Exact Graetz problem solution by using hypergeometric function

Abstract

This paper proposes an exact solution of the classical Graetz problem in terms of an infinite series represented by a nonlinear partial differential equation considering two space variables, two boundary conditions and one initial condition. The mathematical derivation is based on the method of separation of variables whose several stages were illustrated to reach the solution of the Graetz problem.A MATLAB code was used to compute the eigenvalues of the differential equation as well as the coefficient series. In addition, the analytical solution was compared to the numerical values obtained previously by Shah and London. It is important to note that the analytical solution is in good agreement with published numerical data.