Thermal inertia

The thermal inertia is an intensive property of materials related to thermal conductivity and volumetric heat capacity. It is a term often used in the modeling of heat transfer mechanisms.

Origin of the term

The term is actually a scientific analogy, making use of a name borrowed from mechanics where "inertia" defines an effect that opposes the acceleration of a body. Similarly, thermal inertia is a measure of thermal mass and the thermal wave that controls the surface temperature of a material.

In heat transfer models, a higher value of volumetric heat capacity means that the system will require a longer time to reach thermodynamic equilibrium.

Definition

The thermal inertia of a material is defined as the square root of the product between the thermal conductivity and the volumetric heat capacity, where the latter is the product between the density and the specific heat capacity:

I=(kρ ρ c){displaystyle I={sqrt {(krho c)}}}}

• k{displaystyle k} is thermal conductivity, with units [W m⁻¹ K⁻¹]
• ρ ρ {displaystyle rho } is density, in [kg m⁻³]
• c{displaystyle c} is the specific caloric capacity in [J kg⁻¹ K⁻¹]
• I{displaystyle I} has inertia units in the SI [J m⁻² K⁻¹ s^−1/2]. In some old texts non-SI units are used, for example the Kieffers [Cal cm⁻² K⁻¹ s^−1/2].

Use

The term is used, for example, when dynamic effects prevail in an abstract model, such that the steady-state calculation could lead to inaccurate results, in which case it is said, for example: "this material it has a high thermal inertia", or "thermal inertia plays an important role in this system".

In planetary science, the thermal inertia of surface materials is a fundamental property that controls variations in daytime, nighttime, and seasonal temperatures, where it varies depending on the geological materials that are close to the surface.

In remote sensing applications, thermal inertia represents a complex combination of particle size, rock abundance, bedrock outcrops, and degree of elevation. A rough approximation of the thermal inertia can be obtained from the width of the diurnal temperature curve (maximum temperature minus minimum temperature). The temperature of a material with low thermal inertia varies significantly throughout the day, while the temperature of a material with high thermal inertia does not change as drastically.

Understanding and deriving the mechanisms of thermal inertia of a surface can help to recognize small-scale features of the surface, in conjunction with other types of data, thermal inertia can help characterize the surface materials and geological processes responsible of the formation of these materials.

The thermal inertia of the oceans is a major influencer on climate change: the degree of global warming that is ultimately predicted will depend on a fundamental change in radiative forcing, such as a sustained increase in greenhouse gas concentrations