Chatterjee, Dipankar
(2013)
*Lattice kinetic simulation of buoyancy induced MHD flows.*
International Journal of Heat and Mass Transfer, 65.
pp. 533-544.

## Abstract

A lattice kinetic model is proposed in this article for simulating buoyancy induced classical magnetohydrodynamic (MHD) flow in the low Mach number incompressible limit. The model is derived by coupling the passive scalar approach of He et al. [X. He, S. Chen, G.D. Doolen, A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys. 146 (1998) 282–300] for the flow and thermal fields and Dellar formalism [P.J. Dellar, Lattice kinetic schemes for magnetohydrodynamics, J. Comput. Phys. 179 (2002) 95–126] for the magnetic field. Accordingly, the underlying hydrodynamics is monitored by a conventional single relaxation time lattice Boltzmann (LB) model through a density distribution function (DF), which obeys a scalar kinetic equation (KE) associated with external force fields (Lorentz and buoyancy forces). The magnetic field is represented by a vector DF, which obeys a corresponding vector KE and the thermal field is obtained from a separate temperature DF through another scalar KE incorporating the Joule heating effect. The three distribution functions are coupled through the macroscopic density, momentum, magnetic and thermal fields evaluated at lattice points. This allows a reduced lattice to be used for the magnetic distribution function, with a corresponding saving in the storage. Furthermore, the fluid viscosity, magnetic resistivity and thermal diffusivity may be adjusted independently that renders the model to be applicable for a wide variety of non-isothermal MHD problems. The novelty of the work is the computation of the thermal field in conjunction with the hydro-magnetic fields in the LB framework for the buoyancy driven non-isothermal MHD flows. A 9-bit 2D (d2q9) lattice scheme is used for the numerical computation of the hydrodynamic and thermal fields, whereas the magnetic field is simulated by a reduced 5-bit 2D (d2q5) lattice. Simulation of the magnetoconvective buoyancy induced flow (a) past a vertical flat plate, (b) between two differentially heated vertical walls provide excellent agreement with analytical results. Finally, the model is utilized to solve a classical problem of buoyancy driven MHD flow in a square cavity.

Item Type: | Article |
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Subjects: | Lattice Boltzmann Modelling Magnetohydrodynamics Heat transfer |

Depositing User: | Dr. Sarita Ghosh |

Date Deposited: | 21 Sep 2016 09:36 |

Last Modified: | 21 Sep 2016 09:36 |

URI: | http://cmeri.csircentral.net/id/eprint/298 |

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