An exact study on temperature field in a hollow cylinder of finite length which is influenced by a surrounding with harmonic boundary condition is presented. To simulate an idealized situation, it is supposed that the cylinder is homogeneous and isotropic with physical properties independent of temperature and time. Here we impose a harmonic boundary condition on the external surface of the finite cylinder using Fourier analysis. The classical method of separation of variables and Duhamel’s theory is used to calculate the temperature field under periodic boundary condition. Numerical results reve the key effects of frequency of the surrounding temperature, Biot number and shell thickness on the amplitude ratio and phase difference of the cylinder temperature. The presented solution can lead to a better understanding of temperature behavior under harmonic boundary conditions. A limited case is considered and fair agreement with an available solution is obtained.

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