Exact analytical solution to three-dimensional phase change heat transfer problems in biological tissues subject to freezing |
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Authors: | Fang-fang Li Jing Liu Kai Yue |
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Institution: | 1. Thermal Engineering Department, University of Science and Technology Beijing, Beijing 100080, P. R. China 2. Thermal Engineering Department, University of Science and Technology Beijing,Beijing 100080, P. R. China |
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Abstract: | Analytically solving a three-dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult but theoretically important. The moving heat source model and the Green function method are introduced to deal with the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temper-ature transients of tissues under various boundary conditions, such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces, are obtained. Furthermore, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes is also analytically solved. A closed-form analytical solution to the bioheat phase change process is derived by considering contributions from blood perfusion heat transfer, metabolic heat generation, and heat sink of a cryoprobe. The present method is expected to have significant value for analytically solving complex bioheat transfer problems with phase change. |
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Keywords: | threo-dimensional phase change heat transfer problem cryosurgery cry-opreservation moving heat source model bioheat transfer Green's function analytical solution |
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