Complex Potential Functions and Integro-Differential Equation in Elastic Media Problem in Presence of Heat

This paper covered the study of the boundary value problem for isotropic homogeneous perforated infinite elastic media in 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 origin lie inside the hole is conformally mapped outside a unit circle by means of a specific rational mapping . The complex variable method has been applied and it transforms the problem to the integro-differential equation with Cauchy kernel that can be solved to find two complex potential functions which called Gaursat functions. Moreover, the three stress components for the boundary value problem in the thermoelasticity plane are obtained. Many special cases of the conformal mapping and three applications for different cases are discussed and many main results derived from the work.