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International Journal of Engineering Mathematics
Volume 2014, Article ID 905158, 10 pages
http://dx.doi.org/10.1155/2014/905158
Research Article

Influence of Variable Thermal Conductivity on MHD Boundary Layer Slip Flow of Ethylene-Glycol Based Cu Nanofluids over a Stretching Sheet with Convective Boundary Condition

1Department of Mathematics, Sri Venkateswara University, Tirupati 517502, India
2Department of Mathematics, Yogananda Institute of Technology and Science, Tirupati 517520, India

Received 24 May 2014; Revised 2 October 2014; Accepted 2 October 2014; Published 6 November 2014

Academic Editor: J. A. Tenreiro Machado

Copyright © 2014 N. Bhaskar Reddy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Choi, “Enhancing thermal conductivity of fluids with nanoparticle,” in Developments and Applications of Non-Newtonian Flows, D. A. Siginer and P. H. Wang, Eds., vol. 66, pp. 99–105, ASME, New York, NY, USA, 1995. View at Google Scholar
  2. M. Prodanovi, S. Ryoo, and R. A. Rahmani, “Effects of magnetic field on the motion of multiphase fluids containing paramagnetic nanoparticles in porous media,” in Proceedings of the SPE Improved Oil Recovery Symposium, Tulsa, Okla, USA, 2010.
  3. C. T. Nguyen, G. Roy, C. Gauthier, and N. Galanis, “Heat transfer enhancement using Al2O3-water nanofluid for an electronic liquid cooling system,” Applied Thermal Engineering, vol. 27, no. 8-9, pp. 1501–1506, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Akbarinia, M. Abdolzadeh, and R. Laur, “Critical investigation of heat transfer enhancement using nanofluids in microchannels with slip and non-slip flow regimes,” Applied Thermal Engineering, vol. 31, no. 4, pp. 556–565, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. H. Masuda, A. Ebata, K. Teramae, and N. Hishinuma, “Alteration of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles,” Netsu Bussei, vol. 7, pp. 227–233, 1993. View at Google Scholar
  6. J. Buongiorno and W. Hu, “Nanofluid coolants for advanced nuclear power plants,” in Proceedings of the ICAPP, Paper no. 5705, Seoul, Republic of Korea, May 2005.
  7. J. Buongiorno, D. C. Venerus, N. Prabhat et al., “A benchmark study on the thermal conductivity of nanofluids,” Journal Applied Physics, vol. 106, no. 9, Article ID 094312, 2009. View at Publisher · View at Google Scholar
  8. S. K. Das, N. Putra, P. Thiesen, and W. Roetzel, “Temperature dependence of thermal conductivity enhancement for nanofluids,” Journal of Heat Transfer, vol. 125, no. 4, pp. 567–574, 2003. View at Publisher · View at Google Scholar · View at Scopus
  9. L. J. Crane, “Flow past a stretching plate,” Zeitschrift für angewandte Mathematik und Physik, vol. 21, no. 4, pp. 645–647, 1970. View at Publisher · View at Google Scholar
  10. B. K. Dutta, P. Roy, and A. S. Gupta, “Temperature field in flow over a stretching sheet with uniform heat flux,” International Communications in Heat and Mass Transfer, vol. 12, no. 1, pp. 89–94, 1985. View at Publisher · View at Google Scholar · View at Scopus
  11. C. K. Chen and M. I. Char, “Heat transfer of a continuous, stretching surface with suction or blowing,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 568–580, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. W. A. Khan and I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet,” International Journal of Heat and Mass Transfer, vol. 53, no. 11-12, pp. 2477–2483, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. M. Hassani, M. M. Tabar, H. Nemati, G. Domairry, and F. Noori, “An analytical solution for boundary layer flow of a nanofluid past a stretching sheet,” International Journal of Thermal Sciences, vol. 50, no. 11, pp. 2256–2263, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. P. Rana and R. Bhargava, “Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: a numerical study,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 212–226, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. A. Hamad and M. Ferdows, “Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: a Lie group analysis,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 132–140, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. M. Q. Al-Odat, R. A. Damesh, and T. A. Al-Azab, “Thermal boundary layer on an exponentially stretching continuous surface in the presence of magnetic field effect,” International Journal of Applied Mechanics and Engineering, vol. 11, no. 2, pp. 289–299, 2006. View at Google Scholar
  17. A. J. Chamkha and A. M. Aly, “MHD free convection flow of a nanofluid past a vertical plate in the presence of heat generation or absorption effects,” Chemical Engineering Communications, vol. 198, no. 3, pp. 425–441, 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. V. Aliakbar, A. Alizadeh-Pahlavan, and K. Sadeghy, “The influence of thermal radiation on MHD flow of Maxwellian fluids above stretching sheets,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 3, pp. 779–794, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. M. S. Khan, M. M. Alam, and M. Ferdows, “Effects of magnetic field on radiative flow of a nanofluid past a stretching sheet,” Procedia Engineering, vol. 56, pp. 316–322, 2013. View at Publisher · View at Google Scholar
  20. W. Ibrahim and B. Shankar, “MHD boundary layer flow and heat transfer of a nanofluid past a permeable stretching sheet with velocity, thermal and solutal slip boundary conditions,” Computers & Fluids, vol. 75, pp. 1–10, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. M. E. Sparrow and D. R. Cess, Radiation Heat Transfer, Brooks/Cole, Belmont, Calif, USA, 1970.
  22. N. M. Özisik, Radiative Transfer and Interaction with Conduction and Convection, John Wiley & Sons, New York, NY, USA, 1973.
  23. R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer, Hemisphere, New York, NY, USA, 2nd edition, 1992.
  24. J. R. Howell, “Radiative transfer in porous media,” in Handbook of Porous Media, K. Vafai, Ed., pp. 663–698, CRC Press, New York, NY, USA, 2000. View at Google Scholar
  25. H. S. Takhar, R. S. R. Gorla, and V. M. Soundalgekar, “Radiation effects on MHD free convection flow of a gas past a semi-infinite vertical plate,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 6, no. 2, pp. 77–83, 1996. View at Google Scholar · View at Scopus
  26. M. A. Hossain and H. S. Takhar, “Radiation effect on mixed convection along a vertical plate with uniform surface temperature,” Heat and Mass Transfer, vol. 31, no. 4, pp. 243–248, 1996. View at Publisher · View at Google Scholar · View at Scopus
  27. A. Yoshimura and R. K. Prud'homme, “Wall slip corrections for Couette and parallel disk viscometers,” Journal of Rheology, vol. 32, no. 1, pp. 53–67, 1988. View at Publisher · View at Google Scholar · View at Scopus
  28. V. P. Shidlovskiy, Introduction to the Dynamics of Rarefied Gases, American Elsevier Publishing, New York, NY, USA, 1967.
  29. S. Mansur and A. Ishak, “The magnetohydrodynamic boundary layer flow of a nanofluid past a stretching/shrinking sheet with slip boundary conditions,” Journal of Applied Mathematics, vol. 2014, Article ID 907152, 7 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  30. H. I. Andersson, “Slip flow past a stretching surface,” Acta Mechanica, vol. 158, no. 1-2, pp. 121–125, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  31. C. Y. Wang, “Flow due to a stretching boundary with partial slip—an exact solution of the Navier-Stokes equations,” Chemical Engineering Science, vol. 57, no. 17, pp. 3745–3747, 2002. View at Publisher · View at Google Scholar · View at Scopus
  32. C. Y. Wang, “Stagnation slip flow and heat transfer on a moving plate,” Chemical Engineering Science, vol. 61, no. 23, pp. 7668–7672, 2006. View at Publisher · View at Google Scholar · View at Scopus
  33. T. Fang, J. Zhang, and S. Yao, “Slip MHD viscous flow over a stretching sheet—an exact solution,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 11, pp. 3731–3737, 2009. View at Publisher · View at Google Scholar · View at Scopus
  34. T. Hayat, M. Qasim, and S. Mesloub, “MHD flow and heat transfer over permeable stretching sheet with slip conditions,” International Journal for Numerical Methods in Fluids, vol. 66, no. 8, pp. 963–975, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  35. A. Abu Bakar, M. K. A. W. Wan Zaimi, R. Hamid A, B. Bidin, and A. Ishak, “Boundary layer flow over a stretching sheet with a convective boundary condition and slip effect,” World Applied Sciences Journal, vol. 17, pp. 49–53, 2012. View at Google Scholar
  36. O. D. Makinde and A. Aziz, “Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition,” International Journal of Thermal Sciences, vol. 50, no. 7, pp. 1326–1332, 2011. View at Publisher · View at Google Scholar · View at Scopus
  37. O. D. Makinde and A. Aziz, “MHD mixed convection from a vertical plate embedded in a porous medium with a convective boundary condition,” International Journal of Thermal Sciences, vol. 49, no. 9, pp. 1813–1820, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. O. D. Makinde, “Similarity solution of hydromagnetic heat and mass transfer over a vertical plate with a convective surface boundary condition,” International Journal of Physical Sciences, vol. 5, no. 6, pp. 700–710, 2010. View at Google Scholar · View at Scopus
  39. O. D. Makinde, “On MHD heat and mass transfer over a moving vertical plate with a convective surface boundary condition,” Canadian Journal of Chemical Engineering, vol. 88, no. 6, pp. 983–990, 2010. View at Publisher · View at Google Scholar · View at Scopus
  40. S. V. Subhashini, N. Samuel, and I. Pop, “Double-diffusive convection from a permeable vertical surface under convective boundary condition,” International Communications in Heat and Mass Transfer, vol. 38, no. 9, pp. 1183–1188, 2011. View at Publisher · View at Google Scholar · View at Scopus
  41. A. Ishak, “Similarity solutions for flow and heat transfer over a permeable surface with convective boundary condition,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 837–842, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  42. T. Hayat, Z. Iqbal, M. Mustafa, and S. Obaidat, “Boundary layer flow of an Oldroyd-B fluid with convective boundary conditions,” Heat Transfer: Asian Research, vol. 40, no. 8, pp. 744–755, 2011. View at Publisher · View at Google Scholar · View at Scopus
  43. A. Alsaedi, M. Awais, and T. Hayat, “Effects of heat generation/absorption on stagnation point flow of nanofluid over a surface with convective boundary conditions,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 11, pp. 4210–4223, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  44. M. Khan, R. Ali, and A. Shahzad, “MHD Falkner-Skan flow with mixed convection and convective boundary conditions,” Walailak Journal of Science and Technology, vol. 10, no. 5, pp. 517–529, 2013. View at Google Scholar · View at Scopus
  45. C. Y. Wang, “Analysis of viscous flow due to a stretching sheet with surface slip and suction,” Nonlinear Analysis: Real World Applications, vol. 10, no. 1, pp. 375–380, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  46. T. Fang, J. Zhang, and S. Yao, “Slip MHD viscous flow over a stretching sheet—an exact solution,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 11, pp. 3731–3737, 2009. View at Publisher · View at Google Scholar · View at Scopus
  47. S. Mukhopadhyay and H. I. Andersson, “Effects of slip and heat transfer analysis of flow over an unsteady stretching surface,” Heat and Mass Transfer, vol. 45, no. 11, pp. 1447–1452, 2009. View at Publisher · View at Google Scholar · View at Scopus
  48. K. Bhattacharyya, S. Mukhopadhyay, and G. C. Layek, “Slip effects on boundary layer stagnation-point flow and heat transfer towards a shrinking sheet,” International Journal of Heat and Mass Transfer, vol. 54, no. 1–3, pp. 308–313, 2011. View at Publisher · View at Google Scholar · View at Scopus
  49. F. Aman, A. Ishak, and I. Pop, “Mixed convection boundary layer flow near stagnation-point on vertical surface with slip,” Applied Mathematics and Mechanics. English Edition, vol. 32, no. 12, pp. 1599–1606, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  50. T. Fang, S. Yao, J. Zhang, and A. Aziz, “Viscous flow over a shrinking sheet with a second order slip flow model,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 7, pp. 1831–1842, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  51. L. P. Jentoft, Y. Tenzer, D. Vogt, J. Liu, R. J. Wood, and R. D. Howe, “Flexible, stretchable tactile arrays from MEMS barometers,” in Proceedings of the 16th International Conference on Advanced Robotics (ICAR '13), November 2013. View at Publisher · View at Google Scholar · View at Scopus
  52. M. Arunachalam and N. R. Rajappa, “Forced convection in liquid metals with variable thermal conductivity and capacity,” Acta Mechanica, vol. 31, no. 1-2, pp. 25–31, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  53. T. C. Chiam, “Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet,” Acta Mechanica, vol. 129, no. 1-2, pp. 63–72, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  54. M. A. Seddeek and A. M. Salem, “Laminar mixed convection adjacent to vertical continuously stretching sheets with variable viscosity and variable thermal diffusivity,” Heat and Mass Transfer/Waerme- und Stoffuebertragung, vol. 41, no. 12, pp. 1048–1055, 2005. View at Publisher · View at Google Scholar · View at Scopus
  55. J. Maxwell, A Treatise on Electricity and Magnetism, Oxford University Press, Cambridge, UK, 2nd edition, 1904.
  56. H. C. Brinkman, “The viscosity of concentrated suspensions and solutions,” The Journal of Chemical Physics, vol. 20, pp. 571–581, 1952. View at Publisher · View at Google Scholar · View at Scopus
  57. V. R. Prasad, N. B. Reddy, R. Muthucumaraswamy, and B. Vasu, “Finite difference analysis of radiative free convection flow past an impulsively started vertical plate with variable heat and mass flux,” Journal of Applied Fluid Mechanics, vol. 4, no. 1, pp. 59–68, 2011. View at Google Scholar · View at Scopus