Title: Lattice Boltzmann method for heat diffusion in axis-symmetric geometries

Authors: A.A. Mohamad

Addresses: Department of Mechanical and Manufacturing Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB, T2N 1N4, Canada

Abstract: Lattice Boltzmann Methods (LBM) have been used to solve momentum, heat and mass transport equations mainly in Cartesian coordinate system. In the present work, the LBM is extended to solve transports in axis-symmetric geometries, such as pipes and spheres. Heat diffusion and conduction in solids without and with heat generation were tested. The heat diffusion equation for axis-symmetric problem is reduced to diffusion equation as in Cartesian coordinate with an extra term due to the surface area variation along the radial direction. The extra term is treated as a source term (forcing term) in LBM. The extra term can be approximated by using finite difference or more accurately as a flux term. The results predicted by LBM are well compared with analytical solutions and finite volume method.

Keywords: LBM; lattice Boltzmann method; heat diffusion; mass diffusion; axis-symmetric geometries; pipes; spheres.

DOI: 10.1504/PCFD.2009.027766

Progress in Computational Fluid Dynamics, An International Journal, 2009 Vol.9 No.8, pp.490 - 494

Published online: 10 Aug 2009 *

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