Abstract.
The present article is devoted to probe the behavior of a three-dimensional micropolar nanofluid over an exponentially stretching surface in a porous medium. The mathematical model is constructed in the form of partial differential equations using the boundary layer approach. Then by employing similarity transformations, the modelled partial differential equations are transformed to ordinary differential equations. The solution of subsequent ODEs is derived by utilizing the BVP-4C technique alongside the shooting scheme. The graphical illustrations are presented to interpret the salient features of pertinent physical parameters on the concerned profiles for different kinds of nanoparticles, namely copper, titania and alumina with water as the base fluid. For a better understanding of the fluid flow, the numerical variation in the local skin friction coefficients, \( Cf_{x}\) and \( Cf_{y}\) , and local Nusselt number is analyzed through tables. We can see, from the present study, that the omission of porous matrix enhances the flow of the fluid. Microrotation has a decreasing impact on the skin friction whereas it increases the rate of the heat transfer of the nanofluid.
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References
B.C. Sakiadis, AIChE J. 7, 26 (1961)
F.K. Tsou, E.M. Sparrow, R. Jh Goldstein, Int. J. Heat Mass Transfer 10, 219 (1967)
P.S. Gupta, A.S. Gupta, Can. J. Chem. 55, 744 (1977)
Ramya, Dodda, R. Srinivasa Raju, J. Anand Rao, J. Nanofluids 6, 541 (2017)
R. Ellahi, R. Ellahi, A. Zeeshan, A. Zeeshan, Mohsan Hassan, Mohsan Hassan, Int. J. Numer. Methods Heat Fluid Flow 26, 2160 (2016)
E. Magyari, B. Keller, J. Phys. D: Appl. Phys. 32, 577 (1999)
I-Chung Liu, Hung-Hsun Wang, Yih-Ferng Peng, Chem. Eng. Commun. 200, 253 (2013)
B. Ahmad, Z. Iqbal, Front. Heat Mass Transf. 8, 22 (2017)
S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, CA, USA, Vol. 231 (ASME, 1995) pp. 99-105
Jacopo Buongiorno, J. Heat Transf. 128, 240 (2006)
J.A. Esfahani, M. Akbarzadeh, Saman Rashidi, M.A. Rosen, R. Ellahi, Int. J. Heat Mass Transfer 109, 1162 (2017)
N. Shehzad, A. Zeeshan, R. Ellahi, K. Vafai, J. Mol. Liq. 222, 446 (2016)
Kamel Milani Shirvan, Mojtaba Mamourian, Soroush Mirzakhanlari, Rahmat Ellahi, Powder Technol. 313, 99 (2017)
S.U. Rahman, R. Ellahi, S. Nadeem, QM Zaigham Zia, J. Mol. Liq. 218, 484 (2016)
M. Akbarzadeh, S. Rashidi, M. Bovand, R. Ellahi, J. Mol. Liq. 220, 1 (2016)
Saman Rashidi, Javad Aolfazli Esfahani, Rahmat Ellahi, J. Appl. Sci. 7, 431 (2017)
Kamel Milani Shirvan, Rahmat Ellahi, Mojtaba Mamourian, Mohammad Moghiman, Int. J. Heat Mass Transfer 107, 1110 (2017)
R. Ellahi, M.H. Tariq, M. Hassan, K. Vafai, J. Mol. Liq. 229, 339 (2017)
M.M. Bhatti, A. Zeeshan, R. Ellahi, Microvasc. Res. 110, 32 (2017)
Kamel Milani Shirvan, Mojtaba Mamourian, Soroush Mirzakhanlari, R. Ellahi, J. Mol. Liq. 220, 888 (2016)
Mohsan Hassan, Ahmad Zeeshan, Aaqib Majeed, Rahmat Ellahi, J. Magn. & Magn. Mater. 443, 36 (2017)
Sohail Nadeem, Rizwan Ul Haq, Zafar Hayat Khan, Alex. Eng. J. 53, 219 (2014)
Avtar Singh Ahuja, J. Appl. Phys. 46, 3408 (1975)
A. Cemal Eringen, Int. J. Eng. Sci. 2, 205 (1964)
A. Cemal Eringen, J. Appl. Math. Mech. 16, 1 (1966)
Grzegorz Lukaszewicz, Micropolar fluids: theory and applications, in Springer Science & Business Media (Springer, 1999)
A. Cemal Eringen, Microcontinuum field theories: II. Fluent media, Vol. 2, Springer Science & Business Media (Springer, 2001)
Ali J. Chamkha, M. Jaradat, I. Pop, Int. J. Fluid Mech. Res., https://doi.org/10.1615/InterJFluidMechRes.v30.i4.10 (2003)
Mohamed Abd El-Aziz, Can. J. Phys. 87, 359 (2009)
B. Mohanty, S.R. Mishra, H.B. Pattanayak, Alex. Eng. J. 54, 223 (2015)
Syed Tauseef Mohyud-Din, Saeed Ullah Jan, Umar Khan, Naveed Ahmed, Neural Comput. Appl., https://doi.org/10.1007/s00521-016-2493-3 (2016)
S.T. Hussain, Sohail Nadeem, Rizwan Ul Haq, Eur. Phys. J. Plus 129, 161 (2014)
M.T. Kamel, D. Roach, M.H. Hamdan, in Proceedings of the WSEAS International Conference on Mathematics and Cpmputers in Science and Engineering no. 11 (WSEAS, 2009)
Michael W. Heruska, Layne T. Watson, Kishore Kumar Sankara, Comput. Fluids 14, 117 (1986)
Heidar Hashemi, Zafar Namazian, S.A.M. Mehryan, J. Mol. Liq. 236, 48 (2017)
M. Turkyilmazoglu, Int. J. Nonlinear Mech. 83, 59 (2016)
A. Zeeshan, R. Ellahi, M. Hassan, Eur. Phys. J. Plus 129, 261 (2014)
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Subhani, M., Nadeem, S. Numerical analysis of 3D micropolar nanofluid flow induced by an exponentially stretching surface embedded in a porous medium. Eur. Phys. J. Plus 132, 441 (2017). https://doi.org/10.1140/epjp/i2017-11660-0
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DOI: https://doi.org/10.1140/epjp/i2017-11660-0