New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method

Abstract

Featured Application: The amount of heat transferred by conduction is given by Fourier's law.For the study of these phenomena, the application of computational techniques that allow the design of machines and devices used in engineering becomes crucial. Abstract: In this paper, a new constitutive matrix [M τ ] 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 [M λ ] 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 [M τ ] are of the order of 0.0025%, much lower than those obtained with the matrix [M λ ].