An analysis is made of the unsteady heat flow through a solid cylindri¬cal wire containing heat sources and a coating in the form of a cylindrical shell. The differential equations are linearized and the solutions are found by the method of Laplace transforms. The response of a constant-current coated wire is obtained for two step-like initiating conditions: (1) a change in convective cooling and (2) a change in power or current input. The response of a constant-temperature coated wire is obtained for a step-like change in convective cooling. An equivalent time constant for each of the three cases is computed. The fre¬quency responses of the wire to sinusoidal initiating disturbances are derived in each case by applying Duhamel's theorem. Bare wire responses are obtained by letting the coating thickness shrink to zero.
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