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.
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.
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.
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.
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.
This work is supported by the National Natural Science Foundation of China through Grant No. 11572056, and the Scientific Research Fund of Hunan Provincial Education Department through Grant No. 15A006. The authors are also grateful to two anonymous reviewers for many constructive comments that led to the improvement of this paper.
Xie, N., He, Y., Yao, M. and Jiang, C. (2016), "Lattice Boltzmann simulation of transient natural convection of air in square cavity under a magnetic quadrupole field", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 8, pp. 2441-2461. https://doi.org/10.1108/HFF-07-2015-0277Download as .RIS
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