This project was an applied exploration of Partial Differential Equations (PDEs) in modeling heat transfer within thermal protection systems, based on the CHarring Ablator Response (CHAR) framework developed by NASA. While not original research, the project was a technical exercise in replicating and understanding the key physical principles presented in the CHAR paper (Salazar et al., 2016).

By designing a simulation of concentric spherical shells in MATLAB, we investigated how thermal conductivity and emissivity affect heat distribution during spacecraft re-entry conditions. We formulated and solved the steady-state heat equation in spherical coordinates, applying real boundary conditions to mimic high-temperature environments. This allowed us to visually analyse temperature gradients, surface heating effects, and material responses.

The project helped reinforce how mathematical tools like PDEs and numerical solvers can be directly applied to aerospace challenges. It also deepened my understanding of material behaviour under extreme conditions and improved my ability to translate theoretical knowledge into simulation-driven insight.

Mathematical