Journal of the Korean Physical Society

Korean Physical Society (한국물리학회)
권호 표지
DOI QR코드

DOI QR Code

Entropy Generation Minimization in MHD Boundary Layer Flow over a Slendering Stretching Sheet in the Presence of Frictional and Joule Heating

  • Received : 2018.04.20
  • Accepted : 2018.05.28
  • Published : 2018.11.15
⟨ Previous Next ⟩

Abstract

In the present paper, we study the entropy analysis of boundary layer flow over a slender stretching sheet under the action of a non uniform magnetic field that is acting perpendicular to the flow direction. The effects of viscous dissipation and Joule heating are included in the energy equation. Using similarity transformation technique the momentum and thermal boundary layer equations to a system of nonlinear differential equations. Numerical solutions are obtained using the shooting and fourth-order Runge-Kutta method. The expressions for the entropy generation number and Bejan number are also obtained using a suggested similarity transformation. The main objective of this article is to investigate the effects of different governing parameters such as the magnetic parameter ($M^2$), Prandtl number (Pr), Eckert number (Ec), velocity index parameter (m), wall thickness parameter (${\alpha}$), temperature difference parameter (${\Omega}$), entropy generation number (Ns) and Bejan number (Be). All these effects are portrayed graphically and discussed in detail. The analysis reveals that entropy generation reduces with decreasing wall thickness parameter and increasing temperature difference between the stretching sheet and the fluid outside the boundary layer. The viscous and magnetic irreversibilities are dominant in the vicinity of the stretching surface.

Keywords

References

  1. L. J. Crane, ZAMP 21, 645 (1970).
  2. T. Fang and J. Zhang. Commun. Nonlinear Sci. Numer. Simulat. 14, 2853 (2009). https://doi.org/10.1016/j.cnsns.2008.10.005
  3. M. Z. Salleh, R. Nazar and I. Pop, J. Taiwan Inst. Chem. Eng. 41, 651 (2010). https://doi.org/10.1016/j.jtice.2010.01.013
  4. S. Yao, T. Fang and Y. Zhong, Commun. Nonlinear Sci. Numer. Simulat. 16, 752 (2011). https://doi.org/10.1016/j.cnsns.2010.05.028
  5. M. I. Khan, T. Hayat, M. I. Khan and A. Alsaedi, Int. J. Heat and Mass Trans. 113, 310 (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.082
  6. M. Farooq, M. I. Khan, M. Waqas, T. Hayat, A. Alsaedi and M. I. Khan, J. Mol. Liq. 221, 1097 (2016). https://doi.org/10.1016/j.molliq.2016.06.077
  7. M. I. Khan, M. Waqas, T. Hayat, M. I. Khan and A. Alsaedi, Int. J. Mech. Sci. 131, 426 (2017).
  8. T. Hayat, M. I. Khan, M. Waqas, A. Alsaedi and M. I. Khan, J. Mol. Liq. 223, 960 (2016). https://doi.org/10.1016/j.molliq.2016.09.019
  9. K. Vajravelu, App. Math. Comp. 124, 281 (2001). https://doi.org/10.1016/S0096-3003(00)00062-X
  10. A. Ishak, R. Nazar and I. Pop, Heat. Mass. Trans. 44, 921 (2008). https://doi.org/10.1007/s00231-007-0322-z
  11. K. L. Hsiao, Energy 59, 494 (2013). https://doi.org/10.1016/j.energy.2013.06.041
  12. E. M. A. Elbashbeshy, Arch. Mech. 53, 643 (2001).
  13. K. Bhattacharyya and K. Vajravelu, Commun. Nonlinear Sci. Numer. Simulat. 17, 2728 (2012). https://doi.org/10.1016/j.cnsns.2011.11.011
  14. Y. I. Seini and O. D. Makinde, Math. Prob. Eng. 2013, 1 (2013).
  15. B. Shen, L. Zheng and S. Chen, AIP Advances. 5, 107133 (2015). https://doi.org/10.1063/1.4934796
  16. S. Mukhopadhyay and K. Bhattacharyya, J. Egypt. Math. Soc. 20, 229 (2012). https://doi.org/10.1016/j.joems.2012.08.019
  17. D. Pal and P. Saha, Int. J. Mech. Sci. 119, 208 (2016). https://doi.org/10.1016/j.ijmecsci.2016.09.026
  18. L. C. Zheng, X. Jin, X. X. Zhang and J. H. Zhang, Acta Mech. Sin. 29, 667 (2013). https://doi.org/10.1007/s10409-013-0066-6
  19. C. Y. Wang, Acta Mech. 72, 261 (1988). https://doi.org/10.1007/BF01178312
  20. T. Fang, J. Zhang and Y. Zhong, Appl. Math. Comput. 218, 7241 (2012).
  21. L. Lee, Phys. Fluids 10, 822 (1967).
  22. M. M. Khader and A. M. Megahed, Eur. Phys. J. Plus. 128, 1 (2013). https://doi.org/10.1140/epjp/i2013-13001-9
  23. S. P. A. Devi and M. Prakash, J. Soc. Ind. Appl. Math. 18, 245 (2014).
  24. S. P. A. Devi and M. Prakash, J. Braz. Soc. Mech. Eng. 38, 423 (2015).
  25. S. P. A. Devi and M. Prakash, J. Nigerian. Math. Soc. 34, 318 (2015). https://doi.org/10.1016/j.jnnms.2015.07.002
  26. A. Bejan, Entropy generation through heat and fluid flow (Wiley, New York, 1982).
  27. O. D. Makinde, Mech. Research Commu. 33, 692 (2006). https://doi.org/10.1016/j.mechrescom.2005.06.010
  28. M. M. Rashidi, F. Mohammadi, S. Abbasbandy and M. S. Alhuthali, J. App. Fluid Mech. 8, 753 (2015). https://doi.org/10.18869/acadpub.jafm.67.223.22916
  29. I. Ullah, S. Shae and I. Khan, J. King Saud Uni. Sci. 29, 250 (2017). https://doi.org/10.1016/j.jksus.2016.05.003
  30. O. D. Makinde, A. S, Eegunjobi and M. S. Tshehla, Entropy 17, 7811 (2015). https://doi.org/10.3390/e17117811
  31. A. S. Butt and A. Ali, Eur. Phys. J. Plus. 128, 1 (2013). https://doi.org/10.1140/epjp/i2013-13001-9
  32. M. M. Rashidi, M. Ali, N. Freidoonimehr and F. Nazari, Energy 55, 497 (2013). https://doi.org/10.1016/j.energy.2013.01.036
  33. W. A. Khan, R. Culham and A. Aziz, ASME J. Heat Trans. 137, 1 (2015).
  34. A. Aziz, Entropy 8, 50 (2006). https://doi.org/10.3390/e8020050
  35. M. I. Khan, S. Ullah, T. Hayat, M. I. Khan and A. Alsaedi, J. Mol. Liq. 260, 279 (2018). https://doi.org/10.1016/j.molliq.2018.03.067
  36. M. I. Afridi and M. Qasim, In. J. App. Comput. Math. 16, 1 (2018).
  37. M. I Afridi, M. Qasim and S. Saleem, J. Nanofluids 7, 1 (2018). https://doi.org/10.1166/jon.2018.1437
  38. M. I. Afridi and M. Qasim, J. Nanofluids 7, 783 (2017).
  39. M. M. Khader and A. M. Megahed, App. App. Math. 2, 817 (2015).
  40. M. M. Khader and A. M. Megahed, J. App. Mech. Tech. Phys. 56, 241 (2015). https://doi.org/10.1134/S0021894415020091
  41. M. I. Afridi, M. Qasim and S. Shafie, Eur. Phys. J. Plus. 132, 2 (2017). https://doi.org/10.1140/epjp/i2017-11273-7

Cited by

  1. Entropy Generation Due to Heat and Mass Transfer in a Flow of Dissipative Elastic Fluid Through a Porous Medium vol.141, pp.2, 2018, https://doi.org/10.1115/1.4041951
  2. Numerical Investigation of Aligned Magnetic Flow Comprising Nanoliquid over a Radial Stretchable Surface with Cattaneo-Christov Heat Flux with Entropy Generation vol.11, pp.12, 2019, https://doi.org/10.3390/sym11121520
  3. Hall Effect on Radiative Casson Fluid Flow with Chemical Reaction on a Rotating Cone through Entropy Optimization vol.22, pp.4, 2020, https://doi.org/10.3390/e22040480
  4. Mixed convection flow over a stretching sheet of variable thickness: Analytical and numerical solutions of self‐similar equations vol.49, pp.6, 2020, https://doi.org/10.1002/htj.21813
  5. Entropy generation on convectively heated surface of casson fluid with viscous dissipation vol.95, pp.11, 2018, https://doi.org/10.1088/1402-4896/abbaf2
  6. Radiative MHD Casson Nanofluid Flow with Activation energy and chemical reaction over past nonlinearly stretching surface through Entropy generation vol.10, pp.None, 2018, https://doi.org/10.1038/s41598-020-61125-9