Mathematical Solution on MHD Stagnation Point Flow of Ferrofluid

Abstract:

This study presents a numerical investigation on the magnetohydrodynamic (MHD) stagnation point flow of a ferrofluid with Newtonian heating. The black oxide of iron, magnetite (Fe₃O₄) which acts as magnetic materials and water as a base fluid are considered. The two dimensional stagnation point flow of cold ferrofluid against a hot wall under the influence of the uniform magnetic field of strength is located some distance behind the stagnation point. The effect of magnetic and volume fraction on the velocity and temperature boundary layer profiles are obtained through the formulated governing equations. The governing equations which are in the form of dimensional non-linear partial differential equations are reduced to dimensionless non-linear ordinary differential equations by using appropriate similarity transformation. Then, they are solved numerically by using the Keller-box method which is programmed in the Matlab software. It is found that the cold fluid moves towards the magnetic source that is close to the hot wall. Hence, leads to the better cooling rate and enhances the heat transfer rate. Meanwhile, an increase of the magnetite nanoparticles volume fraction, increases the ferrofluid capabilities in thermal conductivity and consequently enhances the heat transfer.

• Periodical: Defect and Diffusion Forum (Volume 399)
• Pages: 38-54
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.399.38
• Online since: February 2020
• Authors: Siti Hanani Mat Yasin, Muhammad Khairul Anuar Mohamed, Zulkhibri Ismail, Mohd Zuki Salleh*
• Keywords: Ferrofluid, Keller-Box Method, Magnetohydrodynamic, Newtonian Heating

References

[1] S.U.S. Choi, J.A. Eastman. Enhancing thermal conductivity of fluids with nanoparticles. In Proc. Conf. on ASME International Mechanical Engineering Congress & Exposition, San Francisco, USA. (1995) 99-105.

[2] S.K. Das, S.U.S. Choi, H.E. Patel, Heat transfer in nanofluids - A review, Heat transfer engineering 27 (2006) 3-19.

DOI: 10.1080/01457630600904593

[3] Y. Li, S. Tung, E. Schneider, S. Xi, A review on development of nanofluid preparation and characterization, Powder Technology 196 (2009) 89-101.

DOI: 10.1016/j.powtec.2009.07.025

[4] S. Kakaç, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, International Journal of Heat and Mass Transfer 52 (2009) 3187-3196.

DOI: 10.1016/j.ijheatmasstransfer.2009.02.006

[5] R. Taylor, S. Coulombe, T. Otanicar, P. Phelan, A. Gunawan, W. Lv, G. Rosengarten, R. Prasher, H. Tyagi, Small particles, big impacts: a review of the diverse applications of nanofluids, Journal of applied physics 113 (2013) 1.

DOI: 10.1063/1.4754271

[6] N.A.C. Sidik, H.A. Mohammed, O.A. Alawi, S. Samion, A review on preparation methods and challenges of nanofluids, International Communications in Heat and Mass Transfer 54 (2014) 115-125.

DOI: 10.1016/j.icheatmasstransfer.2014.03.002

[7] R.E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, New York, (1985).

[8] A.N. Darus, Analisis pemindahan haba: Olakan, Dewan Bahasa dan Pustaka, Kuala Lumpur, (1995).

[9] J.L. Neuringer, R.E. Rosensweig, Ferrohydrodynamics, The Physics of Fluids 7 (1964) 1927-1937.

DOI: 10.1063/1.1711103

[10] J.L. Neuringer, Some viscous flows of a saturated ferro-fluid under the combined influence of thermal and magnetic field gradients, International Journal of Non-Linear Mechanics 1 (1966) 123-137.

DOI: 10.1016/0020-7462(66)90025-4

[11] W. Khan, Z. Khan, R.U. Haq, Flow and heat transfer of ferrofluids over a flat plate with uniform heat flux, The European Physical Journal Plus 130 (2015) 1-10.

DOI: 10.1140/epjp/i2015-15086-4

[12] N. Sandeep, C. Raju, C. Sulochana, V. Sugunamma, Effects of aligned magneticfield and radiation on the flow of ferrofluids over a flat plate with non-uniform heat source/sink, International Journal of Science and Engineering 8 (2015) 151-158.

[13] N. Ramli, S. Ahmad, I. Pop, Slip effects on MHD flow and heat transfer of ferrofluids over a moving flat plate, AIP Conference Proceedings 1870 (2017) 040015.

DOI: 10.1063/1.4995847

[14] M.R. Ilias, N.A. Rawi, S. Shafie, MHD Free Convection Flow and Heat Transfer of Ferrofluids over a Vertical Flat Plate with Aligned and Transverse Magnetic Field, Indian Journal of Science and Technology 9 (2016) 1-7.

DOI: 10.17485/ijst/2016/v9i36/97347

[15] M.R. Ilias, N.A. Rawi, N.H. Ab Raji, S. Shafie, Unsteady aligned MHD boundary layer flow and heat transfer of magnetic nanofluid past a vertical flat plate with leading edge accretion, ARPN Journal of Engineering and Applied Sciences 13 (2018) 340-351.

DOI: 10.18178/ijmerr.9.2.197-206

[16] Z.H. Khan, W.A. Khan, M. Qasim, I.A. Shah, MHD Stagnation Point Ferrofluid Flow and Heat Transfer Toward a Stretching Sheet, IEEE Transactions on Nanotechnology 13 (2014) 35-40.

DOI: 10.1109/tnano.2013.2286991

[17] I. Mustafa, T. Javed, A. Ghaffari, Heat transfer in MHD stagnation point flow of a ferrofluid over a stretchable rotating disk, Journal of Molecular Liquids 219 (2016) 526-532.

DOI: 10.1016/j.molliq.2016.03.046

[18] Z. Abbas, M. Sheikh, Numerical study of homogeneous–heterogeneous reactions on stagnation point flow of ferrofluid with non-linear slip condition, Chinese Journal of Chemical Engineering 25 (2017) 11-17.

DOI: 10.1016/j.cjche.2016.05.019

[19] C.S.K. Raju, N. Sandeep, M. Jayachandra Babu, J.V. Ramana Reddy, Stagnation-point flow of a ferrofluid towards a stretching sheet, Journal of Nanofluids 5 (2016) 245-252.

DOI: 10.1166/jon.2016.1209

[20] J. Merkin, Natural-convection boundary-layer flow on a vertical surface with Newtonian heating, International Journal of Heat and Fluid Flow 15 (1994) 392-398.

DOI: 10.1016/0142-727x(94)90053-1

[21] E. Blums, Heat and mass transfer phenomena, in: S. Odenbach (Eds.), Ferrofluids: Magnetically Controllable Fluids and Their Applications, Springer Berlin, 2002, pp.124-139.

[22] R.K. Tiwari, M.K. Das, Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, International Journal of Heat and Mass Transfer 50 (2007) 2002-2018.

DOI: 10.1016/j.ijheatmasstransfer.2006.09.034

[23] S.H.M. Yasin, M.K.A. Mohamed, Z. Ismail, B. Widodo, M.Z. Salleh, Numerical Solution on MHD Stagnation Point Flow in Ferrofluid with Newtonian Heating and Thermal Radiation Effect, CFD Lettters 11 (2019) 21-31.

DOI: 10.1088/1742-6596/1366/1/012008

[24] S.S. Molokov, R. Moreau, H.K. Moffatt, Magnetohydrodynamics: Historical evolution and trends, Vol. 80, Springer Science & Business Media, (2007).

[25] S. Hussain, S.E. Ahmed, Unsteady MHD forced convection over a backward facing step including a rotating cylinder utilizing Fe3O4-water ferrofluid, Journal of Magnetism and Magnetic Materials 484 (2019) 356-366.

DOI: 10.1016/j.jmmm.2019.04.040

[26] M.K.A. Mohamed, M.I. Anwar, S. Shafie, M.Z. Salleh, A. Ishak. Effects of Magnetohydrodynamic on the Stagnation Point Flow past a Stretching Sheet in the Presence of Thermal Radiation with Newtonian Heating. In Proc. Conf. on International Conference on Mathematical Sciences and Statistics 2013, (2014) 155-163.

DOI: 10.1007/978-981-4585-33-0_16

[27] N. Bachok, A. Ishak, I. Pop, Stagnation-point flow over a stretching/shrinking sheet in a nanofluid, Nanoscale Research Letters 6 (2011) 623-632.

DOI: 10.1186/1556-276x-6-623

[28] M. Turkyilmazoglu, Unsteady convection flow of some nanofluids past a moving vertical flat plate with heat transfer, Journal of heat transfer 136 (2014) 031704.

DOI: 10.1115/1.4025730

[29] H. Brinkman, The viscosity of concentrated suspensions and solutions, The Journal of chemical physics 20 (1952) 571-571.

DOI: 10.1063/1.1700493

[30] J.C. Maxwell, A treatise on Electricity and Magnetism Clarendon Press Oxford, 1873.

[31] T. Cebeci, P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer, Springer, New York, (1988).

[32] T.Y. Na, Computational Method in Engineering Boundary Value Problems, Academic Press, New York, (1979).

[33] M.K.A. Mohamed, M.Z. Salleh, R. Nazar, A. Ishak, Stagnation point flow over a stretching sheet with Newtonian heating, Sains Malaysiana 41 (2012) 1467-1473.

[34] N.S. Gibanov, M.A. Sheremet, H.F. Oztop, N. Abu-Hamdeh, Effect of uniform inclined magnetic field on mixed convection in a lid-driven cavity having a horizontal porous layer saturated with a ferrofluid, International Journal of Heat and Mass Transfer 114 (2017) 1086-1097.

DOI: 10.1016/j.ijheatmasstransfer.2017.07.001

[35] M. Sheikholeslami, M.M. Rashidi, Effect of space dependent magnetic field on free convection of Fe3O4–water nanofluid, Journal of the Taiwan Institute of Chemical Engineers 56 (2015) 6-15.

DOI: 10.1016/j.jtice.2015.03.035

[36] D. Toghraie, S.M. Alempour, M. Afrand, Experimental determination of viscosity of water based magnetite nanofluid for application in heating and cooling systems, Journal of Magnetism and Magnetic Materials 417 (2016) 243-248.

DOI: 10.1016/j.jmmm.2016.05.092

[37] A. Malekzadeh, A. Pouranfard, N. Hatami, A.K. Banari, M. Rahimi, Experimental Investigations on the Viscosity of Magnetic Nanofluids under the Influence of Temperature, Volume Fractions of Nanoparticles and External Magnetic Field, Journal of Applied Fluid Mechanics 9 (2016).

DOI: 10.18869/acadpub.jafm.68.225.24022

[38] H. Haiza, I. Yaacob, A.Z.A. Azhar, Thermal Conductivity of Water Based Magnetite Ferrofluids at Different Temperature for Heat Transfer Applications, Solid State Phenomena 280 (2018) 36-42.

DOI: 10.4028/www.scientific.net/ssp.280.36

[39] B. Ghosh, M. Poshtan, Investigating the Lorentz Force Effect in Reducing Calcite Scaling in Pipe Flow, International Journal of Electronic and Electrical Engineering 6 (2013) 87-98.