Application of Fourier Series and the Method of Variables Separation in Solving Heat Conduction Problems

Student: Abubakar Abdulkadir Saleh (Project, 2025)
Department of
Northwest University, Kano, Kano State

Abstract

This thesis explores the application of Fourier series in solving partial differential equations (PDEs),
focusing on the one- and two-dimensional heat equations. Using the method of separation of variables,
Fourier series effectively decompose complex heat transfer problems into simpler forms, enabling precise
temperature distribution modeling over time. The study demonstrates the accuracy and efficiency of
this approach in solving PDEs commonly used in engineering and physics. Future research may extend
these methods to three-dimensional heat equations and more advanced boundary conditions for broader
practical applications.

Keywords
Fourier Series Variable Separation Heat Conduction Partial Differential Equation Mathematical Modeling Heat Equation
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