COMPARATIVE STUDY OF TWO NUMERICAL METHODS FOR SOLVING THE GRAETZ PROBLEM: THE ORTHOGONAL COLLOCATION AND CRANK-NICHOLSON METHODS
Keywords:Temperature profile, laminar flow, orthogonal collocation, Crank-Nicholson method, Convection
The present set of themes related to the investigations of heat transfer by convection and the transport phenomenon in a cylindrical pipe in laminar flow, commonly called the Graetz Problem, which is to explore the evolution of the temperature profile for a fluid flow in fully developed laminar flow. A numerical method was developed in this work, for visualization of the temperature profile in the fluid flow, whose strategy of calculation is based on the orthogonal collocation method followed by the finite difference method (Crank-Nicholson method). The calculations were effected through a FORTRAN computer program, and the results show that the orthogonal collocation method gives better results than the Crank-Nicholson method. The results of the present work concerning the variation of the dimensionless temperature with the axial distance for the two cases are compared with the available known results to support its accuracy.
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