Abstract
The effect of an external magnetic field on the mixed convection \(\hbox {Fe}_{{3}}\hbox {O}_{{4}}/\)water ferrofluid flow in a horizontal porous channel was studied numerically. The governing equations using the Darcy–Brinkman–Forchheimer formulation were solved by employing the finite volume method. The computations were carried out for a range of volume fractions of nanoparticles \(0\le \varphi \le 0.05\), magnetic numbers \(0\le \hbox {Mn} \le 100\), Reynolds numbers \(100\le \hbox {Re}\le 500\), Darcy numbers \(\hbox {10}^{{-3}}\le \hbox {Da}\le 10^{{-1}}\) and porosity parameters \(0.7\le \varepsilon \le 0.9\) while fixing the Grashof number at \(10^{{4}}\). Results show the formation of recirculation zone in the vicinity of the magnetic source under the influence of Kelvin force. It grows as the magnetic number increases. The friction factor increases by increasing the magnetic number and diminishes with the increase in Darcy number. The flow accelerates as the magnetic field intensifies. The heat transfer rate increases by increasing the volume fraction of the nanoparticles and the magnetic number. The effect of magnetic field on the hydrodynamic and thermal behaviours of the ferrofluid flow considerably intensifies by increasing Reynolds number and Darcy number. The combined effect of ferromagnetic nanoparticles and magnetic field on the enhancement rate of heat transfer becomes more pronounced at high values of Reynolds number, permeability and/or porosity parameter.
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M Mokhtari, S Hariri, M B Gerdroodbary and R Yeganehd, Chem. Eng. Process. 117, 70 (2017)
M Hassan, C Fetecau, A Majeed and A Zeeshan, J. Magn. Magn. Mater. 465, 531 (2018)
M Ashouri and M B Shafii, J. Magn. Magn. Mater. 442, 270 (2017)
Y E Kamış and K Atalık, J. Magn. Magn. Mater. 454, 196 (2018)
M Bezaatpour and H Rostamzadeh, Appl. Therm. Eng. 164, 114462 (2020)
N S Gibanov, M A Sheremet and H F Oztop, Heat Transf. 72(1), 64 (2017)
M Sheikholeslami, S A M Mehryan, A Shafe and M A Sheremet, J. Mol. Liq. 277, 388 (2019)
F Selimefendigil, H F Oztop, M A Sheremet and N Abu-Hamdeh Energy 12(4), 666 (2019)
H S Seo, J C Lee, I J Hwang and Y J Kim, Mater. Res. Bull. 58, 10 (2014)
V M Job and S R Gunakala, Int. J. Mech. Sci. 144, 357 (2018)
B Ghorbani, S Ebrahimi and K Vijayaraghavan, Int. J. Heat Mass Transf. 127, 544 (2018)
M M Bhatti, M A Yousif, S R Mishra and A Shahid, Pramana – J. Phys. 93(6), 88 (2019)
W Nessab, H Kahalerras, B Fersadou and D Hammoudi, Appl. Therm. Eng. 150, 271 (2019)
A Salehpour and M Ashjaee, J. Magn. Magn. Mater. 480, 112 (2019)
M Bahiraei, M Hangi and A Rahbari, Appl. Therm. Eng. 147, 991 (2019)
Y Cheng and D Li, Appl. Therm. Eng. 163, 114306 (2019)
S Nadeem, S Ahmad and N Muhammad, Pramana – J. Phys. 94(1): 1 (2020)
R Djeghiour, B Meziani and O Ourrad, Pramana – J. Phys. 94(1): 50 (2020)
M Amani, M Ameri and A Kasaeian, Int. J. Therm. Sci. 127, 242 (2018)
M Izadi, H F Oztop, M A Sheremet, S A M Mehryan and N A Hamdeh, Heat Transf. 76(6), 479 (2019)
F Fadaei, M Shahrokhi, A M Dehkordi and Z Abbasi, J. Magn. Magn. Mater. 475, 304 (2019)
M Bezaatpour and M Goharkhah, J. Magn. Magn. Mater. 476, 506 (2019)
M Izadi, R Mohebbi, A A Delouei and H Sajjadi, Int. J. Mech. Sci. 151, 154 (2019)
M Ghalambaz, M Sabour, S Sazgara, I Pop and R Trâmbiţaş, J. Magn. Magn. Mater. 497, 166024 (2020)
M Sheikholeslami and M M Rashidi, Eur. Phys. J. Plus 130(6), 115 (2015)
Z Mehrez and A El Cafsi, J. Therm. Anal. Calorim. 135(2), 1417 (2019)
A Jarray, Z Mehrez and A El Cafsi, Eur. Phys. J. Spec. Top. 228(12), 2677 (2019)
H C Brinkman, J. Chem. Phys. 20, 571 (1952)
J C Maxwell, A treatise on electricity and magnetism (Oxford University Press, Cambridge 1904) pp. 435–441
A Chorin, J. Math. Comput. 22, 745 (1968)
R Temam, Bull. Soc. Math. France 98, 115 (1968)
B P Leonard, Int. J. Numer. Methods Fluids 8, 1291 (1988)
Z Mehrez, A El Cafsi, A Belghith and P Le Quéré, Can. J. Phys. 93(12), 1615 (2015)
Z Mehrez and A El Cafsi, Int. J. Appl. Comput. Math. 3(1), 489 (2017)
F Zamzari, Z Mehrez, A El Cafsi, A Belghith and P Le Quéré, J. Hydrodyn. 29(4), 632 (2017)
G Evans and S Paolucci, Int. J. Numer. Methods Fluids 11(7), 1001 (1990)
G Comini, M Manzan and G Cortella, Numer. Heat Transf. 31(2), 217 (1997)
M Nourollahi, M Farhadi and K Sedighi, Therm. Sci. 14(2), 329 (2010)
N M Sahraoui, S Houat and N Saidi, Eur. Phys. J. Appl. Phys. 78(3), 34806 (2017)
Z Mehrez, M Bouterra, A El Cafsi, A Belghith and P Le Quéré, Appl. Fluid Mech. 3(2), 1 (2010)
F Zamzari, Z Mehrez, A E Cafsi and A Belghith, Int. J. Exergy 17(2), 219 (2015)
Z Mehrez, M Bouterra, A El Cafsi, A Belghith and A Quéré, Eng. Appl. Sci. 5(2), 7366 (2010)
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Jarray, A., Mehrez, Z. & El Cafsi, A. Effect of magnetic field on the mixed convection \(\hbox {Fe}_{3}\hbox {O}_{{{4}}}/\hbox {water}\) ferrofluid flow in a horizontal porous channel. Pramana - J Phys 94, 156 (2020). https://doi.org/10.1007/s12043-020-02015-7
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DOI: https://doi.org/10.1007/s12043-020-02015-7