A rod of length l has one end maintained at temperature t0 and is exposed to an environment of temperature t. An electrical heating element is placed in the rod so that heat is generated uniformly along the length at a rate q. Derive an expression (a) for the temperature distribution in the rod and (b) for the total heat transferred to the environment. Obtain an expression for the value of q that will make the heat transfer zero at the end that is maintained at t0.
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