Effect of Rotation and Suspended Particles on Micropolar Fluid Heated and Soluted from Below Saturating Porous Medium

Pushap Lata Sharma; Sumit Gupta

doi:https://doi.org/10.14445/22315373/IJMTT-V65I9P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 9 | Year 2019 | Article Id. IJMTT-V65I9P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I9P512

Effect of Rotation and Suspended Particles on Micropolar Fluid Heated and Soluted from Below Saturating Porous Medium

Pushap Lata Sharma ,Sumit Gupta

Citation :

Pushap Lata Sharma ,Sumit Gupta, "Effect of Rotation and Suspended Particles on Micropolar Fluid Heated and Soluted from Below Saturating Porous Medium," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 9, pp. 72-83, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I9P512

Abstract

This paper deals with the convection of micropolar fluids heated and soluted from below in the presence of suspended particles (fine dust) and uniform vertical rotation Ω(0,0,Ω) in a porous medium and using the Boussinesq approximation, the linearized stability theory and normal mode analysis, the exact solutions are obtained for the case of two free boundaries. It is found that the presence of the suspended particles number density, the rotation parameter, stable solute parameter and medium permeability bring oscillatory modes which were non–existent in their absence. It is found that the presence of coupling between thermal and micropolar effects, rotation parameter, solute parameter and suspended particles may introduce overstability in the system. Graphs have been plotted by giving numerical values to the parameters accounting for rotation Ω(0,0,Ω), solute parameter, the dynamic microrotation viscosity K and coefficient of angular viscosity Ý to depict the stability characteristics, for both the cases of stationary convection and overstability. It is found that Rayleigh number for the case of overstability and stationary convection increases with increase in rotation parameter, solute parameter and decreases with increase in micropolar coefficients and medium permeability, for a fixed wave number, implying thereby the stabilizing effect of rotation parameter, solute parameter and destabilizing effect of micropolar coefficients and medium permeability on the thermosolutal convection of micropolar fluids.

Keywords

Micropolar fluid, rotation, suspended particles (fine dust), solute parameter, medium permeability, microrotation, coefficient of angular viscosity..

References

[1] A.C. Eringen, “Theory of micropolar fluids”,J. Math. Mech.1966, 16, 1.
[2] Y. Kazakia and T. Ariman, “Generalization of thermal effects on micropolar fluid”, Rheol. Acta.1971, 10, 319.
[3] A.C. Eringen, “Theory of thermomicrofluid”, J. Math. Anal. Appl.1972, 38,480.
[4] S. Chandrasekhar, “Hydrodynamic and hydromagnetic stability”, Dover Publication, New York.1961.
[5] G. Ahmadi, “Stability of a micropolar fluid heated from below” Int. J. Engng. Sci. 1976, 4, 8.
[6] C. Pérez-Garcia, J.M. Rubi and J. Casas-Vazquez, “On the stability of micropolar fluids,” J. Non-Equilib. Thermodyn.1981, 6, 65.
[7] H.N.W. Lekkerkerker, “J. Physique”,1977,38, L-277.
[8] H.N.W.Lekkerkerker,“Thermodynamic analysis of the oscillatory convective instability in a binary liquid mixture”, Physica. 1978, 93A, 307.
[9] R.Bradley,“Overstable electroconvective instabilities” J.Mech. Appl. Math.1978, 31,383.
[10] W.G. Laidlaw, “Oscillatory instabilities of nematic liquid crystals in electric and magnetic fields”, Phys. Rev. 1979, A20, 2188.
[11] J. Boussinesq, “Theorie Analytique de la Chaleur. Gauthier-Villars”, Paris. 1903,2, 172.
[12] P.G. Saffman, “On the stability of a laminar flow of a dusty gas”.J. Fluid Mech.1962,13, 120-128.
[13] J.W. Scanlon and L.A. Segel, “Some effects of suspended particles on the onset of Bénard convection,” Phys. Fluids.1973, 16,1573.
[14] R.C. Sharma and K.N. Sharma, J. Math. Phys. Sci.1982, 16, 167-181.
[15] V.I. Palaniswamy and C.M. Purushotam, “Stability of shear flow of stratified fluids with fine dust”,Phys. Fluids.1981, 24.
[16] E.R.Lapwood, “Convection of fluid in a porous medium”, Proc. Camb. Phil. Soc. 1948, 45, 508.
[17] R.A.Wooding, “Rayleigh instability of a thermal boundary layer in flow through a porous medium,” J. Fluid Mech. 1960, 9,183.
[18] J.A.M.McDonnel ,“Cosmic Dust”, John Wiley and Sons. Toronto. 1978,330.
[19] P.G. Saffman and G.I. Taylor, “The penetration of a fluid into a porous medium or Hele– Shaw cell containing a more viscous fluid,”Proc. R. Soc. London.1958, 245A, 312-329.
[20] M.K. Brakke, “Zone electrophoresis of dyes, proteins and viruses in density gradient columns of sucrose solutions,” Arch. Biochem. Biophys.1955, 55, 175.
[21] G. Veronis, “On finite amplitude instability in thermohaline convection”. J. Marine Res.1971, 23, 1.
[22] T.J. McDougall, “J.Phys Oceangr”, 1985, 15, 1532.
[23] J.Y.Holyer, “J .Fluid Mech,”1983, 137, 347.
[24] A. Brandt and H.J.S. Fernando, “Double-Diffusive convection,”Americal Geophysical Union.1996.
[25] R.C. Sharma and U. Gupta. “Thermal convection in micropolar fluids in porous medium”. Int. J. Engng. Sci. 1995, 33, 1887-91.
[26] V. Sharma and S. Gupta. “Thermal convection of micropolar fluid in the presence of suspended particles in rotation”. Arch. Mech.2008, 60,403-419. (Poland).
[27] V. Sharma and S. Gupta. “Thermosolutal convection of micropolar fluid in the presence of suspended particles”. Journal of Chemical, Biological and Physical Sciences.2016, 6(3), 1057-1068.