Analytic solutions of initial-boundary-value problems of transient conduction using symmetries

TL;DR

This paper applies Lie symmetry methods to derive analytic solutions for initial-boundary-value problems in transient heat conduction, demonstrating a systematic approach and validating results with numerical comparisons.

Contribution

It introduces a systematic extension of symmetry methods to solve boundary value problems in heat conduction, providing explicit analytic solutions.

Findings

Analytic solutions derived using symmetry methods

Comparison shows good agreement with numerical solutions

Method applicable to various boundary conditions

Abstract

Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a manner highlighting the systematic procedure of extending the symmetry method for a PDE to investigate BVPs of the PDE. A comparative analysis of numerical and closed form solutions is carried out for a physical problem of heat conduction in a semi-infinite solid bar made of AISI 304 stainless steel.