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Math. Comput. Appl. 2004, 9(2), 321-332; doi:10.3390/mca9020321

An Infinite Plate with a Curvilinear Hole and Flowing Heat

1
Department of Mathematics, Faculty of Science, Zagazig University, Egypt
2
Department of Mathematics, Faculty of Education, Alexandria University, Egypt
*
Author to whom correspondence should be addressed.
Published: 1 August 2004
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Abstract

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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MDPI and ACS Style

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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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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