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Two identical copper bars are each of length a. Initially, one is at and the other is at ; they are then joined together end to end, and thermally isolated. Obtain in the form of a Fourier series an expression for the temperature at any point a distance from the join at a later time . Bear in mind the heat flow conditions at the free ends of the bars.
Taking estimate the time it takes for one of the free ends to attain a temperature of . The thermal conductivity of copper is , and its specific heat capacity is .
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