Applications of linear algebra to the study of mathematical modelling of the physical phenomena of heat conduction by electricity

Abstract

The study of the phenomenon of electrical conduction has its origin in two historical antecedents, Fourier's law and Maxwell's equations. The mathematical formulation of electrical conduction has been extensively studied and the differential equations describing the phenomenon are known. The mathematical solution of the physical model of electrical conduction employs different techniques, the best known of which are the Fourier series, Grenn functions and Bessel equations. The purpose of this research is to present a model of heat conduction with the use of electric current that dissipates heat by convection. The research proposes a method for solving the mathematical model associated with the conduction phenomenon using linear algebra. The advantage of using linear algebra will allow to establish a step-by-step procedure that could be used to study phenomena related to heat conduction, in addition to allowing its implementation through programming. In order to establish the fit of the method derived from linear algebra, the analytical solution and the solution proposed in the research were compared to verify that the proposed method fits with a small error