FOURIER ANALYSIS IN HEAT CONDUCTION PROBLEMS: A CASE STUDY ON ONE-DIMENSIONAL ROD MODELS
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Rodika Utama
Moh. Toifur
Dimas Nurachman
Misconceptions The study of heat conduction has long been a central topic in applied mathematics and physics, providing fundamental insights into the diffusion of thermal energy across various media. This research focuses on solving the one-dimensional heat conduction equation using Fourier analysis as a mathematical tool to obtain an exact solution under specified boundary and initial conditions. By applying separation of variables and Fourier series expansion, the temperature distribution of the rod is represented as an infinite series that converges to the exact solution. To validate the analytical solution, a numerical simulation based on the finite difference method is also performed, allowing comparison of accuracy and convergence. The results show that Fourier analysis provides a reliable and elegant framework to model heat conduction problems, with numerical methods serving as a complementary approach for cases where closed-form solutions are intractable. This study highlights the significance of Fourier techniques not only in mathematical physics but also in practical applications such as material science and thermal engineering.
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