Effects of Suction–Injection–Combination (SIC) on the onset of Rayleigh–Bénard Electroconvection in a Micropolar Fluid

Authors

  • S Pranesh Department of Mathematics, Christ University, Bangalore, India
  • Tarannum Sameena Department of Professional Studies, Christ University, Bangalore, India
  • Baby Riya Research Scholar, Department of Mathematics, Christ University, Bangalore,

DOI:

https://doi.org/10.12723/mjs.34.5

Keywords:

Micropolar fluids, Rayleigh–Bénard convection, Suction–injection–combination and electroconvection.

Abstract

The effect of Suction – injection combination on the onset of Rayleigh – Bénard electroconvection micropolar fluid is investigated by making a linear stability analysis. The Rayleigh-Ritz technique is used to obtain the eigenvalues for different velocity and temperature boundary combinations. The influence of various parameters on the onset of convection has been analysed. It is found that the effect of Prandtl number on the stability of the system is dependent on the SIC being pro-gravity or anti-gravity. A similar Pe-sensitivity is found in respect of the critical wave number. It is observed that the fluid layer with suspended particles heated from below is more stable compared to the classical fluid layer without suspended particles.

Author Biographies

S Pranesh, Department of Mathematics, Christ University, Bangalore, India

Department of Mathematics,

Tarannum Sameena, Department of Professional Studies, Christ University, Bangalore, India

Department of Professional Studies, Christ University, Bangalore, India

Baby Riya, Research Scholar, Department of Mathematics, Christ University, Bangalore,

Research Scholar, Department of Mathematics, Christ University, Bangalore,

References

H. Power, Bio-Fluid Mechanics, Advances in Fluid Mechanics, W.I.T. Press, U.K. 1995.

G. Lukaszewicz, Micropolar fluid theory and applications, Birkhauser, Boston. 1999.

A. C. Eringen, Micro Continuum field theory, Springer Verlag, New York. 1999.

A. C. Eringen, “Theory of micropolar fluids, Journal of Mathematics and Mechanics,” vol. 16, pp. 1-18, 1996.

A. B. Datta, and V. U. K. Sastry, “Thermal instability of a horizontal layer of micropolar fluid heated from below,” International Journal of Engineering Science, vol. 14, no. 7, pp. 631-637, 1976.

G. Ahmadi, “Stability of a micropolar fluid layer heated from below,” International Journal of Engineering Science, vol. 14, no. 1, pp. 81-89, 1967.

S. P. Bhattacharyya, and S. K. Jena, “On the Stability of Hot Layer of Micropolar Fluid,” International Journal of Engineering Science, vol. 21, no. 9, pp. 1019-1024, 1983.

P. G. Siddheshwar, and S. Pranesh, “Magnetoconvection in a micropolar fluid,” International Journal of Engineering Science, USA, vol. 36, pp. 1173-1181, 1998.

P. G. Siddheshwar, and S. Pranesh, “Effects of non-uniform temperature gradients and magnetic field on the onset of convection in fluids with suspended particles under microgravity conditions,” Indian Journal of Engineering and Materials Sciences, vol. 8, pp. 77-83, 2001.

P. G. Siddheshwar, and S. Pranesh, “Effect of temperature / gravity modulation on the onset of magneto-convection in weak electrically conducting fluids with internal angular momentum,” Journal of Magnetism and Magnetic Materials, USA, vol. 192, pp. 159-176, 1999.

P. G. Siddheshwar, and S. Pranesh, “Magnetoconvection in fluids with suspended particles under 1g and g,” International Journal of Aerospace Science and Technology, France, vol. 6, pp. 105-114, 2001.

S. Pranesh, and Riya Baby, “Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh-Bénard Electro Convection in a Micropolar Fluid,” Applied Mathematics, vol. 3, pp. 442-450, 2012.

S. Pranesh and N. Arun Kumar, “Effect of Non-Uniform Basic Concentration Gradient on the Onset of Double-Diffusive Convection in Micropolar Fluid”. Applied Mathematics, vol. 3, pp. 417-424, 2012.

H. Bénard, “ Les tourbillions cellularies dans une nappe liquide transportant de la chaleut par convection en regime permanent, Annales de chimie et de physique, vol. 23, pp. 62. 1901.

D. L. Shvartsblat, “Steady convection motions in a plane horizontal fluid layer with permeable boundaries,” Fluid Dynamics, vol. 4, No. 5, pp. 54-59, 1969.

D. A. Nield, “Through flow effects in the Rayleigh-Bénard convective instability problem,” Journal of Fluid Mechanics, vol. 185, pp. 353-360, 1987.

P. G. Siddheshwar, and S. Pranesh, “Suction-Injection effects on the onset of Rayleigh-Bénard-Marangoni convection in a fluid with suspended particles,” Acta Mechanica, vol. 152, pp. 241-252, 2001.

I. S. Shivakumara, and S. P. Suma, “Effects of through flow and internal heat generation on the onset of convection in a fluid layer,” Acta Mechanica, vol. 140, No. 3, pp. 207-217, 2000.

Y. N. Murty, and V. V. Ramana Rao, “Effect of through flow on Marangoni convection in micropolar fluids,” Acta Mechanica, vol. 138, No. 3, pp. 211, 2000.

Y. N. Murty, “Effect of throughflow and magnetic field on Bénard convection in micropolar fluids”. Acta Mechanica, vol. 150, No. 1, pp. 11-21, 2001.

Y. N. Murty, “Effect of throughflow and magnetic field on Marangoni convection in micropolar fluids,” Applied Mathematics and Computation, vol. 173, pp. 1288-1299. 2006.

Published

2021-08-28

Issue

Vol. 14 No. 3 (2015): Mapana Journal of Sciences

Section

Research Articles

License

Copyright (c) 2015 S Pranesh, Tarannum Sameena, Baby Riya

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.