Ali Belhocine and Wan Zaidi Wan Omar

DOI: 10.14456/sjst-psu.2018.106

pp. 840 - 853

Abstract

This paper proposes anexact solution in terms of an infinite series to the classical Graetz problem 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 are elaborated to reach the
solution of the Graetz problem. MATLAB was used to compute the eigenvalues of the differential equation as well as the
coefficient series. However, both the Nusselt number as an infinite series solution and the Graetz number are based on the heat
transfer coefficient and the heat flux from the wall to the fluid. In addition, the analytical solution was compared to the numerical
values obtained by the same author using a FORTRAN program, showing that the orthogonal collocation method gave better
results. It is important to note that the analytical solution is in good agreement with published numerical data. 

Keywords

• Graetz problem
• Sturm-Liouville problem
• partial differential equation
• dimensionless variable