AIMS Mathematics, 2018, 3(1): 195-210. doi: 10.3934/Math.2018.1.195.

Research article

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Numerical investigation of ferrofluid convection with Kelvin forces and non-Darcy effects

Department of Mathematics, TED University, Ziya Gokalp Caddesi, No:47–48, 06420, Kolej-Cankaya, Ankara, Turkey

In this study, natural convection in a porous, ferrofluid-filled cavity is numerically investigatedutilizing the multiquadric (MQ) radial basis function (RBF) based pseudo spectral (PS) method.The influence of Kelvin forces, Brinkman and Forchheimer terms and a magnetic source is also takeninto account. Results reveal that convective heat transfer is inhibited with the rise of Hartmann number,and with the decrease in Darcy number while it is enhanced with the increase in porosity of the porousmedium, solid volume fraction and Rayleigh number. At a small Rayleigh number, the average Nusseltnumber enhances with the augmentation of magnetic number.
  Article Metrics

Keywords ferrofluid; porous media; natural convection; radial basis functions; multiquadrics; magnetic source

Citation: Bengisen Pekmen Geridönmez. Numerical investigation of ferrofluid convection with Kelvin forces and non-Darcy effects. AIMS Mathematics, 2018, 3(1): 195-210. doi: 10.3934/Math.2018.1.195


  • 1. H. Aminfar, M. Mohammadpourfard, S. Ahangar Zonouzi, Numerical study of the ferrofluid flow and heat transfer through a rectangular duct in the presence of a non-uniform transverse magnetic field, J. Magn. Magn. Mater., 327 (2013), 31–42.
  • 2. H. C. Brinkman, (1952) The viscosity of concentrated suspensions and solutions, J. Chem. Phys., 20 (1952), 571–581.
  • 3. S. U. S. Choi, J. A. Eastman, Enhancing thermal conductivity of fluid with nanoparticles, ASME Mechanical Engineering Congress & Exposition, Nov 12–17, Sanfrancisco, 1995.
  • 4. G. E. Fasshauer, Meshfree Approximation Methods with Matlab, World Scientific Publications, Singapore, 2007.
  • 5. G. E. Fasshauer, M. McCourt, Kernel-based Approximation Methods using MATLAB, World Scientific Publications, Singapore, 2015.
  • 6. M. A. Geschwendtner, The Eckert number phenomenon: Experimental investigations on the heat transfer from a moving wall in the case of a rotating cylinder, Heat and Mass Transfer, 40 (2004), 551–559.
  • 7. M. Ghasemian, Z. N. Ashrafi, M. Goharkhah, et al. Heat transfer characteristics of Fe3O4 ferrofluid flowing in a mini channel under constant and alternating magnetic fields, J. Magn. Magn. Mater., 381 (2015), 158–167.
  • 8. G. H. R. Kefayati, Natural convection of ferrofluid in a linearly heated cavity utilizing LBM, J. Mol. Liq., 191 (2014), 1–9.
  • 9. G. H. R. Kefayati, Simulation of ferrofluid heat dissipation effect on natural convection at an inclined cavity filled with Kerosene/Cobalt utilizing the Lattice Boltzmann Method, Numer. Heat Tr. A-Appl., 65 (2014), 509–530.
  • 10. K. Khanafer, K. Vafai, M. Lightstone, Buoyancy-driven heat transfer enchancement in a twodimensional enclosure utilizing nanofluids, Int. J. Heat Mass Tran., 46 (2003), 3639–3653.
  • 11. P. A. K. Lam, K. A. Prakash, A numerical study on natural convection and entropy generation in a porous enclosure with heat sources, Int. J. Heat Mass Tran., 69 (2014), 390–407.
  • 12. S. Malik, A. K. Nayak, MHD convection and entropy generation of nanofluid in a porous enclosure with sinusoidal heating, Int. J. Heat Mass Tran., 111 (2017), 329–345.
  • 13. J. C. Maxwell-Garnett, Colors in metal glasses and in metallic films, Phil. Trans. Soc. A., 203 (1904), 385–420.
  • 14. M. Muthtamilselvan, P. Kandaswamy, J. Lee, Heat transfer enhancement of copper-water nanofluids in a lid-driven enclosure, Commun. Nonlinear Sci. Numer. Simulat., 15 (2010), 1501–1510.
  • 15. M. M. Rahman, S. Mojumder, S. Saha, et al. Numerical and statistical analysis on unsteady magnetohydrodynamic convection in a semi-circular enclosure filled with ferrofluid, Int. J. Heat Mass Tran., 89 (2015), 1316–1330.
  • 16. B. Geridonmez Pekmen, RBF simulation of natural convection in a nanofluid-filled cavity, AIMS Mathematics, 1 (2016), 195–207.
  • 17. B. Geridonmez Pekmen, Numerical simulation of natural convection in a porous cavity filled with ferrofluid in presence of magnetic source, J. Therm. Eng., 4 (2017), 1756–1769.
  • 18. M. Sheikholeslami, D. D. Ganji, Ferrohydrodynamic and magnetohydrodynamic effects on ferrofluid flow and convective heat transfer, Energy, 75 (2014), 400–410.
  • 19. M. Sheikholeslami, KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel, Phys. Lett. A, 378 (2014), 3331–3339
  • 20. M. Sheikholeslami, Effect of uniform suction on nanofluid flow and heat transfer over a cylinder, J. Braz. Soc. Mech. Sci. Eng., 37 (2015), 1623–1633.
  • 21. M. A. Sheremet, H. F. Oztop, I. Pop, et al. MHD free convection in a wavy open porous tall cavity filled with nanofluids under an effect of corner heater, Int. J. Heat Mass Tran., 103 (2016), 955– 964.
  • 22. R. K. Tiwari, M. K. Das, Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Tran., 50 (2007), 2002–2018.
  • 23. E. E. Tzirtzilakis, M. A. Xenos, Biomagnetic fluid flow in driven cavity, Meccanica, 48 (2013), 187–200.


This article has been cited by

  • 1. Bengisen Pekmen Geridonmez, Free Convection in a Wavy Walled Cavity With a Magnetic Source Using Radial Basis Functions, Journal of Heat Transfer, 2019, 141, 4, 042501, 10.1115/1.4042782
  • 2. Bengisen Pekmen Geridönmez, Magnetic source effect on EG-CuO nanofluid in a semi-annulus using RBFs, International Journal for Computational Methods in Engineering Science and Mechanics, 2019, 1, 10.1080/15502287.2019.1604583
  • 3. Abuzar Abid Siddiqui, Mustafa Turkyilmazoglu, A New Theoretical Approach of Wall Transpiration in the Cavity Flow of the Ferrofluids, Micromachines, 2019, 10, 6, 373, 10.3390/mi10060373

Reader Comments

your name: *   your email: *  

© 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved