1/2 or J⋅m⁻²⋅K⁻¹⋅s^−1/2.
• Non-SI units of kieffers: Cal⋅cm⁻²⋅K⁻¹⋅s^−1/2, are also used informally in older references.^[i]

When a constant flow of heat is abruptly imposed upon a surface,${\displaystyle r}$ performs nearly the same role in limiting the surface's initialdynamic "thermal inertia" response:

${\displaystyle U_{dyn}(t)\approx \frac{r}{\sqrt{t}};t>0}$

as the rigid body'sstatic heat transfer coefficient${\displaystyle U}$ plays in determining the surface's steady-state temperature.^[8][9]

• List of thermodynamic properties
• Thermal analysis

• Thermodynamic properties
• Physical quantities
• Heat transfer

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