Applications of the method of lines for modeling the physical phenomenon of heat conduction

Abstract

Abstract It is claimed that most of the fundamental principles that govern the physical phenomena of interest in engineering applications can be described by differential equations. Therefore, the ability to analyze, solve and understand differential equations is essential for decision-making in the applied areas. In this sense, studying efficient methods to solve differential equations is a fundamental contribution in advancing the understanding of relevant physical models in engineering applications. The purpose of this research allowed to study the differential equation associated with Fourier’s heat transfer law and calculate its solution by two different methods than the traditional method. From this context, the study is related to the phenomenon of heat conduction in a metal bar under ideal conditions to later carry out its application in a particular case. First, the solution of the differential equation that models the physical phenomenon derived from the use of Fourier’s physical heat law is calculated with the use of statistical tools; then, a solution scheme is implemented using method of lines. Given the nature of the investigation, the solutions by both methods are compared about what is expected in the physical interpretation of Fourier’s law.