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Solution of Two-dimensional Transient Heat Conduction in a Hollow Sphere under Harmonic boundary condition

In this study, an analytical modeling of two dimensional heat conduction in a hollow sphere, subjected to time dependent periodic boundary condition at the inner and the outer surfaces, is performed. The thermo physical properties of the material are assumed to be isotropic and homogenous. Also, the effects of the temperature oscillations frequency on the boundaries, the thickness variation of the hollow sphere and thermo physical properties of the ambient and the sphere involved in some dimensionless numbers are studied. The results show that the obtained temperature distribution contains two characteristics, the dimensionless amplitude and the dimensionless phase difference. Comparison between the present results and the findings of the previous study as related to a two- dimensional solution of the hollow sphere subjected to the simple harmonic condition shows a good agreement.