Finite element of the heat conduction equation with temperature dependent coefficients

A finite element formulation is derived for the equation of heat conduction with temperature dependent conductivity and heat capacity. The derivation of the finite element model is based on a variational formulation of the heat conduction equation which, together with generalized coordinates, yields an equation of similar form to Lagrange's equation in mechanics. The obtained equation is of special interest for applying the finite element method to solve problems with temperature-dependent properties.