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.
Highlights
The Laplace’s equation arises in many branches of physics, from which it attracts a wide band of researchers
The mathematical technique used in the present analysis is the parametergroup transformation
The group methods, as a class of methods lead to the reduction of the number of independent variables, were first introduced by Birkhoff [6] in 1948, where he made use of one-parameter transformation groups
Summary
The Laplace’s equation arises in many branches of physics, from which it attracts a wide band of researchers. We present a general procedure for applying one-parameter group transformation to the Laplace’s equation in a triangular domain. The equation is solved analytically for the general form of the triangular domain and boundary conditions. The method of solution depends on the application of a one-parameter group transformation to the partial differential equation (2.1).
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