Methods for Solving Heat Conduction Problems

This article provides comprehensive guidance for beginners on solving heat conduction problems using MATLAB. We begin by introducing the background and fundamental concepts of heat conduction, along with its mathematical formulation. The core section details step-by-step implementation methodologies in MATLAB, including key functions like pdepe() for parabolic PDE solutions and finite difference discretization techniques. Practical code examples demonstrate temperature distribution calculations with boundary condition handling. Additionally, we explore common heat conduction scenarios such as transient heat transfer in solids and steady-state problems, explaining corresponding numerical solutions through matrix operations and iterative methods. Each example includes code annotations highlighting critical algorithmic steps like stability criteria for explicit schemes. The objective is to deliver an accessible yet technically thorough MATLAB resource for heat conduction problem-solving, combining theoretical foundations with executable implementation strategies.