Abstract.
The objective of the present article is to discuss the effects of viscous dissipation and Joule heating on entropy generation in a hydromagnetic boundary layer flow. Governing equations are reduced to self-similar equations via suitable similarity transformations. The expressions for the volumetric entropy generation rate and the Bejan number are also obtained using similarity transformations. The exact solution of the transformed energy equation is computed using the Laplace transform treatment. The obtained exact solutions are utilized to calculate the entropy generation number and the Bejan number. The impacts of Prandtl number, viscous dissipation parameter (Eckert number), magnetic parameter, mass suction and temperature difference parameter on entropy generation and Bejan number are discussed graphically. The increasing value of the temperature difference parameter reduces the entropy generation. The entropy generation increases with the increasing values of the magnetic parameter, the Eckert number, the mass suction parameter and the Prandtl number.
Similar content being viewed by others
References
A. Hussanan, M.Z. Salleh, I. Khan, S. Shafie, J. Mol. Liq. 229, 482 (2017)
S. Das, R.N. Jana, O.D. Makinde, Alex. Eng. J. 55, 253 (2016)
S. Aman, I. Khan, Z. Ismail, M.Z. Salleh, Neural Comput. Appl. (2016) DOI: 10.1007/s00521-016-2688-7
I. Khan, F. Ali, N. Mustapha, S. Shafie, Bound. Value Probl. 2015, 8 (2015)
L.J. Crane, Z. Angew. Math. Phys. 4, 645 (1970)
E.H. Aly, A. Ebaid, J. Comput. Theor. Nanosci. 10, 2591 (2013)
T. Fang, J. Zhang, S. Yao, Commun. Nonlinear Sci. Numer. Simul. 14, 3731 (2009)
T. Fang, J. Zhang, Commun. Nonlinear Sci. Numer. Simul. 14, 2853 (2009)
E.M.A. Elbashbeshy, T.G. Emam, M.S.A. Wahed, Heat Mass Transf. 50, 57 (2014)
M. Turkyilmazoglu, Int. J. Heat Mass Transfer 106, 127 (2017)
M. Turkyilmazoglu, J. Thermophys. Heat Transf. 25, 595 (2011)
Z.H. Khan, M. Qasim, N. Ishfaq, W.A. Khan, Commun. Theor. Phys. 67, 449 (2017)
M.Z. Salleh, R. Nazar, I. Pop, J. Taiwan Inst. Chem. Eng. 41, 651 (2010)
M. Qasim, S. Noreen, Eur. Phys. J. Plus 129, 7 (2014)
A.B. Parsa, M.M. Rashidi, O.A. Beg, S.M. Sadr, Comput. Biol. Med. 43, 1142 (2013)
M.M. Rashidi, E. Momoniat, B. Rostami, J. Appl. Math. 2012, 780415 (2012)
O.A. Beg, M.M. Rashidi, T.A. Beg, M. Asadi, J. Mech. Med. Biol. 12, 1250051 (2012)
A.J. Chamkha, A.M. Aly, Z.A.S. Raizah, Appl. Comput. Math. 6, 34 (2017)
K. Vajravelu, K.V. Prasad, Chiu-On Ng, H. Vaidya, Int. J. Appl. Comput. Math. (2016) DOI: 10.1007/s40819-016-0291-3
O.A. Beg, M.J. Uddin, M.M. Rashidi, N. Kavyani, J. Eng. Thermophys. 23, 79 (2014)
B. Ganga, S.M.Y. Ansari, N.V. Ganesh, A.K.A. Hakeem, J. Heat Mass Transf. 3, 153 (2016)
K.L. Hsiao, Appl. Therm. Eng. 98, 850 (2016)
A. Bejan, J. Heat Transf. 101, 718 (1979)
A. Bejan, Heat Fluid Flow 8, 258 (1987)
A.S. Butt, A. Ali, A. Mehmood, Int. J. Exergy 20, 318 (2016)
S. Das, S. Chakraborty, R.N. Jana, O.D. Makinde, Appl. Math. Mech. 36, 1593 (2015)
A.K.A. Hakeem, M. Govindaraju, B. Ganga, M. Kayalvizhi, Sci. Iran. 23, 1524 (2016)
M.M. Rashidi, N. Freidoonimehr, Int. J. Comput. Methods Eng. Sci. Mech. 15, 345 (2014)
O.D. Makinde, Int. J. Exergy 10, 142 (2012)
M.M. Rashidi, F. Mohammadi, S. Abbasbandy, M.S. Alhuthali, J. Appl. Fluid Mech. 8, 753 (2015)
S. Das, R.N. Jana, O.D. Makinde, J. Heat Mass Transf. Res. 2, 51 (2015)
A. Khan, I. Khan, F. Ali, S. Shafie, J. Porous Media 19, 175 (2016)
M. Govindaraju, B. Ganga, A.K.A. Hakeem, Front. Heat Mass Transf. 8, 1 (2017)
M. Mushtaq, S. Asghar, M.A. Hussain, Heat Mass Transf. 15, 137 (2011)
M.I. Afridi, M. Qasim, I. Khan, S. Shafie, A.S. Alshomrani, Entropy 19, 1 (2017)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Afridi, M.I., Qasim, M. & Shafie, S. Entropy generation in hydromagnetic boundary flow under the effects of frictional and Joule heating: Exact solutions. Eur. Phys. J. Plus 132, 404 (2017). https://doi.org/10.1140/epjp/i2017-11704-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/i2017-11704-5