Lattice Boltzmann method for thermomagnetic convection of paramagnetic fluid in square cavity under a magnetic quadrupole field

2017 ◽  
Vol 24 (5) ◽  
pp. 1174-1182 ◽  
Author(s):  
Nan Xie ◽  
Chang-wei Jiang ◽  
Yi-hai He ◽  
Ming Yao
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Square Cavity ◽  
Quadrupole Field ◽  
Thermomagnetic Convection ◽  
Magnetic Quadrupole ◽  
Boltzmann Method ◽  
Magnetic Quadrupole Field

Lattice Boltzmann simulation of transient natural convection of air in square cavity under a magnetic quadrupole field

2016 ◽  
Vol 26 (8) ◽  
pp. 2441-2461 ◽  
Author(s):  
Nan Xie ◽  
Yihai He ◽  
Ming Yao ◽  
Changwei Jiang
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Natural Convection ◽  
Lattice Boltzmann ◽  
Distribution Functions ◽  
Square Cavity ◽  
Quadrupole Field ◽  
Content Type ◽  
Magnetic Quadrupole ◽  
Magnetic Quadrupole Field

Purpose The purpose of this paper is to apply the lattice Boltzmann method (LBM) with multiple distribution functions model, to simulate transient natural convection of air in a two-dimensional square cavity in the presence of a magnetic quadrupole field, under non-gravitational as well as gravitational conditions. Design/methodology/approach The density-temperature double distribution functions and D2Q9 model of LBM for the momentum and temperature equations are currently employed. Detailed transient structures of the flow and isotherms at unsteady state are obtained and compared for a range of magnetic force numbers from 1 to 100. Characteristics of the natural convection at initial moment, quasi-steady state and steady state are presented in present work. Findings At initial time, effects of the magnetic field and gravity are both relatively limited, but the effects become efficient as time evolves. Bi-cellular flow structures are obtained under non-gravitational condition, while the flow presents a single vortex structure at first under gravitational condition, and then emerges a bi-cellular structure with the increase of magnetic field force number. The average Nusselt number generally increases with the augment of magnetic field intensity. Practical implications This paper will be useful in the researches on crystal material and protein growth, oxygen concentration sensor, enhancement or suppression of the heat transfer in micro-electronics and micro-processing technology, etc. Originality/value The current study extended the application of LBM on the transient natural convective problem of paramagnetic fluids in the presence of an inhomogeneous magnetic field.

SIMULATION OF NATURAL CONVECTION IN A SQUARE CAVITY BY TAYLOR SERIES EXPANSION- AND LEAST SQUARES-BASED LATTICE BOLTZMANN METHOD

2002 ◽  
Vol 13 (10) ◽  
pp. 1399-1414 ◽  
Author(s):  
C. SHU ◽  
Y. PENG ◽  
Y. T. CHEW
Keyword(s):  
Natural Convection ◽  
Least Squares ◽  
Lattice Boltzmann Method ◽  
Series Expansion ◽  
Taylor Series ◽  
Lattice Boltzmann ◽  
Taylor Series Expansion ◽  
Uniform Grid ◽  
Square Cavity ◽  
Boltzmann Method

The Taylor series expansion- and least squares-based lattice Boltzmann method (TLLBM) was used in this paper to extend the current thermal model to an arbitrary geometry so that it can be used to solve practical thermo-hydrodynamics in the incompressible limit. The new explicit method is based on the standard lattice Boltzmann method (LBM), Taylor series expansion and the least squares approach. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. Numerical simulations of natural convection in a square cavity on both uniform and nonuniform grids have been carried out. Favorable results were obtained and compared well with the benchmark data. It was found that, to get the same order of accuracy, the number of mesh points used on the nonuniform grid is much less than that used on the uniform grid.

Convection Study in a Square Cavity using Lattice Boltzmann Method

2018 ◽  
Author(s):  
Luiz Czelusniak ◽  
Vinicius Pessoa Mapelli ◽  
Luben Cabezas Gómez ◽  
Matheus Guzella
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Square Cavity ◽  
Boltzmann Method
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