Abstract.
The significance of the different shapes of molybdenum disulfide nanoparticles contained in ethylene glycol has recently attracted researchers, because of the numerical or experimental analyses on the shapes of molybdenum disulfide and the lack of fractionalized analytic approaches. This work is dedicated to examining the shape impacts of molybdenum disulfide nanofluids in the mixed convection flow with magnetic field and a porous medium. Ethylene glycol is chosen as the base fluid in which molybdenum disulfide nanoparticles are suspended. Non-spherically shaped molybdenum disulfide nanoparticles, namely, platelet, blade, cylinder and brick, are utilized in this analysis. The modeling of the problem is characterized by employing the modern approach of Atangana-Baleanu fractional derivatives and the governing partial differential equations are solved via Laplace transforms with inversion. Solutions are obtained for temperature distribution and velocity field and expressed in terms of compact form of \( \mathbf{M}\) -function, \( \mathbf{M}_{b}^{a}(T)\) . In the end, a figures are drawn to compare the different non-spherically shaped molybdenum disulfide nanoparticles. Furthermore, the Atangana-Baleanu fractional derivatives model has been compared with ordinary derivatives models and discussed graphically by setting various rheological parameters.
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References
W.O. Winer, Wear 10, 422 (1967)
Khan Ilyas, Gul Aaiza, Shafie Sharidan, J. Porous Media 20, 435 (2017)
Y. Zhang, S. Gu, B. Yan, J. Ren, J. Mater. Chem. 22, 14843 (2012)
Y. Zhang, C. Li, D. Jia, B. Li, Y. Wang, M. Yang, X. Zhang, J. Mater. Process. Technol. 232, 100 (2016)
A. Dankert, L. Langouche, M.V. Kamalakar, S.P. Dash, ACS Nano 8, 476 (2014)
S. Das, H.-Y. Chen, A.V. Penumatcha, J. Appenzeller, Nano Lett. 13, 100 (2012)
B. Radisavljevic, M.B. Whitwick, A. Kis, ACS Nano. 5, 9934 (2011)
H. Wang, L. Yu, Y.-H. Lee, Y. Shi, A. Hsu, M.L. Chin, T. Palacios, Nano Lett. 12, 4674 (2012)
B.C. Pak, Y.I. Choi, Exp. Heat Transf. 11, 151 (1998)
G. Shuying, Y. Zhang, B. Yan, Mater. Lett. 97, 169 (2013)
Y. Zhang, S. Gu, B. Yan, J. Ren, J. Mater. Chem. 22, 14843 (2012)
C. Mao, Y. Huang, X. Zhou, H. Gan, J. Zhang, Z. Zhou, Int. J. Adv. Manuf. Technol. 71, 1221 (2014)
B. Shen, Minimum quantity lubrication grinding using nanofluids, PhD dissertation (University of Michigan, 2008)
J.J. McBride, E.F. Westrum, J. Chem. Thermodyn. 8, 37 (1976)
E. Benavente, M. Santa Ana, G. González, Phys. Status Solidi B 241, 2444 (2004)
J. Liu, G.-M. Choi, D.G. Cahill, J. Appl. Phys. 116, 233107 (2014)
Y. Ding, B. Xiao, RSC Adv. 5, 18391 (2015)
K. Asma, I. Khan, S. Sharidan, Eur. Phys. J. Plus 130, 57 (2015)
K. Asma, I. Khan, S. Sharidan, J. Mol. Liq. 221, 1175 (2016)
E.V. Timofeeva, J.L. Routbort, D. Singh, J. Appl. Phys. 106, 014304 (2009)
N. Athirah, M. Zin, I. Khan, S. Sharidan, J. Mol. Liq. 222, 138 (2016)
R.U. Haq, S. Nadeem, Z.H. Khan, N.F.M. Noor, Physica E 73, 45 (2015)
A. Khalid, I. Khan, S. Shafie, Eur. Phys. J. Plus 130, 57 (2015)
M. Sheikholeslami, D.D. Ganji, Powder Technol. 253, 789 (2014)
T. Hayat, M. Imtiaz, A. Alsaedi, J. Aerospace Eng. 29, 04015063 (2016)
F. Ali, N.A. Sheikh, I. Khan, M. Saqib, J. Magn. & Magn. Mater. 423, 327 (2017)
F. Ali, M. Saqib, I. Khan, N.A. Sheikh, Eur. Phys. J. Plus 131, 377 (2016)
A. Kashif, H. Mukarrum, M. Mahmood, Progr. Fract. Differ. Appl. 3, 69 (2017)
N.A. Sheikh, F. Ali, I. Khan, M. Saqib, Neural. Comput. Appl. (2016) https://doi.org/10.1007/s00521-016-2815-5
Kashif Ali Abro, J. Appl. Environ. Biol. Sci. 6, 71 (2016)
Kashif Ali Abro, Muhammad Anwar Solangi, Muzaffar Hussain Laghari, Int. J. Adv. Appl. Math. Mech. 4, 5 (2017)
Magdy A. Ezzat, Ahmed S. El Karamany, Z. Angew. Math. Phys. 62, 937 (2011)
Magdy A. Ezzat, Can. J. Phys. 72, 311 (1994)
M. Ezzat, M. Zakaria, O. Shaker, F. Barakat, Acta Mech. 119, 147 (1996)
Magdy A. Ezzat, Ahmed S. El-Karamany, Can. J. Phys. 81, 823 (2003)
R. Hamilton, O. Crosser, Ind. Eng. Chem. Fund. 1, 187 (1962)
E.V. Timofeeva, J.L. Routbort, D. Singh, J. Appl. Phys. 106, 014304 (2009)
S. Das, R. Jana, Alexa. Eng. J. 54, 55 (2015)
A. Abdon, D. Baleanu, Thermal Sci. 20, 763 (2016)
A.S. Nadeem, A. Farhad, S. Muhammad, K. Ilyas, S.A.A. Jan, S.A. Ali, S.A. Metib, Results Phys. 7, 789 (2017)
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Ali Abro, K., Hussain, M. & Mahmood Baig, M. An analytic study of molybdenum disulfide nanofluids using the modern approach of Atangana-Baleanu fractional derivatives. Eur. Phys. J. Plus 132, 439 (2017). https://doi.org/10.1140/epjp/i2017-11689-y
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DOI: https://doi.org/10.1140/epjp/i2017-11689-y