Numerical Simulation of Heat Diffusion in a Homogeneous Bar

Abstract

Heat transfer phenomena are caused by the heterogeneity of an intensive physical magnitude between two systems [1,6]. The temperature parameter T is one of these quantities which will be responsible for a particular transport problem [13]. This will be a transfer of heat energy heat which can be carried out in three processes: conduction, convection and radiation [12,13]. Our goal is to find the analytical solution $T(x, t)$ of the heat diffusion inside a homogeneous bar of conduction coefficient $\lambda $ of section S, of length L, maintained at a constant temperature $T_{0}$ on each of its ends, and initially heated at a temperature $T_i$ over a length of $2l$ with well-defined boundary conditions and compare it with the numerical solution using the explicit finite difference scheme by studying the stability and consistency of the scheme [2,3,5,11]. The mathematical and numerical modeling results of thermal diffusion in general makes it possible to thoroughly study the application in different fields such as chemistry, metallurgy, and micro-electronics manufacturing [8,9].