Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction–radiation problem

Mishra, Subhash C.; Lankadasu, A.; Beronov, Kamen N.

doi:10.1016/j.ijheatmasstransfer.2004.10.041

Cited by 120 publications

(80 citation statements)

References 17 publications

(58 reference statements)

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“…30 Besides, LBM can be coupled to a conventional numerical scheme to provide a convenient way to simulate multifield coupling problems such as the thermo-convective problems, thermo-magnetic systems, double diffusion models, coupled convection and radiation heat transfer problems, etc. In recent years, three different combinations have been proposed, namely, the combination of lattice-Boltzmann and finite difference method (LB-FDM), 13,14,31 the hybrid technique of lattice-Boltzmann and finite volume method (LB-FVM) [32][33][34][35] and the combination of lattice-Boltzmann and finite element method (LB-FEM). 36 One of the main advantages of LBM is that it is easy and robust to deal with the natural convection problems in complex geometries.…”

Section: Introductionmentioning

confidence: 99%

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Luo

Tan

2014

AIP Advances

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Transitions and bifurcations of transient natural convection in a horizontal annulus with radiatively participating medium are numerically investigated using the coupled lattice Boltzmann and direct collocation meshless (LB-DCM) method. As a hybrid approach based on a common multi-scale Boltzmann-type model, the LB-DCM scheme is easy to implement and has an excellent flexibility in dealing with the irregular geometries. Separate particle distribution functions in the LBM are used to calculate the density field, the velocity field and the thermal field. In the radiatively participating medium, the contribution of thermal radiation to natural convection must be taken into account, and it is considered as a radiative term in the energy equation that is solved by the meshless method with moving least-squares (MLS) approximation. The occurrence of various instabilities and bifurcative phenomena is analyzed for different Rayleigh number Ra and Prandtl number Pr with and without radiation. Then, bifurcation diagrams and dual solutions are presented for relevant radiative parameters, such as convection-radiation parameter Rc and optical thickness τ. Numerical results show that the presence of volumetric radiation changes the static temperature gradient of the fluid, and generally results in an increase in the flow critical value. Besides, the existence and development of dual solutions of transient convection in the presence of radiation are greatly affected by radiative parameters. Finally, the advantage of LB-DCM combination is discussed, and the potential benefits of applying the LB-DCM method to multi-field coupling problems are demonstrated.

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Section: Introductionmentioning

confidence: 99%

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Luo

Tan

2014

AIP Advances

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“…Some studies compare FVM and LBM for solving 2D conduction-radiation problem. It was shown that LBM approach was faster than FVM [32].…”

Section: Introductionmentioning

confidence: 99%

Solution of inverse heat conduction problem using the lattice Boltzmann method

Kameli

Kowsary

2012

International Communications in Heat and Mass Transfer

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“…Mishra et al [31] derived LBE to solve material energy equation with radiation term as a source. The radiation source term was computed using collapsed dimension method and then substituted into the LBE form of energy equation.…”

Section: Homogeneous Radiative Porous Burnermentioning

confidence: 99%

Coupled radiative and conjugate heat transfer in participating media using lattice Boltzmann methods

McCulloch

Bindra

2016

Computers & Fluids

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Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction–radiation problem

Cited by 120 publications

References 17 publications

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Radiation effects on bifurcation and dual solutions in transient natural convection in a horizontal annulus

Solution of inverse heat conduction problem using the lattice Boltzmann method

Coupled radiative and conjugate heat transfer in participating media using lattice Boltzmann methods

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