Average Temperature in a Cylindrical Bar

by Clayton Whitelaw

Submitted : Spring 2009

This project involves finding the Average temperature in a cylindrical bar, given that between the angles pi and 2pi, the surface remains at a constant temperature To. The equation to solve for T involves a Fourier series. Each coefficient is a separate, definite integral from 0 to pi. The first Fourier coefficient is solved, then the second equation is solved for T and substituted it into the final equation for the average temperature. My result is that the average temperature is To[1+(alpha/pi)].

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