Thermal conductivity represents the rate at which heat is transferred by conduction through a given unit area of a given material when the temperature difference or gradient is normal to the cross-sectional area. The coefficient of thermal conductivity can be defined as the quantity of heat that travels through a unit volume of a material structure at a given time when the temperature gradient is one degree.

In physics, the thermal conductivity is the property of a material's ability to conduct heat, primarily as in Fourier's Law for heat conduction. Heat transfer across materials of high thermal conductivity occurs at a higher rate than across materials of low thermal conductivity. The law of heat conduction, also known as Fourier's law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat is flowing.

where is the heat flux, is the temperature, and is the effective thermal conductivity [W/mK, Watts per meter Kelvin]. When the temperature at inlet , at outlet , also the thickness of the material L, are known, the effective thermal conductivity is expressed as

In general, the effective thermal conductivity is a second order tensor

If the material is isotropic, that is, its properties are the same in all directions, instead of the tensor , a scalar constant can be used.

Compute Thermal Conductivity determines the effective (homogenized) thermal conductivity tensor of a structure. To achieve this, the Poisson equation

is solved in the 3D structure model. Each material within the structure is characterized by its local thermal conductivity . The constituent materials can be with isotropic, transverse isotropic or orthotropic conductivity.

The resulting material is in general anisotropic, and a conductivity tensor is needed to prescribe complete thermal behavior. To reduce computational time, it is also possible to limit calculations to certain columns of the conductivity tensor, if heat flux in only one direction is of interest.