Effect of rotation on a ferromagnetic fluid heated and soluted from below in the presence dust particles

• Published in: Applied mathematics and computation 2006-06, Vol.177 (2), p.614-628
• Main Authors: Sunil, Sharma, Anu, Shandil, R.G.
• Format: Article
• Language: English
• Subjects: Computational methods in fluid dynamics; Dust particles; Exact sciences and technology; Ferromagnetic fluid; Fluid dynamics; Fundamental areas of phenomenology (including applications); Magnetization; Magnetohydrodynamics and electrohydrodynamics; Mathematical analysis; Mathematics; Partial differential equations; Physics; Rotation; Sciences and techniques of general use; Thermosolutal convection
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2005.09.092

This paper deals with the theoretical investigation of the effect of rotation on a layer of a ferromagnetic fluid permeated with dust particles, heated and soluted from below subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using a linearized stability theory and a normal mode analysis method. For the case of stationary convection, non-buoyancy magnetization and dust particles have always a destabilizing effect, whereas stable solute gradient and rotation have a stabilizing effect on the onset of instability. The critical wave number and the critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of buoyancy magnetization M 1. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. It is observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid heated from below in the absence of dust particles, stable solute gradient and rotation. The oscillatory modes are introduced due to the presence of the dust particles, stable solute gradient and rotation, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.