DOI: https://doi.org/10.20535/2521-1943.2020.88.200984

Specific of a viscous fluid flow under the action of a transverse magnetic field

Y. V. Lavrykhin, S. V. Stas, A. N. Mamedov

Abstract


 

Annotation. In this article we considered the flow of viscous electrically conductive fluids in the field of action forces which have a magnetic nature. Done the analysis of the case when the flow is unstabilized, but in their characteristics close to the flow in the hydrodynamic initial section. In this case, besides the viscous friction forces,have a significant effect on the flow the inertial forces from convective acceleration and mass forces, related with the action of ponderomotive forces arising in the presence of a magnetic field. In this case, the term appears in the equations of motion characteristic of the description of the hydrodynamic initial section, which characterize the action of forces with a magnetic nature, that is, the value    shows on the effect of the manifestation of ponderomotive forces in the hydrodynamic initial section and related with the value of the ratio between the forces of inertia and the forces of viscous friction. The Hartman flow characterizes when the inertia forces are insignificant in this case. On the other side the inertia forces from convective acceleration are much greater than the ponderomotive forces, the flow under consideration is characteristic of the hydrodynamic initial section and is described in the article quite fully. Finally, these equations can be used to describe the Poiseuille motion, when ponderomotive forces and inertia forces are too small. In general case, in the presence of all types of forces represented in the equation of motion, we are working with a hydrodynamic initial section, whose value depends on both the Reynolds criterion and the Hartman criterion. The nature of this dependence is presented in the article as a picture, where the differential pressure in the general case can be represented as the sum of the differential pressure for a stabilized flow and additional, related with the action of inertia and ponderomotive forces. The experiments show, that the action of ponderomotive forces appear itself in the form of a flow-inhibiting effect. At the same time, inertial forces from convective acceleration contribute to the accelerated movement of fluid in flow core in the hydrodynamic initial section and inhibition within the forming boundary layer. Finally, the process of flow formation in the hydrodynamic initial section depends on the relationship between these forces. In the work, this process is characterized by the relationship between the Reynolds criterion and the Hartman criterion.


Keywords


hydrodynamic initial section; inertia forces; ponderomotive forces; Reynolds criterion; Hartman criterion; pressure drop

References


Perminov, A., (2016), The Movement Of Fluids With Different Rheology In External Force Fields. Doctor of Physico-Mathematical Sciences.

Perminov, A. and Nikulin, I., (2016), Mathematical Model of the Processes of Heat and Mass Transfer and Diffusion of the Magnetic Field in an Induction Furnace. Journal of Engineering Physics and Thermophysics, 89(2), pp.397-409. https://doi.org/10.1007/s10891-016-1389-5.

Nikulin, I. and Perminov, A., (2019), Mathematical modelling of frequency and force impacts on averaged metal flows in alternating magnetic field. International Journal of Heat and Mass Transfer, 128, pp.1026-1032. https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.130

Malekzadeh, A., Heydarinasab, A. and Dabir, B., (2011), Magnetic field effect on fluid flow characteristics in a pipe for laminar flow. Journal of Mechanical Science and Technology, 25(2), pp.333-339. https://doi.org/10.1007/s12206-010-1223-5.

Taheri, M., (2019), The influence of magnetic field on the fluid flow in the entrance region of channels: analytical/numerical solution. SN Applied Sciences, 1(10). https://doi.org/10.1007/s42452-019-1244-3.

L-Shahed, M., (2006), MHD of a fractional viscoelastic fluid in a circular tube. Mechanics Research Communications, 33(2), pp.261-268. https://doi.org/10.1016/j.mechrescom.2005.02.017.

Nagaraju, G. and Garvandha, M., (2019), Magnetohydrodynamic viscous fluid flow and heat transfer in a circular pipe under an externally applied constant suction. Heliyon, 5(2), p.e01281. https://doi.org/10.1016/j.heliyon.2019.e01281.

Kakarantzas, S., Benos, L., Sarris, I., Knaepen, B., Grecos, A. and Vlachos, N., (2017), MHD liquid metal flow and heat transfer between vertical coaxial cylinders under horizontal magnetic field. International Journal of Heat and Fluid Flow, 65, pp.342-351. https://doi.org/10.1016/j.heliyon.2019.e01281.

Sheikholeslami, M., Jalili, P. and Ganji, D., (2018), Magnetic field effect on nanofluid flow between two circular cylinders using AGM. Alexandria Engineering Journal, 57(2), pp.587-594. https://doi.org/10.1016/j.aej.2017.02.010

Tyabin, N.V., Tsentovsky, E.M. (1964), Proceedings of the Institute of Chemical Technology, Issue 32.

Shercliff, J., (1965), A Textbook Of Magnetohydrodynamics. Oxford [etc.]: Pergamon Press.

Vatazhin, A., Li︠u︡bimov, G. and Regirer, S., (1970), Magnitogidrodinamicheskie techenii︠a︡ v kanalakh. Moskva: "Nauka.."

Qian, S. and Bau, H., (2009), Magneto-hydrodynamics based microfluidics. Mechanics Research Communications, 36(1), pp.10-21. https://doi.org/10.1016/j.mechrescom.2008.06.013.

Weng, H., (2013), Hydrodynamic Modeling of Targeted Magnetic-Particle Delivery in a Blood Vessel. Journal of Biomechanical Engineering, 135(3). https://doi.org/10.1115/1.4023137.

Christiansen, E., Jensen, G. and Tao, F., (1966), Laminar flow heat transfer. AIChE Journal, 12(6), pp.1196-1202.

Yakhno, O., Matiega, V., Krivosheev, V. (2004), Hydrodynamic initial section. Chernivtsi: Zelena Bukovyna. 141p.

McKelvey, J., Zelenev, U., Pašinin, B. and Rodin, E., (1965), Pererabotka Polimerov. Moskva: Izdatel'stvo "Himiâ.."

Shi-I, Bay, (1964), Magnetic gas dynamics and plasma dynamics. (version by V. P. Korobeynikov, P. I. Chushkin; editor A. G. Kulikovskiy). Moskva: "Mir". 301p.

Yakhno, O., Mamedov, A. and Stas, S., (2019), Influence of transverse magnetic field on flow destabilization in the channel. Bulletin of the National Technical University "KhPI". Series: Hydraulic machines and hydraulic units, 0(1), pp.25-29. https://doi.org/10.20998/2411-3441.2019.1.04


GOST Style Citations






Copyright (c) 2020 Mechanics and Advanced Technologies

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

________________

©Mechanics and Advanced Technologies

National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 

Address: 37, Prospect Peremohy, 03056, Kyiv-56, Ukraine

tel: +380 (44) 204-95-37

http://journal.mmi.kpi.ua/