Presence of Heat on an Infinite Plate with a Curvilinear Hole Having Two Poles

Abstract

In the present paper Cauchy integral methods have been applied to derive exact and expressions for Goursat's function for the first and second fundamental problems of isotropic homogeneous perforated infinite elastic media in the presence of uniform flow of heat. For this, we considered the problem of a thin infinite plate of specific thickness with a curvilinear hole where the origins lie in the hole is conformally mapped outside a unit circle by means of a specific rational mapping. Moreover, the three stress components xx σ , yy σ and xy σ of the boundary value problem in the thermoelasticity plane are obtained. Many special cases of the conformal mapping and four applications for different cases are discussed and many main results are derived from the work.