This project was completed for my AERSP 313 Aerospace Analysis course, which covered mathematical topics and methods relevant to future aerospace courses. 

We were tasked to design a cooling system for a hypersonic vehicle that will fly in the atmosphere. To begin, analytical methods were used to solve the PDE Heat Equation. I then used numerical discretization to create a set of equations to be inputted into MATLAB. This code consisted of an initialization procedure, a linear solver using LU decomposition, a for-loop that solved the PDE for time, and a procedure to solve the problem analytically. In the end, I was the first student in three years to achieve first-order accuracy when non-linear boundary conditions were implemented into the problem.