Title: An approximate numerical solution to the Graetz problem with constant wall temperature

Authors: Ali Belhocine

Addresses: Faculty of Mechanical Engineering, University of Sciences and the Technology of Oran USTO, L.P 1505 El-Mnaouer, 31000 Oran, Algeria

Abstract: 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, is 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 visualisation 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 orthogonal collocation method giving better results than Crank-Nicholson method.

Keywords: temperature profile; laminar flow; partial differential equations; PDEs; orthogonal collocation; Crank-Nicholson method; convection; Graetz problem; constant wall temperature; heat transfer; transport phenomenon; cylindrical pipes; fluid flow; visualisation; finite difference method; FDM.

DOI: 10.1504/IJCSM.2017.083126

International Journal of Computing Science and Mathematics, 2017 Vol.8 No.1, pp.35 - 51

Received: 18 Apr 2015
Accepted: 20 Feb 2016
Published online: 21 Mar 2017 *

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