Symmetries of two-dimensional heat transfer equation, order reduction and exact solutions

Document Type : Research Article

Authors

1 PhD Candidate, Faculty of Mathematical Sciences, Shahrood University of Technology

2 Assistant Professor, Faculty of Mathematical Sciences, Shahrood University of Technology

Abstract

In this paper, we analyze the exact solutions of two-dimensional heat transfer equation by using a class of differential operators, called symmetries of differential equations. Firstly, we introduce the general form of the two-dimensional heat transfer equation. Then, we will find the exact solutions of the equations by using the mentioned differential operators in some special cases. It is noteworthy that this method could be extended to all kinds of system of differential equations.

Keywords