THERMAL SCIENCE

International Scientific Journal

Yanhai Lin

,

Liancun Zheng

,

Botong Li

,

Xinxin Zhang

MAGNETOHYDRODYNAMIC THIN FILM AND HEAT TRANSFER OF POWER LAW FLUIDS OVER AN UNSTEADY STRETCHING SHEET WITH VARIABLE THERMAL CONDUCTIVITY

ABSTRACT
This paper presents an investigation on the MHD thin film flow and heat transfer of a power law fluid over an unsteady stretching sheet. The effects of power law viscosity on a temperature field are taken into account with a modified Fourier’s law Proposed by Zheng by assuming that the temperature field is similar to the velocity field. The governing equations are reduced to a system of nonlinear ordinary differential equations. The numerical solutions are obtained by using the shooting method coupled with the Runge-Kutta method. The influence of the Hartmann number, the power law exponent, the unsteadiness parameter, the thickness parameter and the generalized Prandtl number on the velocity and temperature fields are presented graphically and analyzed. Moreover, the critical formula for parameters are derived which indicated that the magnetic field has no effect on the critical value.
KEYWORDS
power law fluids, thin film, stretching sheet, MHD, heat transfer
PAPER SUBMITTED: 2013-05-27
PAPER REVISED: 2014-03-07
PAPER ACCEPTED: 2014-03-08
PUBLISHED ONLINE: 2014-04-05
DOI REFERENCE: https://doi.org/10.2298/TSCI130527034L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 6, PAGES [1791 - 1800]
REFERENCES
  1. Wang, C.Y., Liquid Film on an Unsteady Stretching Surface, Quarterly of Applied Mathematics, 48 (1990), pp. 601-610
  2. Andersson, H.I., et al., Flow of a Power Law Fluid Film on an Unsteady Stretching Surface, Journal of Non-Newtonian Fluid Mechanics, 62 (1996), pp. 1-8
  3. Andersson, H.I., et al., Heat Transfer in a Liquid Film on an Unsteady Stretching Surface, International Journal of Heat and Mass Transfer, 43 (2000), pp. 69-74
  4. Liu, I.C., Andersson, H.I., Heat Transfer in a Liquid Film on an Unsteady Stretching Sheet, International Journal of Thermal Sciences, 47 (2008), pp. 766-772
  5. Chen, C.H., Heat Transfer in a Power Law Fluid Film over a Unsteady Stretching Sheet, Heat and Mass Transfer, 39 (2003), pp. 791-796
  6. Chen, C.H., Effect of Viscous Dissipation on Heat Transfer in a Non-Newtonian Liquid Film over an Unsteady Stretching Sheet, Journal of Non-Newtonian Fluid Mechanics, 135 (2006), pp. 128-135
  7. Chen, C.H., Marangoni Effects on Forced Convection of Power Law Liquids in a Thin Film over a Stretching Surface, Physics Letters A, 370 (2007), pp. 51-57
  8. Wang, C., Analytic Solutions for a Liquid Film on an Unsteady Stretching Surface, Heat Mass Transfer, 42 (2006), pp. 759-766
  9. Wang, C., Pop, I., Analysis of the Flow of a Power Law Fluid Film on an Unsteady Stretching Surface by Means of Homotopy Analysis Method, Journal of Non-Newtonian Fluid Mechanics, 138 (2006), pp. 161-172
  10. Huang, K.H., Tsai, R., Huang, C.H., Chebyshev Finite Difference Approach to Modeling the Thermoviscosity Effect in a Power Law Liquid Film on an Unsteady Stretching Surface, Journal of Non-Newtonian Fluid Mechanics, 165 (2010), pp. 1351-1356
  11. Vajravelu, K., Prasad, K.V., Ng, C.O., Unsteady Flow and Heat Transfer in a Thin Film of Ostwald-de Waele Liquid over a Stretching Surface, Communications in Nonlinear Science and Numerical Simulation, 17 (2012), pp. 4163-4173
  12. Dandapat, B.S., Santra, B., K., Andersson, H.I., Thermocapillarity in a Liquid Film on an Unsteady Stretching Surface, International Journal of Heat and Mass Transfer, 46 (2003), pp. 3009-3015
  13. Noor, N.F.M., Hashim, I., Thermocapillarity and Magnetic Field Effects in a Thin Liquid Film on an Unsteady Stretching Surface, International Journal of Heat and Mass Transfer, 53 (2010), pp. 2044-2051
  14. Dandapat, B.S., Santra, B., Vajrabelu, K., The Effects of Variable Fluid Properties and Thermocapillarity on the Flow of a Thin Film on an Unsteady Stretching Sheet, International Journal of Heat and Mass Transfer, 50 (2007), pp. 991-996
  15. Abel, M.S., Tawade J., Nandeppanavar, M.M., Effect of Non-uniform Heat Source on MHD Heat Transfer in a Liquid Film over an Unsteady Stretching Sheet, International Journal of Non-Linear Mechanics, 44 (2009), pp. 990-998
  16. Abel, M.S., Mahesha, N., Tawade, J., Heat Transfer in a Liquid Film over an Unsteady Stretching Surface with Viscous Dissipation in Presence of External Magnetic Field, Applied Mathematical Modelling, 33 (2009), pp. 3430-3441
  17. Nandeppanavar, M.M., et al., Heat Transfer in a Liquid Film over an Unsteady Stretching Sheet, International Journal of Heat and Mass Transfer, 55 (2012), pp. 1316-1324
  18. Aziz, R.C., Hashim, I., Abbasbandy, S., Effects of Thermocapillarity and Thermal Radiation on Flow and Heat Transfer in a Thin Liquid Film on an Unsteady Stretching Sheet, Mathematical Problems in Engineering, 127320 (2012), pp. 1-14
  19. Hussan, M., Mustafa, N., Asghar, S., Mass Transfer Analysis for Unsteady Thin Film Flow over Stretched Heated Plate, International Journal of Physical Sciences, 7(12) (2012), pp. 1903-1909
  20. Abbas, Z., et al., Unsteady Flow of a Second Grade Fluid Film over an Unsteady Stretching Sheet, Mathematical and Computer Modelling, 48 (2008), pp. 518-526
  21. Rashidi, M.M., Keimanesh, M., Using Differential Transform Method and Pade Approximant for Solving MHD Flow in a Laminar Liquid Film from a Horizontal Stretching Surface, Mathematical Problems in Engineering, 491319 (2010), pp. 1-14
  22. Aziz, R.C., Hashim, I., Liquid Film on Unsteady Stretching Sheet with General Surface Temperature and Viscous Dissipation, Chinese Physics Letter, 27(11) (2010), pp. 1-4
  23. Aziz, R.C., Hashim, I., Alomari, A.K., Thin Film Flow and Heat Transfer on an Unsteady Stretching Sheet with Internal Heating, Meccanica, 46 (2011), pp. 349-357
  24. Bachok, N., Ishak, A., Pop, I., Unsteady Boundary-layer Flow and Heat Transfer of a Nanofluid over a Permeable Stretching/Shrinking Sheet, International Journal of Heat and Mass Transfer, 55 (2012), pp. 2102-2109
  25. Xu, H., Pop, I., You, X.C., Flow and Heat Transfer in a Nano-liquid Film over an Unsteady Stretching Surface, International Journal of Heat and Mass Transfer, 60 (2013), pp. 646-652
  26. Abdel-Rahman, G.M., Effects of Variable Viscosity and Thermal Conductivity on Unsteady MHD Flow of Non-Newtonian Fluid over a Stretching Porous Sheet, Thermal Science, 17(4) (2013), pp. 1035-1047
  27. Khalal, L., Feddaoui, M., Mediouni, T., Numerical Study of Heat and Mass Transfer during Evaporation of a Turbulent Binary Liquid Film, Thermal Science, DOI:10.2298/TSCI120927025K
  28. Zheng, L.C., Zhang, X.X., Lu, C.Q., Heat Transfer for Power Law Non-Newtonian Fluids, Chinese Physics Letter, 23 (2006), pp. 3301-3304
  29. Zheng, L.C., Zhang, X.X., Ma, L.X., Fully Developed Convective Heat Transfer for Power Law Fluids in a Circular Tube, Chinese Physics Letter, 25(1) (2008), pp. 195-197
  30. Zheng, L.C., et al., Similarity and BPES Comparative Solutions to the Heat Transfer Equation for Incompressible Non-Newtonian Fluids: Case of Laminar Boundary Energy Equation, The European Physical Journal Applied Physics, 55 (2011), pp. 1-5
  31. Li, B.T., Zheng, L.C., Zhang, X.X., A New Model for Flow and Heat of a Power Law Fluid in a Pipe, Thermal Science, 15(2011), pp. 127-130
  32. Li, B.T., Zheng, L.C., Zhang, X.X., Heat Transfer in Pseudo-Plastic Non-Newtonian Fluids with Variable Thermal Conductivity, Energy Conversion and Management, 52(1) (2011), pp. 355-358
  33. Zheng, L.C., Lin, Y.H., Zhang, X.X., Marangoni Convection of Power Law Fluids Driven by Power Law Temperature Gradient, Journal of The Franklin Institute, 349 (2012), pp. 2585-2597
PDF VERSION [DOWNLOAD]
Magnetohydrodynamic thin film and heat transfer of power law fluids over an unsteady stretching sheet with variable thermal conductivity

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence