Applications of differential equations to model the physical phenomenon of heat transfer with an internal energy source

Abstract

Abstract The mathematical modeling of the physical phenomenon of conduction in the presence of heat sources has various uses in engineering ranging from heat diffusion, pollution generation in large cities and chemical reactions. From the mathematical theory, the study of physical phenomena with the presence of heat is approached from techniques of polynomial approximation, analysis of variations and numerical methods. In this research a mathematical model is proposed to study the heat conduction in a metal bar with a heat source. In the first part of the work, by the application of the method of the parameter variation, the exact solution of the mathematical model is calculated. Subsequently, by means of a case study of the physical phenomenon of heat conduction with internal energy source, with the use of computational simulation, the convergence of the Fourier series linked to the physical phenomenon is shown. The mathematical method proposed in the paper can be applied to other physical phenomena such as wave propagation, electric potential, and chemical reactions.