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 A highly conduction solid cylinder of radius a and length l is surrounded by co-axial layer of a material having thermal conductivity K and negligible heat capacity. Temperature of surrounding space (out side the layer) is T0, which is higher than temperature of the cylinder. If heat capacity per unit volume of cylinder material is s and outer radius of the layer is b, calculate time required to increase temperature of the cylinder from T1 to T2 . Assume and faces to be thermally insulated.

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On integrating with respect to dx we get

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