Applications of the Poisson and diffusion equations to materials science

Abstract

The scope of a variety of experiments involving the transfer of heat in engineering applications is evident in research on thermal studies throughout the department of Norte de Santander, Colombia. From the energy optimization processes in the brickworks of the province of Ocaña to the didactic use in the Universidad Francisco Santander, Ocaña, Colombia. In this sense, mathematical models will be a fundamental tool in the understanding of thermal transfer processes. The aim of this work is to establish a mathematical model by numerical methods to determine the physical process of heat transfer in liquid crystal. For the data acquisition, an experiment that measures thermal properties on an aluminum plate was designed. We proceed to propose a mathematical model that uses the Poisson equation. Also, we proceed to calculate the solution of the equation by the finite difference method and then make a comparison with the analytical solution and the experimental data.