Abstract
Reasonable unsteady three-dimensional explicit analytical solutions are derived with different methods for the widely used bio-heat transfer equation-Pennes equation. The condition to decide temperature oscillation is obtained in this paper. In other cases the temperature would vary monotonously along geometric coordinates as time goes by. There have been very few open reports of explicit unsteady multidimensional exact analytical solutions published in literature. Besides its irreplaceable theoretical value, the analytical solution can also serve as standard solution to check numerical calculation, and therefore promote the development of numerical method of computational heat transfer. In addition, some new special methods have been given originally and deserved further attention.
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