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Prandtl Number Signature on Flow Patterns of Electrically Conducting Fluid in Square Enclosure

Ridha Djebali1,2, Bernard Pateyron2, Mohamed El Ganaoui3

LETTM, University of Tunis El Manar, 2092 Manar II, Tunis, Tunisia. Email address:
CNRS-SPCTS / CEC 12, Rue Atlantis 87068, Limoges, France
LERMAB, Institut Carnot, University Henri Poincaré, Nancy 1, 186 Rue de Lorraine, France.

Computer Modeling in Engineering & Sciences 2012, 88(4), 293-308.


We present in this study a numerical investigation of unsteady two-dimensional natural convection of an electrically conducting fluid in a square cavity under an externally imposed magnetic field. A temperature gradient is applied between the two opposing side walls parallel to y-direction, while the floor and ceiling parallel to x-direction are adiabatic. The flow is characterized by the Rayleigh number Ra raged in 103-106, the Prandtl number Pr ranged in 0.01-10, the Hartman number Ha determined by the strength of the imposed magnetic field ranged in 0-100 and its tilting angle from x-axis ranging from 0 to 90 . The coupled momentum and energy equations associated with the Lorentz retarding force as well as the buoyancy force terms are solved using the single relaxation lattice Boltzmann (LB) approach. The changes in the buoyant flow patterns and temperature contours due to the effects of varying the controlling parameters and associated heat transfer are examined. It was found that the developed thermal LB model gives excellent results by comparison with former experimental and numerical findings. Starting from the values 105 of the Rayleigh number Ra and Ha=0, the flow is unsteady multicellular for low Prandtl number typical of liquid metal. Increasing gradually Pr, the flow undergoes transition to steady bicellular, the transition occurs at a threshold value between Pr=0.01 and 0.1. Increasing more the Prandtl number, the flow structure is distorted due to the viscous forces which outweigh the buoyancy forces and a thermal stratification is clearly established. For high Hartman number, the damping effects suppress the unsteady behaviour and results in steady state with extended unicellular pattern in the direction of Lorentz force and diminishes considerably the heat transfer rate.


Cite This Article

Djebali, R., Pateyron, B., Ganaoui, M. E. (2012). Prandtl Number Signature on Flow Patterns of Electrically Conducting Fluid in Square Enclosure. CMES-Computer Modeling in Engineering & Sciences, 88(4), 293–308.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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