In my graduate course, Advanced Heat Transfer, I was tasked with optimizing the dimensions of a finned cooling plate for a given convective flow. The schematic used for my report is provided below for reference.

In this schematic, fluid is flowing from left to right and is being cooled by the adjacent plate. This project required the optimization of the longitudinal dimension (L_x) and the fin length (L_f) such that the bulk fluid temperature decreased by 10 C°. This poses an interesting problem since there is not one optimal configuration. Instead, there are an infinite amount of configurations that would return that 10 °C decrease. Therefore, in a 2D plane representing dimensions L_x and L_f, there should be a boundary where a 10 °C reduction is achieved.

When researching numerical methods for 2D optimization, there were none immediately apparent that could fit an equation to a surface. In light of this, Nicholas designed a 2D equation optimization algorithm that finds an equation of best fit to a distribution of data. To increase the precision of the algorithm, it is designed to iteratively refine the sampling mesh. A coarse mesh is tested over the surface, then the algorithm tests which points are closest to the 10 °C reduction and increases the mesh size locally. Then, after a specified number of iterations, the algorithm interpolates to find locations that satisfy the temperature decrease and fits an exponential equation to the data.

The results of this method is shown below.

With some modification, this optimization algorithm could be used for any 2D system that can be sampled.

The report passed in for this project is provided here: Project_4.