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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2004, 9(2), 321-332;

An Infinite Plate with a Curvilinear Hole and Flowing Heat

Department of Mathematics, Faculty of Science, Zagazig University, Egypt
Department of Mathematics, Faculty of Education, Alexandria University, Egypt
Author to whom correspondence should be addressed.
Published: 1 August 2004
PDF [623 KB, uploaded 31 March 2016]


In the present paper, we apply the complex variable method (Cauchy method) to derive exact expressions for the Goursat's functions for the boundary value problem of infinite plate weakened by a curvilinear hole. The hole is conformally mapped on the domain outside a unit circle by means of a general rational mapping function. Also the stress components, when an initial heat is uniformly flowing in the perpendicular direction of the hole, are obtained, Some applications are investigated. The interesting cases, when the shape of the hole takes different famous formulas are included as special cases, The work of many previous authors can be considered as special cases of this work.
Keywords: Infinite plat; Curvilinear hole; Cauchy method; Goursatts functions Infinite plat; Curvilinear hole; Cauchy method; Goursatts functions
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Sabbah, A.; Abdou, M.; Ismail, A. An Infinite Plate with a Curvilinear Hole and Flowing Heat. Math. Comput. Appl. 2004, 9, 321-332.

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