Numerical calculation of the effective thermal properties of a composite by finite elements

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Rodney Hechavarría Díaz http://orcid.org/0000-0002-0195-6157
Gonzalo López http://orcid.org/0000-0003-4387-6216
Francisco Pazmiño http://orcid.org/0000-0002-6530-043X
Maritza Ureña http://orcid.org/0000-0002-0667-5581
Andres Hidalgo http://orcid.org/0000-0001-5179-2405

Abstract

The development of new methods for determining the thermal properties of composite materials is always in constant progress. This study proposes a one-dimensional method for the numerical calculation of effective thermal conductivity and diffusivity in heterogeneous solid materials (composite), between [10--20 °C], using the program Solidworks 2016, which is based on the method of Finite Element Calculation. First, the temperature distribution is obtained as a function of the coordinate and time; then, the theoretical model, the Parabolic Heat Diffusion Equation in one dimension, is adjusted to the data obtained in the simulation to obtain the solution. Initially, the temperature distribution in a homogeneous solid copper bar, known material, is modeled under a constant heat flux at $x = L$, yielding thermal conductivity and diffusivity values in accordance with those reported in the literature, with a relative error of 0.01% and 0.7% respectively. Then, the temperature distribution is modeled in a heterogeneous solid bar based on copper (65.7%)--lead (34.3%) and, under the same heat flow condition, the simulated values of temperature in function of the time with which the effective thermal conductivity and diffusivity of this compound are calculated. The obtained results show consistency and reliability because they are within the range established by previous studies.