Abstract.
Main theme of the article is to examine the entropy generation analysis for the magneto-hydrodynamic mixed convection flow of water functionalized carbon nanotubes along an inclined stretching surface. Thermophysical properties of both particles and working fluid are incorporated in the system of governing partial differential equations. Rehabilitation of nonlinear system of equations is obtained via similarity transformations. Moreover, solutions of these equations are further utilized to determine the volumetric entropy and characteristic entropy generation. Solutions of governing boundary layer equations are obtained numerically using the finite difference method. Effects of two types of carbon nanotubes, namely, single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs) with water as base fluid have been analyzed over the physical quantities of interest, namely, surface skin friction, heat transfer rate and entropy generation coefficients. Influential results of velocities, temperature, entropy generation and isotherms are plotted against the emerging parameter, namely, nanoparticle fraction \(0\le \phi \le 0.2\), thermal convective parameter \(0\le \lambda \le 5\), Hartmann number \(0\le M\le 2\), suction/injection parameter \(-1\le S\le 1\), and Eckert number \(0\le Ec \le 2\). It is finally concluded that skin friction increases due to the increase in the magnetic parameter, suction/injection and nanoparticle volume fraction, whereas the Nusselt number shows an increasing trend due to the increase in the suction parameter, mixed convection parameter and nanoparticle volume fraction. Similarly, entropy generation shows an opposite behavior for the Hartmann number and mixed convection parameter for both single-wall and multi-wall carbon nanotubes.
Similar content being viewed by others
References
Stephen U.S. Choi, J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, presented at ASME International Mechanical Engineering Congress and Exposition, 1995
Kiyuel Kwak, Chongyoup Kim, Korea-Australia Rheol. J. 17, 35 (2005)
Kuafui V. Wong, Omar De Leon, Adv. Mech. Eng. 2010, 519659 (2010)
Abdul Sattar Dogonchi, Davood Domiri Ganji, J. Mol. Liq. 223, 521 (2016)
Riwan Ul Haq, Z.H. Khan, W.A. Khan, Inayat Ali Shah, Int. J. Chem. Reactor Eng. (2016) https://doi.org/10.1515/ijcre-2016-0059
N. Freidoonimehr, M.M. Rashidi, B. Jalilpour, J. Braz. Soc. Mech. Sci. 38, 1999 (2016)
Emad H. Aly, Powder Technol. 301, 760 (2016)
B. Mahanthesh, B.J. Gireesha, R.S. Reddy Gorla, F.M. Abbasi, S.A. Shehzad, J. Magn. & Magn. Mater. 417, 189 (2016)
Muhammad Idrees Afridi, Muhammad Qasim, Ilyas Khan, Sharidan Shafie, Ali Saleh Alshomrani, Entropy 19, 10 (2017)
M. Bilal Ashraf, T. Hayat, A. Alsaedi, J. Appl. Mech. Tech. Phys. 57, 317 (2016)
P. Bala Anki Reddy, Ain Shams Eng. J. 7, 593 (2016)
Ruchika Dhanai, Puneet Rana, Lokendra Kumar, J. Taiwan Inst. Chem. Eng. 66, 283 (2016)
M. Bilal Ashraf, T. Hayat, S.A. Shehzad, A. Alsaedi, AIP Adv. 5, 027134 (2015)
T. Hayat, S. Asad, A. Alsaedi, J. Cent. South Univ. 22, 3180 (2015)
Hashim, Masood Khan, Int. J. Heat Mass Transfer 103, 291 (2016)
Hashim, M. Khan, J. Taiwan Inst. Chem. Eng. 77, 282 (2017)
M. Khan, Hashim, Abdul Hafeez, Chem. Eng. Sci. https://doi.org/10.1016/j.ces.2017.07.024
Hashim, M. Khan, Ali Saleh Alshomrani, J. Magn. & Magn. Mater. 443, 13 (2017)
Hashim, M. Khan, Ali Saleh Alshomrani, Eur. Phys. J. E 40, 8 (2017)
S. Nadeem, Rizwan Ul Haq, C. Lee, Sci. Iran. 19, 1550 (2012)
N.S. Akbar, S. Nadeem, Rizwan Ul Haq, Z.H. Khan, Indian J. Phys. 87, 1121 (2013)
S. Nadeem, Rizwan Ul Haq, Noreen Sher Akbar, Z.H. Khan, Alex. Eng. J. 52, 577 (2013)
S. Nadeem, Rizwan Ul Haq, Z.H. Khan, J. Taiwan Inst. Chem. Eng. 45, 121 (2014)
W.A. Khan, Z.H. Khan, Rizwan Ul Haq, Eur. Phys. J. Plus 130, 86 (2015)
S.T. Hussain, S. Nadeem, Rizwan Ul Haq, Eur. Phys. J. Plus 129, 167 (2014)
A. Bejan, Adv. Heat Transf. 15, 1 (1982)
A. Bejan, Entropy Generation Minimization: The Method of Thermodynamic Optimization of Finite-size Systems and Finite-time Processes (CRC Press, Boca Raton, Fl, 1995)
J. Qing, M.M. Bhatti, M.A. Abbas, M.M. Rashidi, M. El-Sayed Ali, Entropy 18, 123 (2016)
N. Dalir, M. Dehsara, S.S. Nourazar, Energy 79, 351 (2015)
Sajjad-ur Rehman, Rizwan-ul Haq, Z.H. Khan, C. Lee, J. Taiwan Inst. Chem. Eng. 63, 226 (2016)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Soomro, F.A., Rizwan-ul-Haq, Khan, Z.H. et al. Numerical study of entropy generation in MHD water-based carbon nanotubes along an inclined permeable surface. Eur. Phys. J. Plus 132, 412 (2017). https://doi.org/10.1140/epjp/i2017-11667-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2017-11667-5