Temperature Distribution in a Cylindrical Bar

by Natalie Edinger

Submitted : Fall 2011

The first step for this project was researching what cylindrical heat flow and temperature distribution was applied to, in order to put this problem in a real world context. Next, you had to solve the three given integrals in the project by using trigonometric identities and simple integration rules. When the calculations were complete for these individual functions, these function were used to finish evaluating the series. Since there were multiple different situations, there were two different versions of the series.

After examining the series that came out of the equation, the interesting series was the one that really showed the relationship of temperature and radius was the series for even n-values. The series was then plotted in excel and put the data onto a graph. The graph shows that the temperature doesn’t change as quickly inside the cylindrical bar as it does on the outer edges. Meaning, as you move towards the center of the cylinder the temperature increases.

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