Integral transformation of elliptic problems within irregular domains: Fully developed channel flow
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 1 December 1997
Abstract
Employs the integral transform method in the hybrid numerical‐analytical solution of fully developed laminar flow within a class of irregularly shaped ducts, with respect to the co‐ordinate system chosen to represent the geometry under consideration. A quite general formulation of a two‐dimensional steady‐state diffusion problem is initially considered, and a formal solution is provided. The original partial differential equation is analytically transformed into an infinite system of ordinary differential equations for the transformed velocity field in the flow direction. On truncation to a sufficiently large finite order, adaptively chosen to meet prescribed accuracy requirements, well‐established numerical schemes for boundary value problems are utilized, readily available in scientific subroutines libraries. Illustrates convergence rates for a few typical duct geometries and critically examines previously reported numerical solutions.
Keywords
Citation
Barbuto, F.A.A. and Machado Cotta, R. (1997), "Integral transformation of elliptic problems within irregular domains: Fully developed channel flow", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 7 No. 8, pp. 778-793. https://doi.org/10.1108/09615539710193065
Publisher
:MCB UP Ltd
Copyright © 1997, MCB UP Limited