International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 22, Pages 1369-1382

Group method analysis of two-dimensional plate in heat flux

Mina B. Abd-el-Malek,1 Fayez H. Michael,2 and Samy M. A. El-Mansi1

1Department of Mathematics, School of Engineering and Sciences, The American University in Cairo, Cairo 11511, Egypt
2Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt

Received 24 June 2002

Copyright © 2003 Mina B. Abd-el-Malek et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The group transformation theoretic approach is applied to present an analytic study of the temperature distribution in a triangular plate, Ω, placed in the field of heat flux, along one boundary, in a form of polynomial functions of any degree “n.” The Laplace's equation has been reduced to second-order linear ordinary differential equation with an appropriate boundary conditions. Exact solution has been obtained for general shape of Ω and different boundary conditions.