Effect of helical force on the stationary convection in binary ferrofluid
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ORIGINAL PAPER
Effect of helical force on the stationary convection in binary ferrofluid P Hounsou, A V Monwanou, C H Miwadinou*
and J B Chabi Orou
Institut de Mathe´matiques et de Sciences Physiques, BP: 613, Porto Novo, Benin Received: 23 March 2019 / Accepted: 19 July 2019
Abstract: This paper presents the study of the onset of instability in a horizontal layer of binary ferrofluid mixture under the effect of helical force and heated from below with free boundary conditions. Explicit expressions of the stationary convection thresholds are determined. The results indicate that each of the parameters M1 , M3 , w, wm and the helical force accelerates the onset of the stationary convection, while the parameter M2 delays it. It is shown that all the magnetic parameters and the separation ratio contract the size of the convection cells, while the helical force enlarges it. Keywords: Thermal convection; Magnetic fluid; Binary mixture; Helical force PACS Nos.: 44.25.?f; 47.10.ad; 47.20.Bp; 47.55.pb
1. Introduction Since their appearance in the second half of the twentieth century, the theory of ferrofluids has attracted the attention of many researchers given their applications in various fields. Ferrofluids, also known as magnetic fluids, are colloidal suspensions of nanosized ferromagnetic particles stably dispersed in organic or non-organic carrier fluids, such as water, kerosene and hydrocarbon. The magnetic particles are usually magnetite Fe3O4 or cobalt. Commercial productions of these fluids have resulted in their use in a variety of engineering applications [1]. In addition, heat transfer through magnetic fluids, in particular, has been one of the leading areas of scientific study due to its technological applications [1, 2]. Other important applications of ferrofluids lie in the biomedicine area where the carrier liquid is blood, and it has rheological properties [3–10]. Hydrodynamics of ferrofluids began with the fundamental work of Neuringer and Rosensweig [11]. Finlayson [12] investigated convective instability of a ferromagnetic fluid layer heated from below in the presence of a uniform vertical magnetic field by using linear stability theory and predicted the critical temperature gradient for the onset of convection when both buoyancy and magnetic forces are considered. He has derived an exact solution for the case of
*Corresponding author, E-mail: [email protected]; [email protected]
free boundaries and approximate solutions (for stationary convection) of rigid boundaries. Gotoh and Yamada [13] examined the linear convective instability of a magnetic fluid layer confined between two horizontal ferromagnetic boundaries. Heat transfer through strongly magnetized in magnetic fluid was considered by Blennerhassett et al. [14] where linear and weakly nonlinear analyses were performed. Effects of rotation on the convective instability of a horizontal layer of magnetic fluid have been studied by Gupta and Gupta [15] and by Venkatasubramanian and Kaloni [16]. Kaloni and Lou [17] derived an am
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