Electrical conductivity measures a material's ability to conduct an electric current. Ohm’s Law relates the electric potential  and the magnitude of current density :

Ohm's law is the electrical analogue of Fourier's law. When the electrical potential at inlet , at outlet , also the thickness of the material L, are known, the effective thermal conductivity is expressed as

Like the thermal conductivity, the electrical conductivity for isotropic materials is constant in all directions and can be characterized by a scalar. For anisotropic materials, is a tensor.

The effective electrical conductivity is determined by solving the Poisson equation

in the 3D structure model, where denotes the local electrical conductivity of the constituent materials.

The algorithm in ConductoDict (Wiegmann and Zemitis, 2006) has been used for many applications, in industrial settings (e.g. thermal insulation) and for academic purposes. Publications include heat transfer properties of medium density fiberboard (MDF) samples (Thoemen et al., 2008), of cast iron microstructures (Velichko, 2008, Velichko et al., 2009), of the gas diffusion layer in fuel cells (Schulz et al., 2007, Becker et al., 2008, Becker et al., 2009, Zamel et al., 2010, Veyret and Tsotridis, 2010, Pfrang et al., 2010) and electrical conductivity of Ag/SnO2 (Jeanvoinea et al., 2010).