THERMAL SCIENCE

International Scientific Journal

Fazle Mabood

,

Waqar Ahamed Khan

,

Mohammad Mehdi Rashidi

THE NEW ANALYTICAL STUDY FOR BOUNDARY-LAYER SLIP FLOW AND HEAT TRANSFER OF NANOFLUID OVER A STRETCHING SHEET

ABSTRACT
In this article, the semi-analytical/numerical technique known as the homotopy analysis method (HAM) is employed to derive solutions for partial slip effects on the heat transfer of nanofluids over a stretching sheet. An accurate analytical solution is presented which depends on the Prandtl number, slip factor, Lewis number, Brownian motion number, and thermophoresis number. The variation of the reduced Nusselt and reduced Sherwood numbers with Brownian motion number, and thermophoresis number for various values Prandtl number, slip factor, Lewis number is presented in tabular and graphical forms. The results of the present article show the flow velocity and the surface shear stress on the stretching sheet and also reduced Nusselt number and reduced Sherwood number are strongly influenced by the slip parameter. It is found that hydrodynamic boundary layer decreases and thermal boundary layer increases with slip parameter. Comparison of the present analysis is made with the previously existing literature and an appreciable agreement in the values is observed for the limiting case.
KEYWORDS
nanofluid, velocity slip, stretching sheet, auxiliary parameter, HAM solution
PAPER SUBMITTED: 2014-04-24
PAPER REVISED: 2015-01-31
PAPER ACCEPTED: 2015-03-06
PUBLISHED ONLINE: 2015-04-04
DOI REFERENCE: https://doi.org/10.2298/TSCI140424035M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 1, PAGES [289 - 301]
REFERENCES
  1. Choi, S. U. S., Eastman, J. A., Enhancing Thermal Conductivity of Fluids with Nanoparticles, Mater. Sci., 231 (1995), pp. 99-105
  2. Khanafer, K., et al., Buoyancy Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids, Int. J. Heat Mass Transf., 46 (2013), 19, pp. 3639-3653
  3. Wong, K. V., Leon, O. D., Applications of Nanofluids: Current and Future, Adv. Mech. Eng., 2010 (2010), pp. 1-12
  4. Hwang, K. S., et al., Buoyancy Driven Heat Transfer of Water-Based Al2O3 Nanofluids in a Rectangular Cavity, Int. J. Heat Mass Transf., 50 (2007), pp. 4003-4010
  5. Mansur, S., Ishak, A., The Flow and Heat Transfer of a Nanofluid past a Stretching/Shrinking Sheet with a Convective Boundary Condition, Abst. Appl. Analy., 2013 (2013), Article ID 350647, 9 pages
  6. Sharma, R., et al., Partial Slip Flow and Heat Transfer over a Stretching Sheet in a Nanofluid, Math. Prob. Eng., 2013 (2013), Article ID 724547, 7 pages
  7. Wang, C. Y., Free Convection on a Vertical Stretching Surface, J. Appl. Math. Mech., 69 (1989), pp. 418-420
  8. Rashidi M. M., Erfani, E., The Modified Differential Transform Method for Investigating Nano Boundary-Layers over Stretching Surfaces, Int. J. Numer. Meth. Heat Fluid Flow 21 (2011), pp. 864-883 Sheikholeslami M., Effect of Variable Magnetic Field On Ferrofluid Flow and Heat Transfer Considering Constant Heat Flux Boundary Condition, The Eur. Phys. J. Plus., (2014) 129- 248
  9. Mabood F., et al., MHD Boundary Layer Flow and Heat Transfer of nanofluids over a Nonlinear Stretching Sheet: A Numerical Study, J. Magn. Magn. Mater., 374 (2015), pp. 569-576
  10. Sheikholeslami M., et al., KKL Correlation for Simulation of Nanofluid Flow and Heat Transfer in a Permeable Channel, Phy. Lett., A 378 (2014), pp. 3331-3339
  11. Sheikholeslami M., Ganji D. D., Ferrohydrodynamic and Magnetohydrodynamic Effects on Ferrofluid Flow and Convective Heat Transfer, Energy, 75 (2014), pp. 400-410
  12. Sheikholeslami M., et al., Ferrofluid Flow and Heat Transfer in a Semi Annulus Enclosure in the Presence of Magnetic Source Considering Thermal Radiation, J. Taiwan Inst. Chem. Eng., (2014), dx.doi.org/10.1016/j.jtice.2014.09.026.
  13. Sheikholeslami M., et al., Numerical Simulation of MHD Nanofluid Flow and Heat Transfer Considering Viscous Dissipation, Int. J. Heat Mass Transf., 79 (2014), pp. 212-222
  14. Sheikholeslami M., et al., Lattice Boltzmann Simulation of Magnetohydrodynamic Natural Convection Heat Transfer of Al2O3-Water Nanofluid in a Horizontal Cylindrical Enclosure with an Inner Triangular Cylinder, Int. J. Heat Mass Transf., 80 (2015), pp.16-25
  15. Sheikholeslami M., Ganji D. D., Entropy Generation of Nanofluid in Presence of Magnetic Field using Lattice Boltzmann method, Phys. A doi: dx.doi.org/10.1016/j.physa.2014.09.053
  16. Sheikholeslami M., Ganji D. D., Nanofluid Flow and Heat Transfer Between Parallel Plates Considering Brownian Motion using DTM, Comput. Methods Appl. Mech. Engrg., 283 (2015), pp. 651-663
  17. Nield, D. A., Kuznetsov, A. V., The Cheng-Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid, Int. J. Heat Mass Transf. 52 (2009), pp. 5792-5795
  18. Kuznetsov, A. V., Nield, D. A., Natural convective boundary layer flow of a nanofluid past a vertical plate, Int. J. Therm. Sci., 49 (2010), 2, pp. 243-247
  19. Khan, W. A., Pop, I., Boundary Layer Flow of a Nanofluid past a Stretching Sheet, Int. J. Heat Mass Transf., 53 (2010), (11-12), pp. 2477-2483
  20. Bachok, N., et al., Boundary Layer Flow of Nanofluids over a Moving Surface in a Flowing Fluid, Int. J. Therm Sci., 49 (2010), 9, pp. 1663-1668
  21. Rana, P., Bhargava, R., Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study, Commun. Nonlinear Sci. Numer. Simul., 17 (2012) 212-226
  22. Buongiorno, J., Convective Transport in Nanofluids, J. Heat Transf., 128 (2006), 3, pp. 240-250
  23. Abel, M. S., et al., MHD Flow and Heat Transfer with Effects of Buoyancy, Viscous and Joule Dissipation over a Nonlinear Vertical Stretching Porous Sheet with Partial Slip, Eng., 3 (2011), pp. 285-291
  24. Majumder, M., et al., Nanoscale Hydrodynamics: Enhanced Flow in Carbon Nanotubes, Nature, 438 (2005), 44, pp. 44
  25. Wang, C. Y., Flow due to a Stretching Boundary with Partial Slip-an Exact Solution of the Naviere-Stokes Equations, Chem. Eng. Sci., 57 (2002), 17, pp. 3745-3747
  26. Sahoo, B., Do, Y., Effects of Slip on Sheet-Driven Flow and Heat Transfer of a Third Grade Fluid past a Stretching Sheet, Int. Commun. Heat Mass Transf., 37 (2010), 8, pp. 1064-1071
  27. Noghrehabadi, A., et al., Effect of Partial Slip Boundary Condition on the Flow and Heat Transfer of Nanofluids past Stretching Sheet Prescribed Constant Wall Temperature, Int. J. Therm. Sci., 54 (2012), pp. 253-261
  28. Aly, E. H., et al., Analytical and Numerical Investigations for the Flow and Heat Transfer of Nanofluids over a Stretching Sheet with Partial Slip Boundary Condition, Appl. Math. Inf. Sci., 8 (2014), 4, pp. 1639-1645
  29. Rashidi M. M., et al., Investigation of Entropy Generation in MHD and Slip Flow over a Rotating Porous Disk with Variable Properties, Int. J. Heat Mass Transf., (2014), pp. 892-917
  30. Rashidi M. M., Erfani, E., Analytical Method for Solving Steady MHD Convective and Slip Flow due to a Rotating Disk with Viscous Dissipation and Ohmic Heating, Eng. Comput., 29 (2012), pp. 562-579
  31. Liao, S. J., Beyond perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton, 2003
  32. Rashidi, M. M., et al., Homotopy Simulation of Nanofluid Dynamics from a Nonlinearly Stretching Isothermal Permeable Sheet with Transpiration, Meccanica, 49 (2014), pp. 469-482
  33. Rashidi, M. M., Erfani, E., A new Analytical Study of MHD Stagnation-Point Flow in Porous Media with Heat Transfer, Comput. Fluids 40 (2011), pp. 172-178
  34. Hayat, T., Nawaz, M., Unsteady Stagnation Point Flow of Viscous Fluid Caused by an Impulsively Rotating Disk, J. Taiwan Inst. Chem. Eng., 42 (2011), 1, pp. 41-49
  35. Sajid, M., Hayat, T., Influence of Thermal Radiation on the Boundary Layer Flow due to an Exponentially Stretching Sheet, Int. Commun. Heat Mass Transf., 35 (2008), 3, pp. 347-356
  36. Nadeem, S., et al., MHD Stagnation Flow of a Micropolar Fluid Through a Porous Medium, Meccanica, 45 (2010), pp. 869-880
  37. Ziabakhsh, Z., et al., Analytical Solution of the Stagnation-Point Flow in a Porous Medium by using the Homotopy Analysis Method, J. Taiwan Inst. Chem. Eng., 40 (2009), pp. 91-97
  38. Rashidi, M. M., et al., Approximate Solutions for the Burger and Regularized Long Wave Equations by means of the Homotopy Analysis Method, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 3, pp. 708-717
  39. Rashidi M. M., Dinarvand, S., Purely Analytic Approximate Solutions for Steady Three-Dimensional Problem of Condensation Film on Inclined Rotating Disk by Homotopy Analysis Method, Nonlinear Anal Real World Appl., 10 (2009), pp. 2346-2356
  40. Mabood F., et al., Approximate Analytical Solution for Influnce of Heat Transfer on MHD Stagnation point Flow in Porous Medium, Comput. Fluids 100 (2014), pp. 72-78
  41. Rashidi, M. M., et al., Analytic Approximate Solutions for Steady Flow over a Rotating Disk in Porous Medium with Heat Transfer by Homotopy Analysis Method, Computer & Fluids, 54 (2012), pp.1-9
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The new analytical study for boundary-layer slip flow and heat transfer of nanofluid over a stretching sheet

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