Numerical Heat Analysis

I was tasked with analyzing a theoretical heat transfer problem for an internally cooled turbine blade given a specific set of data. Below are some of the techniques I used to solve this problem.

General Overview of the Problem

The specific problem that was given was to model the temperature distribution of air flow over a heated turbine blade to prevent it from being damaged. Even though this was a hypothetical problem, this is a very real scenario that happens to gas turbine engines and finding ways to combat this issue will help improve performance of these engines and reduce the cost it takes to repair them.

Using Iterative Methods

When examining this problem, the best way to find a solution would be to use iterative mathematical solutions. I created all the diagrams from scratch showcasing both how to explain the heat transfer occurring across the blade and how to derive the equations necessary to perform the iterative methods.

Programming to find solutions

Once I derived all the equations, I then used Gauss-Seidel iteration techniques to derive the temperature distribution across the blade using the programming software MATLAB. Through MATLAB, I then graphically displayed the values and concluded that the method of cooling the blades with cold air will yield successful results in this hypothetical scenario.