Exact Analytical Solution to Three Dimensional Phase Change Heat Transfer Problems in Biological Tissues Subject to Freezing
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摘要: 对冻结过程中的三维生物传热相变问题进行分析求解是低温生物医学中一个困难而有重要理论意义的课题．围绕离体生物材料的低温冻存过程，引入移动热源模型及Green函数法，求得几组不同边界（全对流、全定温和复合边界）条件下，生物组织瞬态温度场的三维精确解表达式；进一步地，针对低温手术中生物活体组织受单枚或多枚冷冻探针的作用问题，考虑了血液灌注率、代谢热产及探针冷源的存在，同样推导出相应边界条件下瞬态温度场的精确解．该方法对于处理复杂生物传热问题的分析求解有重要的理论参考价值．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.
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[1] Diller K R. Modeling of bioheat transfer processes at high and low temperature[J].Advances in Heat Transfer,1992,22:157-357. doi: 10.1016/S0065-2717(08)70345-9 [2] 刘静.低温生物医学工程学原理[M].北京：科学出版社，2007. [3] 华泽钊，任禾盛.低温生物医学技术[M].北京：科学出版社，1994. [4] Deng Z S，Liu J.Modeling of multidimensional freezing problem during cryosurgery by the dual reciprocity boundary element method[J].Engineering Analysis With Boundary Elements，2004，28(2)：97-108. doi: 10.1016/S0955-7997(03)00128-0 [5] 蔡睿贤, 张娜.生物导热基本方程的一维不定常解析解[J].自然科学进展,1998,8(6):331-336. [6] Budman H, Shitzer A,Dayan J.Analysis of the inverse problem of freezing and thawing of a binary-solution during cryosurgical processes[J].ASME Journal of Biomechanical Engineering,1995,117(2):193-202. doi: 10.1115/1.2796001 [7] Liu J，Zhou Y X.Analytical study on the freezing and thawing process of biological skin with finite thickness[J].Heat and Mass Transfer,2002,38(4/5):319-326. doi: 10.1007/s002310100216 [8] Ozisik M N.热传导[M].俞昌铭主译.北京：高等教育出版社，1983. [9] Deng Z S，Liu J.Analytical study on bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies[J].ASME Journal of Biomechanical Engineering，2002，124(6)：638-649. doi: 10.1115/1.1516810 -
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