Two finite difference case studies modelling steady-state and transient heat conduction through a 2D body.
For a mathematics couse in 2025, I was tasked with modelling heat transfer through a rectangular body using the finite difference method (FDM). I built numerical models of two-dimensional heat conduction, first solving the steady-state problem with mixed boundary conditions with prescribed heat flux, fixed temperature, an insulated edge, and convective heat transfer — using Gauss-Seidel iteration. We then extended this to the transient case for a stainless-steel plate, using the explicit FDM to track how the temperature field evolves over time, stepping forward from an initial condition subject to the stability criterion on the time step.
I used object oriented programming in Python to build the solvers, creating a Body class to represent the 2D domain and its boundary conditions, and a Solver class to implement the numerical methods. The code was structured to allow easy modification of the mesh resolution, boundary conditions, and material properties, enabling a systematic exploration of how these factors influence the solution.