Investigation of thermomagnetic gravitational convection and energy distribution in a vertical layer of ferrofluid

Year 2024, Volume: 10 Issue: 4, 936 - 953, 29.07.2024

Habibur Rahman

Abstract

The applied magnetic field and its inclination angle play important roles in flow stabilization and energy distribution in the flow domain. In this article, the linear stability characteristics and energy distribution due to the combined influence of thermal, magnetic, and gravitational forces in a vertical layer of ferrofluid enclosed by two differentially heated walls are investigated. The objective of this article is to investigate the combined effects of thermogravitational buoyancy and magnetic forces and provide parametric guidance for mixed magnetogravita-tional thermal experiments. The numerical results are obtained by the pseudo-spectral Chebyshev expansion method. It is found that the qualitative change in the shape of the instability boundaries and the area of flow stability expands significantly when the field inclination angle increases. The destabilizing magnetic field variation effect is most pronounced in the nearwall regions, especially near the cold wall. However, the viscous dissipation near the cold wall is also stronger than that close to the hot wall. Consequently, the overall instability pattern shifts toward the hot wall. The thermomagnetic perturbations arising in the layer of ferrofluid tend to make the magnetic and magnetization fields more uniform near the walls. The instability is mostly driven by gravitational buoyancy due to thermal effects compared to magnetic effects. The perturbed kinetic energy is lost due to viscous dissipation and modification of the applied magnetic field in the flow domain. Ferrofluids under the effects of thermal, magnetic, and gravitational forces have potential applications in cancer detection, MRI scanning, oil separation from water, tunable optical filters, digital data storage, vibration dampening, energy conversion devices, etc., and many other engineering branches.

Keywords

Convection, Energy, Ferrofluid, Instability, Magnetic Field

References

• [1] Bashtovoy VG, Berkovsky BM, Vislovich AN. Introduction to thermomechanics of magnetic fluids. New York: Hemisphere Publishing; 1988.
• [2] Odenbach S. Microgravity experiments on thermomagnetic convection in magnetic fluids. J Magn Magn Mater 1995;149:155–157. [CrossRef]
• [3] Polevikov VK, Fertman VE. Investigation of heat transfer through a horizontal layer of a magnetic liquid for the cooling of cylindrical conductors with a current. Magnetohydrodynamics 1977;13:11–16.
• [4] Yamaguchi H, Zhang Z, Shuchi S, Shimada K. Heat transfer characteristics of magnetic fluid in a partitioned rectangular box. J Magn Magn Mater 2002;252:203–205. [CrossRef]
• [5] Charles SW. The Preparation of magnetic fluids. In: Odenbach S, editor. Ferrofluids – Lecture Notes in Physics. Berlin: Springer; 2002. pp. 3–18. [CrossRef]
• [6] Bozhko AA, Putin GF. Heat transfer and flow patterns in ferrofluid convection. Magnetohydrodynamics 2003;39:147–169. [CrossRef]
• [7] Zablotsky D, Mezulis A, Blums E. Surface cooling based on thermomagnetic convection: Numerical simulation and experiment. Int J Heat Mass Transf 2009;52:5302– 5308. [CrossRef]
• [8] Mahfoud B, Moussaoui M. Buoyancy force and magnetic field effects on laminar vortex breakdown and fluid layers. J Ther Engineer 2023;9:12–23. [CrossRef]
• [9] Ghamati M, Askari N, Abbasi M, Moghimi SM, Khodadi SM, Taheri MH. Numerical analysis of coupled fluid flow and natural heat transfer on a vertical flat plate. J Ther Engineer 2024;10:1–9. [CrossRef] [10] Chandrasekhar S. Hydrodynamic and hydromagnetic stability. New York: Courier Corporation; 1981.
• [11] Finlayson BA. Convective instability of ferromagnetic fluids. J Fluid Mech 1970;40:753–767. [CrossRef]
• [12] Bozhko AA, Putin GF. Experimental investigation of thermo-magnetic convection in uniform external field. Bull Acad Sci 1991;55:1149–1156.
• [13] Shliomis MI, Smorodin BL. Convective instability of magnetized ferrofluids. J Magn Magn Mater 2002;252:197–202.
• [14] Hennenberg M, Wessow B, Slavtchev S, Desaive Th, Scheild B. Steady flows of laterally heated ferrofluid layer: Influence of inclined strong magnetic field and gravity level. Phys Fluids 2006;18:093602. [CrossRef]
• [15] Suslov SA. Thermomagnetic convection in a vertical layer of ferromagnetic fluid. Phys Fluids 2008;20:084101. [CrossRef]
• [16] Suslov SA, Bozhko AA, Sidorov AS, Putin GF. Thermomagnetic convective flows in a vertical layer of ferrocolloid: Perturbation energy analysis and experimental study. Phys Rev E Stat Nonlin Soft Matter Phys 2012;86:016301. [CrossRef]
• [17] El-Zahar ER, Rashad AM, Saddek LF. The impact of sinusoidal surface temperature on the natural convective flow of a ferrofluid along a vertical plate. Mathematics 2019;7:1014. [CrossRef]
• [18] Chamkha AJ, Rashad AM, Alsabery AI, Abdelrahman ZMA, Nabwey HA. Impact of partial slip on magneto-ferrofluids mixed convection flow in enclosure. J Ther Sci Engineer Appl 2020;12:051002. [CrossRef]
• [19] Taskesen E, Dirik M, Tekir M, Pazarlioglu HK. Predicting heat transfer performance of Fe3O4-cu/water hybrid nanofluid under constant magnetic field using ANN. J Ther Engineer 2023;9:811–822. [CrossRef]
• [20] Belyaev AV, Smorodin BL. The stability of ferrofluid flow in a vertical layer subject to lateral heating and horizontal magnetic field. J Magn Magn Mater 2010;322:2596–2606. [CrossRef]
• [21] Bozhko AA, Putin GF, Sidorov AS, Suslov SA. Convection in a vertical layer of stratified magnetic fluid. Magnetohydrodynamics 2013;49:143–152. [CrossRef]
• [22] Rahman H, Suslov SA. Thermomagnetic convection in a layer of ferrofluid placed in a uniform oblique external magnetic fluid. J Fluid Mech 2015;764:316–348. [CrossRef]
• [23] Rahman H, Suslov SA. Magneto-gravitational convection in a vertical layer of ferrofluid in a uniform oblique magnetic fluid. J Fluid Mech 2016;795:847–875. [CrossRef]
• [24] Rosensweig RE. Ferrohydrodynamics. Cambridge: Cambridge University Press; 1985.
• [25] Suslov SA, Bozhko AA, Putin GF. Thermo-magneto-convective instabilities in a vertical layer of ferro-magnetic fluid. Available at: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=10a53ce56b2298ffee69c77e7379c44d2d91aebf. Accessed Jun 26, 2024.
• [26] Ku HC, Hatziavramidis D. Chebyshev expansion methods for the solution of the extended Graetz problem. J Comput Phys 1984;56:495–512. [CrossRef]
• [27] Hatziavramidis D, Ku HC. An integral Chebyshev expansion method for boundary-value problems of ODE. type. Comput Math Appl 1985;11:581–586. [CrossRef]
• [28] Suslov SA, Paolucci S. Stability of mixed-convection flow in a tall vertical channel under non-Boussinesq conditions. J Fluid Mech 1995;302:91–115. [CrossRef] Hart JE. Stability of the flow in a differentially heated inclined box. J Fluid Mech 1971;47:547–576. [CrossRef]