对目前比较通用的生物导热基本方程Pennes方程,给出了其三维非定常情况下的代数显式解析解。据知,以前很少有发表过这类严格的几何多维解析解。它除了有不可代替的理论价值外,还可以作为标准解来校验日益发达的数值解以及作为基础来研究计算传热学的数值计算方法。另外,文章的特殊求解方法也有发展价值之处。 At present, the generalized Pennes equation of bio-conductive basic equation is given and its explicit analytic solution of algebra under three-dimensional unsteady conditions is given. It is known that few such rigorous geometric multidimensional analytical solutions have been published before. In addition to its irreplaceable theoretical value, it can also be used as a standard solution to verify the increasingly developed numerical solution as well as to study the numerical calculation method for calculating heat transfer. In addition, the article’s special solution also has value for development.