Table 1.

The fundamental quantities and relationships for two-phase composites.

	Magnetostatics	Electrostatics	Heat Flow	Diffusion	Porous Media
	Definition of scalar potentials ϕ
ϕ	Scalar potential ϕ (A)	Electric potential V (Volt)	Temperature T (°K)	Substance concentration γ (mol/m3)	Hydrostatic pressure p (Pa)
	Definition of vector fields in the vacuum ${\mathrm{E}}_{\mathsf{\alpha }}={\nabla }_{\mathsf{\alpha }}\mathsf{\phi }$, $\mathrm{r}\mathrm{o}{\mathrm{t}}_{\mathsf{\alpha }\mathsf{\beta }}{\mathrm{E}}_{\mathsf{\beta }}=0$
Eα	Intensity of magnetic field Hα (A/m)	Intensity of electric field Eα (V/m)	Not used	Not used	Not used
	Definition of material properties Cαrβ
Cαβ	Magnetic permeability coefficients μ0μαβ (Tm/A)	Electric permittivity coefficients ε0εαβ [(A s)/(V m)]	Heat conduction coefficients kαβ [W/(°K m)]	Diffusion coefficients Dαβ (m2/s)	Proportionality coefficients Kαβ/η [m2/(Pa s)] *
	Definitions of vector fields in a particular medium Dα
Dα	Magnetic flux density Bα (T)	Electric flux Dα (C/m2)	Not used	Not used	Not used
	Constative relations ${\mathrm{D}}_{\mathsf{\alpha }}={\mathrm{C}}_{\mathsf{\alpha }\mathsf{\beta }}{\mathrm{E}}_{\mathsf{\beta }}$
	Physical relations ${\nabla }_{\mathsf{\alpha }}{\mathrm{D}}_{\mathsf{\alpha }}=0$
	Gauss’s Law for magnetism ${\nabla }_{\mathsf{\alpha }}\left({\mathsf{\mu }}_0{\mathsf{\mu }}_{\mathsf{\alpha }\mathsf{\beta }}{\mathrm{H}}_{\mathsf{\beta }}\right)=0$	Gauss’s Law ${\nabla }_{\mathsf{\alpha }}\left({\mathsf{\epsilon }}_0{\mathsf{\epsilon }}_{\mathsf{\alpha }\mathsf{\beta }}{\mathrm{E}}_{\mathsf{\beta }}\right)=\mathsf{\rho }$	Fourier’s Law ${\nabla }_{\mathsf{\alpha }}\left({\mathrm{k}}_{\mathsf{\alpha }\mathsf{\beta }}{\nabla }_{\mathsf{\beta }}\mathrm{T}\right)+\mathrm{Q}=0$	Fick’s Law ${\nabla }_{\mathsf{\alpha }}\left({\mathrm{D}}_{\mathsf{\alpha }\mathsf{\beta }}{\nabla }_{\mathsf{\beta }}\mathsf{\gamma }\right)=0$	Darcy’s Law ${\nabla }_{\mathsf{\alpha }}\left[\left({\mathrm{K}}_{\mathsf{\alpha }\mathsf{\beta }}/\mathsf{\eta }\right){\nabla }_{\mathsf{\beta }}\mathrm{p}\right]=0$

μ₀, magnetic permeability of vacuum, μ₀ = 4π × 10⁻⁷ (Tm/A); ε₀, electric permittivity of vacuum, ε₀ = 8.854187817 × 10⁻¹² [(A s)/(V m)]; * η, dynamic viscosity of fluid (Pas).