Group method analysis of two-dimensional plate in heat flux - Mina B. Abd-el-Malek; Fayez H. Michael; Samy M. A. El-Mansi (International Journal of Mathematics and Mathematical Sciences)
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.