Discrete thermal element modelling of heat conduction in particle systems: Basic formulations
type: Item
instance of: scholarly article
title: Discrete thermal element modelling of heat conduction in particle systems: Basic formulations
zbMATH Open document ID: 1144.80012
published in: Journal of Computational Physics
publication date: 2008-05-16T00:00:00Z
review text: The paper presents a new numerical method for the resolution of the heat problem in a system of discrete and 2D circular neighboring particles. One particle exchanges heat along some arcs of its boundary, the remaining part being assumed isolated. The temperature \(T_{i}\) on the boundary of a particle may be computed in terms of the resultant flux \(Q_{i}\) through this arc and of the temperature \(T_{\text{o}}\) at the center of the particle, using Dini's integral representation, as \(T_{i}=\sum_{j=1,\dots ,n}h_{ij}Q_{j}-T_{\text{o}}\), where the \(h_{ij}\) are positive. The discrete thermal element method (DTEM) consists to introduce the vectors \(\mathbf{T} _{c}=(T_{1},\dots ,T_{n})^{T}\) of temperatures and \(\mathbf{Q} _{c}=(Q_{1},\dots ,Q_{n})^{T}\) of resultant fluxes and the thermal resistance matrix \(\mathbf{H}_{c}=(h_{ij})_{i,j=1,\dots ,n}\), and to write the system \(\mathbf{T}_{c}-\mathbf{e}T_{\text{o}}=\mathbf{H}_{c}\mathbf{Q} _{c}\), with \(\mathbf{e}=(1,\dots ,n)^{T}\). The authors assume that \(\mathbf{ H}_{c}\) is invertible, then eliminate \(T_{\text{o}}\), and approximate \( h_{ii} \) and \(h_{ij}\), \(i\neq j\). In the last parts of the paper, the authors present numerical computations based on this approach for a system of 12 or 1084 particles and compare their results to that obtained with the FEM method. They prove that the error using the DTEM method is smaller than that obtained using this FEM method.
reviewed by: Alain Brillard
Mathematics Subject Classification ID: 80M10
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 5276062
zbMATH Keywords: circular particle
zbMATH Keywords: thermal contact
zbMATH Keywords: boundary (integral) equation/element
author: Y. T. Feng
author: Kuanjin Han
author: Chenfeng Li
author: D. R. J. Owen
MaRDI profile type: Publication
full work available at URL: j.jcp.2008.01.031
OpenAlex ID: W2064320404
cites work: Q3995755
cites work: Transient temperature computation of spheres in three-dimensional random packings
cites work: A fictitious domain method for particulate flows with heat transfer
cites work: LATTICE BOLTZMANN METHOD FOR FLUID FLOWS
cites work: A direct simulation method for particle‐fluid systems
cites work: Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues
cites work: Q3551788
cites work: A novel thermal model for the lattice Boltzmann method in incompressible limit
cites work: Q5785591
cites work: Q5551644
cites work: Contact Mechanics
cites work: Q5535928
cites work: An augmented spatial digital tree algorithm for contact detection in computational mechanics
cites work: On the discrete dynamic nature of the conjugate gradient method
cites work: Filling domains with disks: an advancing front approach
DOI: 10.1016/J.JCP.2008.01.031
description: scientific article; zbMATH DE number 5276062