Analysis of Heat and Fluid Flow Problems in a Multiply-Connected Region, using a Conformal Mapping

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Extension and applicability of conformal mapping used in a finite difference scheme is investigated. Univalence of conformal mapping required is searched in a family of functions possessing parameters, whereas an explicit condition for multiply-connectedness is clearly introduced and several concrete conformal mapping functions for a multiply-connected domain are proposed, supplemented with a transform of a variable if any, since such a conformal mapping function is not uniquely determined as long as only corresponding boundary configurations are specified a priori.