New thermal-conductivity constitutive matrix in fourier's law for heat transfer using the cell method

Abstract

In this paper, a new constitutive matrix [Mτ] for thermal conduction, for tetrahedral meshes, in a steady state thermal regime is developed through a new algebraic methodology, using the Cell Method as a computational method, which is included in the finite formulation. The constitutive matrix defines the behavior of solids when they are under a thermal potential. The results are compared with those obtained for the same problem by means of the constitutive matrix [Mλ] developed previously, taking in both cases with a 2D axisymmetric model as reference, calculated with the finite element method. The errors obtained with the new matrix [Mτ] are of the order of 0.0025%, much lower than those obtained with the matrix [Mλ].