One of my projects in the graduate course “Advanced Heat Transfer” was to find the optimal position for a thermocouple such that the fluctuations in temperature are minimized during the operation of a feedback temperature control. The control system was modeled using a discretized mesh, so only these points could be evaluated for the temperature distribution. A code was developed that would, for a selected node, determine the mean absolute deviation of temperature across the spatial domain as a metric for fluctuation intensity in time. To find the optimal location, all that needs to be done is sample nodes across the mesh and find the lowest deviation.

What complicates this is the size of the mesh. There were, on average, 1275 nodes within the mesh. The code that evaluated the mean absolute deviation took approximately 5 seconds to evaluate one point, so, to sample the entire mesh would take 105 minutes – far too long a time. Instead, a unique optimization algorithm had to be developed that would drastically reduce the number of computations necessary.

An excerpt from my report describes this succinctly:

“To scan the domain, the matrix discretization was subdivided into a larger grid of 3×3 squares. The position of the center of each square is used to compute the mean deviation for that point. The code then searches for the index associated with the smallest mean deviation. When found, all positions within the 3×3 square are input into the mean deviation function. This process cuts the number of node calculations from 1275 to 144 – an 86% reduction.”

A visual of how this algorithm works is provided below.

Ultimately, this is able to generate a surface such as the following.

The report for this project is provided here: Project_3.