Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method

Mishra, Subhash C.; Roy, Hillol K.

doi:10.1016/j.jcp.2006.08.021

Cited by 203 publications

(146 citation statements)

References 30 publications

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“…In applications of the LBM to heat transfer problems involving thermal radiation [24][25][26], boundaries of the geometries were at prescribed temperatures, and implementation of temperature boundary condition has been explained in Mishra and Lankadasu [24]. In the present work, we have extended the application of the LBM to a conduction-radiation problem with flux boundary condition.…”

Section: Implementation Of Flux Boundary Conditions In the Lbmmentioning

confidence: 99%

“…We provide a brief formulation of the FVM and the LBM. Details of the FVM methodology used in the present work can be found in [25] and those of the implementations of the LBM to heat transfer problems involving thermal radiation in [24][25][26].…”

Section: Formulationmentioning

confidence: 99%

“…In comparison with the The FVM is fully conservative and thus it does not suffer from false scattering and the ray effect is less pronounced. In [24][25][26], the FVM has been successfully coupled with the LBM to solve conduction-radiation problems. Thus, in the present work too, in extending the application of the LBM to a new situation, we choose the FVM as the method to provide radiative information.…”

Section: Introductionmentioning

confidence: 99%

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The lattice Boltzmann method and the finite volume method applied to conduction–radiation problems with heat flux boundary conditions

Mondal

Mishra

2008

Numerical Meth Engineering

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SUMMARYThis article deals with the implementation of the lattice Boltzmann method (LBM) in conjunction with the finite volume method (FVM) for the solution of conduction-radiation problems with heat flux and temperature boundary conditions. Problems in 1-D planar and 2-D rectangular geometries have been considered. The radiating-conducting participating medium is absorbing, emitting and scattering. In the 1-D planar geometry, the south boundary is subjected to constant heat flux, while in the 2-D geometry the south and/or the north boundary is at constant heat flux condition. The remaining boundaries are at prescribed temperatures. The energy equation is solved using the LBM and the radiative information for the same is computed using the FVM. In the direct method, by prescribing temperatures at the boundaries, the temperature profile and heat flux are calculated. The computed heat flux values are imposed at the boundaries to establish the correctness of the numerical code in the inverse method. Effects of various parameters such as the extinction coefficient, the scattering albedo, the conduction-radiation parameter, the boundary emissivity and the total heat flux and boundary temperatures are studied on the distributions of temperature, radiative and conductive heat fluxes. The results of the LBM in conjunction with the FVM have been found to compare very well with those available in the literature.

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Section: Implementation Of Flux Boundary Conditions In the Lbmmentioning

confidence: 99%

Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The lattice Boltzmann method and the finite volume method applied to conduction–radiation problems with heat flux boundary conditions

Mondal

Mishra

2008

Numerical Meth Engineering

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“…Compared with other existing numerical techniques, the advantages of LBM include easy handling of complex geometries and boundary conditions (Chang et al, 2009) and efficient implementation for parallel computation (Yasuda et al, 2011). Thus, several studies have been carried out in recent years to validate the approach for many heat transfer (Mishra and Roy, 2007) and reactive flow cases (Hou et al, 1997). However, more studies are still needed to improve the stability of the mass, momentum and energy-conserving LB models.…”

Section: Numerical Techniquementioning

confidence: 99%

Mixed convection heat transfer of nanofluid over microscale vertical duct preceded with a double-step expansion using Lattice Boltzmann Method

Hamdi

Elalimi

Nasrallah

2016

JTST

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“…, is proportional to the concentration gradient dotted with the microscopic velocity at the surface [12][13][14][15][16][17]; hence, we can make the following assumption:…”

Section: Implementation Of the Boundary Conditionmentioning

confidence: 99%

A lattice Boltzmann‐BGK algorithm for a diffusion equation with Robin boundary condition—application to NMR relaxation

Hiorth

Lad

Evje

et al. 2008

Numerical Methods in Fluids

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SUMMARYWe present a lattice Boltzmann-BGK (LBGK) algorithm for a diffusion equation together with a Robin boundary condition, which we apply in the case of nuclear magnetic resonance relaxation. The boundary condition we employ is independent of the direction of the wall. This makes the algorithm very suitable for complicated geometries, such as porous media. We discuss the effect of lattice topology by using, respectively, an eight-speed and a four-speed lattice. The numerical algorithm is compared with analytical results for a square and an equilateral triangle. The eight-speed lattice performs well in both cases. The four-speed lattice performs well for the square, but fails in the case of an equilateral triangle. Comparison with a random walk algorithm is also included. The LBGK algorithm presented here can also be used for a convective diffusion problem if the speed of the fluid can be neglected close to the boundary.

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Solving transient conduction and radiation heat transfer problems using the lattice Boltzmann method and the finite volume method

Cited by 203 publications

References 30 publications

The lattice Boltzmann method and the finite volume method applied to conduction–radiation problems with heat flux boundary conditions

The lattice Boltzmann method and the finite volume method applied to conduction–radiation problems with heat flux boundary conditions

Mixed convection heat transfer of nanofluid over microscale vertical duct preceded with a double-step expansion using Lattice Boltzmann Method

A lattice Boltzmann‐BGK algorithm for a diffusion equation with Robin boundary condition—application to NMR relaxation

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