Exact Analytical Solution to Three Dimensional Phase Change Heat Transfer Problems in Biological Tissues Subject to Freezing

LI Fang-fang; LIU Jing; YUE Kai

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Article Navigation > Applied Mathematics and Mechanics > 2009 > 30(1): 64-74

LI Fang-fang, LIU Jing, YUE Kai. Exact Analytical Solution to Three Dimensional Phase Change Heat Transfer Problems in Biological Tissues Subject to Freezing[J]. Applied Mathematics and Mechanics, 2009, 30(1): 64-74.

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Exact Analytical Solution to Three Dimensional Phase Change Heat Transfer Problems in Biological Tissues Subject to Freezing

1.
Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100080, P. R. China;

Received Date: 2008-02-20
Rev Recd Date: 2008-09-28
Publish Date: 2009-01-15

Abstract

Abstract

Analytically solving three dimensional (3-D) bioheat transfer problem with phase change during a freezing process is extremely difficult, however theoretically importantm. The moving heat source model and the Green function method were introduced for the cryopreservation process of in vitro biomaterials. Exact solutions for the 3-D temperature transients of tissues under various boundary conditions such as totally convective cooling, totally fixed temperature cooling and a hybrid between them on tissue surfaces were obtained. Further, the cryosurgical process in living tissues subject to freezing by a single or multiple cryoprobes was also analytically solved. A closed form analytical solution to the bioheat phase change process by taking account of contributions from blood perfusion heat transfer, metabolic heat generation and heat sink of cryoprobe was derived. The present method is expected to be of significant value for analytically solving complex bioheat transfer problems with phase change.
- three dimensional phase change heat transfer problem,
- cryosurgery,
- cryopreservation,
- moving heat source model,
- bioheat transfer,
- the Green function

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References(9)

References

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