A cylindrical block of metal at a uniform temperature 1.°F has its circular faces thermally insulated. The temperature of the curved sur- face is suddenly raised to and maintained at T,°F. Prove that the tem- perature T of any point in the block at any time is given by: T-T 2. J.,r) Σ T-T Un J. a) where r is the radial coordinate, a is the radius of the cylinder, K is the thermal diffusivity, and an are the positive roots of Jona) = 0 M.Sc., Birmingham 1962. a n=1
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