熱伝導方程式の合流形超幾何関数解

概要

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The unsteady one-dimensional heat conduction equation is transformed into Kummer's equation unifiedly in the linear, cylindrical and spherical coordinate systems. This ordinary differential equation (similarity equation) is solved in terms of the confluent hypergeometric functions. The conditions under which such solutions (similarity ones) exist are that boundaries must lie at the origin and infinity, or otherwise move with their positions proportional to the square root of time. For the already known similarity solutions in the case of fixed boundaries which are expressed in terms of other functions such as an error function, its repeated integrals and the exponential integral function, the corresponding confluent hypergeometric expressions are given. The conduction similarity solutions can be applied to solve such a moving boundary probmem that the moving boundary moves as the square root of time. However, if there is phase change, only one solution exists in each coordinate system.
社団法人日本機械学会の論文
1988-06-25