Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2013), Article ID 403210, 8 pages.

MHD Forced Convection Laminar Boundary Layer Flow of Alumina-Water Nanofluid over a Moving Permeable Flat Plate with Convective Surface Boundary Condition

S. M. AbdEl-Gaied and M. A. A. Hamad

Full-text: Open access

Abstract

This paper analyses a two-dimensional steady forced convection boundary layer viscous incompressible flow of alumina-water nanofluid over a moving permeable vertical flat plate under the effect of a magnetic field normal to the plate. Thermal convective surface boundary condition is applied. The nanofluid formulated in the present study is water dispersed with various volumetric fractions of the alumina (Al2O3) nanoparticles. The plate velocity and the free stream velocities are considered to be proportional to x n , while the magnetic field and suction velocities are taken to be proportional to ( x ) ( n - 1 ) / 2 . The similarity solution of the governing problem is obtained. Numerical studies are presented to show the effect of the nanoparticle volume fraction ϕ, the convective heat transfer parameter b , the power law exponent n , the wall velocity parameter A , and the suction parameter fw on the velocity, temperature, skin-friction coefficient, and Nusselt number.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 403210, 8 pages.

Dates
First available in Project Euclid: 7 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1399493728

Digital Object Identifier
doi:10.1155/2013/403210

Mathematical Reviews number (MathSciNet)
MR3103042

Citation

AbdEl-Gaied, S. M.; Hamad, M. A. A. MHD Forced Convection Laminar Boundary Layer Flow of Alumina-Water Nanofluid over a Moving Permeable Flat Plate with Convective Surface Boundary Condition. J. Appl. Math. 2013, Special Issue (2013), Article ID 403210, 8 pages. doi:10.1155/2013/403210. https://projecteuclid.org/euclid.jam/1399493728


Export citation

References

  • P. M. Congedo, S. Collura, and P. M. Congedo, “Modeling and analysis of natural convection heat transfer in nanofluids,” in Proceedings of the ASME Summer Heat Transfer Conference (HT '09), vol. 3, pp. 569–579, August 2009.
  • B. Ghasemi and S. M. Aminossadati, “Natural convection heat transfer in an inclined enclosure filled with a water-Cuo nanofluid,” Numerical Heat Transfer A, vol. 55, no. 8, pp. 807–823, 2009.
  • C. J. Ho, M. W. Chen, and Z. W. Li, “Effect on natural convection heat transfer of nanofluid in an enclosure due to uncertainties of viscosity and thermal conductivity,” in Proceedings of the ASME/JSME Thermal Engineering Summer Heat Transfer Conference (HT '07), vol. 1, pp. 833–841, July 2007.
  • C. J. Ho, M. W. Chen, and Z. W. Li, “Numerical simulation of natural convection of nanofluid in a square enclosure: effects due to uncertainties of viscosity and thermal conductivity,” International Journal of Heat and Mass Transfer, vol. 51, no. 17-18, pp. 4506–4516, 2008.
  • M. A. A. Hamad, I. Pop, and A. I. Md Ismail, “Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate,” Nonlinear Analysis: Real World Applications, vol. 12, no. 3, pp. 1338–1346, 2011.
  • M. A. A. Hamad and I. Pop, “Scaling transformations for boundary layer stagnation-point flow towards a heated permeable stretching sheet in a porous medium saturated with a nanofluid and heat absorption/generation effects,” Transport in Porous Media, vol. 87, no. 1, pp. 25–39, 2011.
  • M. A. A. Hamad, “Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field,” International Communications in Heat and Mass Transfer, vol. 38, no. 4, pp. 487–492, 2011.
  • E. Abu-Nada and A. J. Chamkha, “Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO-EG-Water nanofluid,” International Journal of Thermal Sciences, vol. 49, no. 12, pp. 2339–2352, 2010.
  • T. Teng, Y. Hung, T. Teng, H. Mo, and H. Hsu, “The effect of alumina/water nanofluid particle size on thermal conductivity,” Applied Thermal Engineering, vol. 30, no. 14-15, pp. 2213–2218, 2010.
  • C. J. Ho, W. K. Liu, Y. S. Chang, and C. C. Lin, “Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: an experimental study,” International Journal of Thermal Sciences, vol. 49, no. 8, pp. 1345–1353, 2010.
  • N. Bachok, A. Ishak, and I. Pop, “Boundary-layer flow of nanofluids over a moving surface in a flowing fluid,” International Journal of Thermal Sciences, vol. 49, no. 9, pp. 1663–1668, 2010.
  • F. M. Hady, F. S. Ibrahim, S. M. Abdel-Gaied, and M. R. Eid, “Effect of heat generation/absorption on natural convective boundary-layer flow from a vertical cone embedded in a porous medium filled with a non-Newtonian nanofluid,” International Communications in Heat and Mass Transfer, vol. 38, no. 10, pp. 1414–1420, 2011.
  • D. Lelea, “The performance evaluation of Al$_{2}$O$_{3}$/water na-nofluid flow and heat transfer in microchannel heat sink,” International Journal of Heat and Mass Transfer, vol. 54, no. 17-18, pp. 3891–3899, 2011.
  • S. K. Nandy and T. R. Mahapatra, “Effects of slip and heat generation/absorption on MHD stagnation flow of nanofluid past a stretching/shrinking surface with convective boundary conditions,” International Journal of Heat and Mass Transfer, vol. 64, pp. 1091–1100, 2013.
  • D. Pal, G. Mandal, and K. Vajravelu, “MHD convection-dissipation heat transfer over a non-linear stretching and shrinking sheets in nanofluids with thermal radiation,” International Journal of Heat and Mass Transfer, vol. 65, pp. 481–490, 2013.
  • A. M. Rohni, S. Ahmad, and I. Pop, “Boundary layer flow over a moving surface in a nanofluid beneath a uniform free stream,” International Journal of Numerical Methods for Heat and Fluid Flow, vol. 21, no. 7, pp. 828–846, 2011.
  • S. K. Das, S. U. S. Choi, W. Yu, and T. Pradeep, Nanofluids: Science and Technology, Wiley, Hoboken, NJ, USA, 2007.
  • X. Wang and A. S. Mujumdar, “Heat transfer characteristics of nanofluids: a review,” International Journal of Thermal Sciences, vol. 46, no. 1, pp. 1–19, 2007.
  • X. Wang and A. S. Mujumdar, “A review on nanofluids, part I: theoretical and numerical investigations,” Brazilian Journal of Chemical Engineering, vol. 25, no. 4, pp. 613–630, 2008.
  • X. Wang and A. S. Mujumdar, “A review on nanofluids, part II: experiments and applications,” Brazilian Journal of Chemical Engineering, vol. 25, no. 4, pp. 631–648, 2008.
  • S. Kakaç and A. Pramuanjaroenkij, “Review of convective heat transfer enhancement with nanofluids,” International Journal of Heat and Mass Transfer, vol. 52, no. 13-14, pp. 3187–3196, 2009.
  • M. E. Ali, “The effect of variable viscosity on mixed convection heat transfer along a vertical moving surface,” International Journal of Thermal Sciences, vol. 45, no. 1, pp. 60–69, 2006.
  • A. Ishak, R. Nazar, and I. Pop, “Boundary layer on a moving wall with suction and injection,” Chinese Physics Letters, vol. 24, no. 8, pp. 2274–2276, 2007.
  • E. Magyari, “The moving plate thermometer,” International Journal of Thermal Sciences, vol. 47, no. 11, pp. 1436–1441, 2008.
  • J. Hoernel, “On the similarity solutions for a steady MHD equation,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 7, pp. 1353–1360, 2008.
  • D. Pal and H. Mondal, “Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge,” Applied Mathematics and Computation, vol. 212, no. 1, pp. 194–208, 2008.
  • R. Kandasamy and I. Muhaimin, “Scaling transformation for the effect of temperature-dependent fluid viscosity with thermophoresis particle deposition on MHD-free convective heat and mass transfer over a porous stretching surface,” Transport in Porous Media, vol. 84, no. 2, pp. 549–568, 2010.
  • G. Herdricha, M. Auweter-Kurtza, M. Fertiga, A. Nawaza, and D. Petkowa, “MHD flow control for plasma technology applications,” Vacuum, vol. 80, pp. 1167–1173, 2006.
  • M. A. Seddeek, A. A. Afify, and M. A. Hanaya, “Similarity solutions for steady MHD Falkner-Skan flow and heat transfer over a wedge by considering the effect of variable viscosity and thermal conductivity,” Applications and Applied Mathematics, vol. 4, pp. 301–313, 2009.
  • M. S. Alam, M. M. Rahman, and M. A. Sattar, “Effects of variable suction and thermophoresis on steady MHD combined free-forced convective heat and mass transfer flow over a semi-infinite permeable inclined plate in the presence of thermal radiation,” International Journal of Thermal Sciences, vol. 47, no. 6, pp. 758–765, 2008.
  • O. Aydin and A. Kaya, “MHD mixed convection of a viscous dissipating fluid about a permeable vertical flat plate,” Applied Mathematical Modelling, vol. 33, no. 11, pp. 4086–4096, 2009.
  • M. M. Rahman and K. M. Salahuddin, “Study of hydromagnetic heat and mass transfer flow over an inclined heated surface with variable viscosity and electric conductivity,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 8, pp. 2073–2085, 2010.
  • A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1064–1068, 2009.
  • H. F. Oztop and E. Abu-Nada, “Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids,” International Journal of Heat and Fluid Flow, vol. 29, no. 5, pp. 1326–1336, 2008.
  • H. Schlichting and K. Gersten, Boundary Layer Theory, McGraw-Hill, NewYork, NY, USA, 8th edition, 2000.
  • W. M. Kays and M. E. Crawford, Convective Heat and Mass Transfer, McGraw Hill, New York, NY, USA, 4th edition, 2005.
  • 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.