A local iteration scheme for nonlinear two-dimensional steady-state heat conduction: A BEM approach
type: Item
instance of: scholarly article
title: A local iteration scheme for nonlinear two-dimensional steady-state heat conduction: A BEM approach
zbMATH Open document ID: 0803.65108
DOI: 10.1016/0307-904X(93)90075-R
author: Cho Lik Chan
published in: Applied Mathematical Modelling
publication date: 1994-06-01T00:00:00Z
review text: The 2D steady-state heat conduction equation with nonlinear boundary conditions and temperature dependent thermal conductivity is reduced to the Laplace equation with nonlinear boundary conditions by Kirchoff's transformation. Applying the boundary element method (BEM) to the last problem, the resulting matrix equation becomes nonlinear. The author proposes a local iterative scheme to reduce this matrix equation to a smaller one whose rank is the same as the number of boundary nodes with nonlinear boundary conditions. That's the point of the paper. Some numerical results obtained for a two-region problem as well as for some cavity problems where radiation determines the heat transfer are displayed. For these specific problems the results look well, in spite of the fact that nothing is proved.
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 580025
zbMATH Keywords: heat conduction equation
zbMATH Keywords: Laplace equation
zbMATH Keywords: Kirchoff's transformation
zbMATH Keywords: boundary element method
zbMATH Keywords: matrix equation
zbMATH Keywords: local iterative scheme
zbMATH Keywords: nonlinear boundary conditions
zbMATH Keywords: numerical results
zbMATH Keywords: radiation
zbMATH Keywords: heat transfer
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
cites work: Q3965703
cites work: Q3318255
cites work: Q3219912
cites work: On the efficiency and accuracy of the boundary element method and the finite element method
cites work: Non-linear heat conduction in composite bodies: A boundary element formulation
cites work: SOLVING NONLINEAR STEADY-STATE POTENTIAL PROBLEMS IN INHOMOGENOUS BODIES USING THE BOUNDARY-ELEMENT METHOD
cites work: Boundary value problems in heat conduction with nonlinear material and nonlinear boundary conditions
cites work: BOUNDARY ELEMENT APPROACH FOR TRANSIENT AND NONLINEAR THERMAL DIFFUSION
cites work: Q4034069
cites work: An algorithm for handling corners in the boundary element method: Application to conduction-convection equations
cites work: Q3994364
full work available at URL: 0307-904x(93)90075-r
OpenAlex ID: W2085154567
description: scientific article; zbMATH DE number 580025