Practical Insight of Ferroconvection in Heterogeneous Brinkman Porous Medium
International Journal of Applied Mathematics and Theoretical Physics
Volume 6, Issue 3, September 2020, Pages: 41-48
Received: Aug. 3, 2019; Accepted: Dec. 23, 2019; Published: Sep. 7, 2020
Views 31      Downloads 30
Authors
Ravisha Mallappa, Department of Mathematics, Dr. Gundmi Shankar Government Women’s First Grade College and Post Graduate Study Centre, Udupi, India
Basavarajaiah Doddagangavadi Mariyappa, Department of Statistics and Computer Science, Dairy Science College, Bengaluru, India
Mamatha Arabhaghatta Lingaraju, Department of Mathematics, Smt. Rukmini Shedthi Memorial National Government Women’s First Grade College, Udupi, India
Prakash Revanna, Department of Mathematics, Rashtreeya Vidyalaya College of Engineering, Bengaluru, India
Article Tools
Follow on us
Abstract
Ferromagnetic fluids are made up of magnetic particles, which are suspended in a carrier liquid such as water, hydrocarbon (mineral oil or kerosene) or fluorocarbon with a surfactant to avoid clumping. Worldwide many literature revealed that, the ferromagnetic fluids application has been diversified in nature and widely used in engineering, technology, agricultural, animal and biomedical sciences etc. (evidence based medicine for cancer patients, fertigation in agriculture). Now a days, the driven applications are using in developing countries. The ferromagnetic fluids analytical applications are very limited scope in Indian scenario due to paucity of literature and technological gap. In the essence of this research gap the present study undertaking to demonstrate the various applications of ferroconvection in a heterogeneous Brinkman porous medium on theoretical basis. The resulting eigenvalue problem is solved numerically using the Galerkin method. The effects of vertical heterogeneity of permeability, Darcy parameter, Magnetic Rayleigh number, nonlinearity of magnetization, and internal heat source on the onset of ferromagnetic convection is investigated.
Keywords
Heterogeneous Porous Medium, Ferrofluid, Ferromagnetic Convection, Variable Permeability, Internal Heat Source
To cite this article
Ravisha Mallappa, Basavarajaiah Doddagangavadi Mariyappa, Mamatha Arabhaghatta Lingaraju, Prakash Revanna, Practical Insight of Ferroconvection in Heterogeneous Brinkman Porous Medium, International Journal of Applied Mathematics and Theoretical Physics. Special Issue: Dynamical Properties of Some Discrete Dynamical Systems. Vol. 6, No. 3, 2020, pp. 41-48. doi: 10.11648/j.ijamtp.20200603.12
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
B. M. Berkovsky, V. F. Medvdev, M. S. Krakov, The Magnetic Fluids, Eng Appln Oxford University Press, Oxford, 1973.
[2]
J. L. Neuringer, R. E. Rosensweig, Ferrohydrodynamics, Phys. Fluids 7 (12) (1964) 1927-1937.
[3]
B. A. Finlayson, Convective instability of ferromagnetic fluids, J. Fluid Mech. 40 (1970) 753–767.
[4]
S. Odenbach, Recent progress in magnetic fluid research, J. Phys. Condens. Matter 16 (2004) R1135–R1150.
[5]
P. N. Kaloni, L. X. Lou, Convective instability of magnetic fluids under alternating magnetic fields, Phy. Rev. E. 71 (2004) 066311-1-12.
[6]
I. Nkurikiyimfura, Y. Wang, Z. Pan, Heat transfer enhancement by magnetic nanofluids - a review, Ren. Sustain. Energy Rev. 21 (2013) 548–561.
[7]
A. N. Afifah, S. Syahrullail, N. A. C. Sidik, Magnetoviscous effect and thermomagnetic convection of magnetic fluid: A review, Ren. Sustain. Energy Rev., 55 (2016) 1030–1040.
[8]
S. E. Borglin, J. Mordis, C. M. Oldenburg, Experimental studies of the flow of ferrofluid in porous media, Transp. Porous Med. 41 (2000) 61-80.
[9]
C. Oldenburg, S. Borglin, G. J. Moridis, Numerical simulation of ferrofluid flow for subsurface environmental engineering applications, Transp. Porous Med. 38 (2000) 319–344.
[10]
I. S. Shivakumara, C. E. Nanjundappa, M. Ravisha, Effect of boundary conditions on the onset of thermomagnetic convection in a ferrofluid saturated porous medium, ASME J. Heat Transf. 131 (2009) 101003-1-101003-9.
[11]
C. E. Nanjundappa, I. S. Shivakumara, M. Ravisha, The onset of buoyancy-driven convection in a ferromagnetic fluid saturated porous medium, Meccan. 45 (2010) 213–226.
[12]
C. E. Nanjundappa, I. S. Shivakumara, R. Arunkumar, Rafael Tadmor, Ferroconvection in a porous medium with vertical Throughflow, Acta Mech. (2015) DOI 10.1007/s00707-014-1267-1.
[13]
H. Sadrhosseini, A. Sehat, M. B. Shafii, Effect of Magnetic field on internal forced convection of ferrofluid flow in porous media, Experimental Heat Transf. 29 (2016) 1–16.
[14]
B. Straughan, Mathematical Aspects of Penetrative Convection, Longman, 1993.
[15]
B. S. Bhadauria, Double-diffusive convection in a saturated anisotropic porous layer with internal heat source, Transp. Porous Med. 92 (2012) 299–310.
[16]
B. Straughan, Resonant penetrative convection with an internal heat source/sink, Acta Appl. Math. 132 (2014) 561–581.
[17]
A. J. Harfash, Resonant penetrative convection in porous media with an internal heat source/sink effect, Appl. Math. Comp. 281 (2016) 323–342.
[18]
N. Rudraiah, G. N. Sekhar, Convection in magnetic fluids with internal heat generation, ASME J. Heat Transf. 113 (1991) 122-127.
[19]
C. E. Nanjundappa, M. Ravisha, Jinho Lee, I. S. Shivakumara, Penetrative ferroconvection in a porous layer, Act. Mech. 216 (1) (2011) 243-257.
[20]
C. E. Nanjundappa, I. S. Shivakumara, Jinho Lee, M. Ravisha, Effect of internal heat generation on the onset of Brinkman Benard convection in a ferrofluid saturated porous layer, Int. J. Thermal Sci. 50 (2011) 160-168.
[21]
C. Braester, P. Vadasz, The effect of a weak heterogeneity of a porous medium on natural convection, J. Fluid Mech. 254 (1993) 345-362.
[22]
D. A. Nield, A. V. Kuznetsov, The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium, Int. J. Heat Mass Transf. 50 (2007) 3329–3339.
[23]
D. A. Nield, A. V. Kuznetsov, The onset of convection in a heterogeneous porous medium with transient temperature profile, Transp. Porous Med. 85 (2010) 691-702.
[24]
A. V. Kuznetsov, D. A. Nield, C. T. Simmons, The effect of strong heterogeneity on the onset of convection in a porous medium: periodic and localized variation, Transp. Porous Med. 81 (2010) 123–139.
[25]
A. V. Kuznetsov, D. A. Nield, C. T. Simmons, The onset of convection in a strongly heterogeneous porous medium with transient temperature profile, Transp. Porous Med. 86 (2011) 851–865.
[26]
S. Rionero, Onset of convection in porous materials with vertically stratified porosity, Acta Mech. 222 (2011) 261-272.
[27]
D. A. Nield, A. V. Kuznetsov, Onset of convection with internal heating in a weakly heterogeneous porous medium. Transp. Porous Med. 98 (2013) 543–552.
[28]
D. A. Nield, A. V. Kuznetsov, Onset of convection with internal heating in a porous medium saturated by a nanofluid, Transp. Porous Med. 99 (2013) 73–83.
[29]
D. A. Nield, A. V. Kuznetsov, The effect of heterogeneity on the onset of double-diffusive convection induced by internal heating in a porous medium: a layered model, Transp. Porous Med. 100 (2013) 83–99.
[30]
A. V. Kuznetsov, D. A. Nield, The effect of strong heterogeneity on the onset of convection induced by internal heating in a porous medium: a layered model, Transp. Porous Med. 99 (2013) 85–100.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186