Mathematical Modeling of Heat Conduction

TL;DR

This paper develops a mathematical model for heat conduction in rods, implements a numerical solution using finite difference methods in Python, and simulates heat transfer in different metals to analyze their behavior.

Contribution

It introduces a detailed mathematical model and a Python-based simulation approach for heat conduction in various metals, demonstrating practical application of numerical methods.

Findings

Simulation results for Aluminum, Copper, and Mild Steel rods.

Finite difference method effectively solves the heat conduction equation.

Discussion of temperature distribution over time.

Abstract

This report describes a mathematical model of heat conduction. The differential equation for heat conduction in one dimensional rod has been derived. The explicit finite difference numerical method is used to solve this differential equation. Then for simulation, a code was written in using python libraries via Jupyter notebook. The simulation carried out for Aluminum, Copper and Mild Steel rods and results were discussed.