International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 22, Pages 1369-1382
doi:10.1155/S0161171203206335
Group method analysis of two-dimensional plate in heat flux
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.
Abstract
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.