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
Mina B. Abd-El-Malek1
, Fayez H. Michael2
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
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.