International Scientific Journal


The non-linear Navier-Stokes equations governed on the nanofluid flow injected through a rotary porous disk in the presence of an external uniform vertical magnetic field can be changed to a system of non-linear partial differential equations by applying similar parameter. In this study, partial differential equations are analytically solved by the modified differential transform method, Pade differential transformation method to obtain self-similar functions of motion and temperature. A very good agreement is observed between the obtained results of Pade differential transformation method and those of previously published ones. Then it has become possible to do a comprehensive parametric analysis on the entropy generation in this case to demonstrate the effects of physical flow parameters such as magnetic interaction parameter, injection parameter, nanoparticle volume fraction, dimensionless temperature difference, rotational Brinkman number and the type of nanofluid on the problem.
PAPER REVISED: 2015-01-21
PAPER ACCEPTED: 2015-02-02
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Supplement 1, PAGES [S197 - S204]
  1. Karman, T. V., et al., On Laminar and Turbulent Friction (in German), ZAMM - Journal of Applied Mathematics and Mechanics, 1 (1921), 4, pp. 233-252
  2. Rashidi, M. M., Mohimanian Pour, S. A., Analytic Solution of Steady Three-Dimensional Problem of Condensation Film on Inclined Rotating Disk by Differential Transform Method, Mathematical Problems in Engineering, 2010 (2010), ID 613230
  3. 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, Computers & Fluids, 54 (2012), pp. 1-9
  4. Davidson, P. A., An Introduction to Magnetohydrodynamics, Cambridge University Press, Cambridge, UK, 2001
  5. Sutton, G. W., Sherman, A., Engineering Magnetohydrodynamics, McGraw-Hill, New York, USA, 1965
  6. Rashidi, M. M., Erfani, E., A New Analytical Study of MHD Stagnation-Point Flow in Porous Media with Heat Transfer, Computers & Fluids, 40 (2011), 1, pp. 172-178
  7. Dinarvand, S., et al., Series Solutions for Unsteady Laminar MHD Flow Near Forward Stagnation Point of an Impulsively Rotating and Translating Sphere in Presence of Buoyancy Forces, Non-linear Analysis: Real World Applications, 11 (2010), 2, pp. 1159-1169
  8. Dorch, S., Magnetohydrodynamics, Scholarpedia., 2 (2007), pp. 2295-2297
  9. Hayat, T., et al., Homotopy Solution for the Unsteady Three-Dimensional MHD Flow and Mass Transfer in a Porous Space, Commun Non-linear Sci Numer Simulat, 2015, in press
  10. 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, 2010 (2010), ID 491319
  11. Rashidi, M. M., et al., Awatif A-Hendi, Simultaneous Effects of Partial Slip and Thermal-Diffusion and Diffusion-Thermo on Steady MHD Convective Flow due to a Rotating Disk, Communications in Nonlinear Science and Numerical Simulations, 16 (2011), 11, pp. 4303-4317
  12. Rashidi, M. M., et al., Parametric Analysis of Entropy Generation in Magneto-Hemodynamic Flow in a Semi-Porous Channel with OHAM and DTM, Applied Bionics and Biomechanics, 11 (2014), 1, pp. 47-60
  13. Rashidi, M. M., Erfani, E., The Modified Differential Transform Method for Investigating Nano Boundary- Layers over Stretching Surfaces, International Journal of Numerical Methods for Heat & Fluid Flow, 21 (2011), 7, pp. 864-883
  14. Rashidi, M. M., et al., DTM-Pade Modeling of Natural Convective Boundary Layer Flow of a Nanofluid past a Vertical Surface, International Journal of Thermal and Environmental Engineering, 4 (2011), 1, pp. 13-24
  15. Bejan, A., in: Advances in Heat Transfer (Eds.: J. P. Hartnet, T. F. Irvine), Academic Press, New York, USA, 1982
  16. Bejan, A., A Study of Entropy Generation in Fundamental Convective Heat Transfer, Journal of Heat Transfer, 101 (1979), 4, pp. 718-725
  17. Butt, A. S., et al., Entropy Generation in the Blasius Flow under Thermal Radiation, Physica Scripta, 85 (2012), 3, 035008
  18. Rashidi, M. M., et al., Parametric Analysis of Entropy Generation in off-Centered Stagnation Flow Towards a Rotating Disc, Non-linear Engineering, 3 (2015), 1, pp. 27-41
  19. Brinkman, H. C., The Viscosity of Concentrated Suspensions and Solutions, Journal of Chemical Physics, 20 (1952), 4, pp. 571
  20. Oztop, H. F., Abu-Nada, E., Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids, International Journal of Heat and Fluid Flow, 29 (2008), 5, pp. 1326-1336
  21. Bejan, A., Entropy Generation Minimization: the Method of Thermodynamic Optimization of Finite-Size Systems and Finite-Time Processes, CRC Press, Boca Raton, Fla., USA, 1996
  22. Arikoglu, A., et al., Effect of Slip on Entropy Generation in a Single Rotating Disk in MHD Flow, Applied Energy, 85 (2008), 12, pp. 1225-1236
  23. Bejan, A., Entropy Generation through Heat and Fluid Flow, John Wiley and Sons, New York, USA, 1982
  24. Ismail, H. N. A., Abde Rabboh, A. A., A Restrictive Pade Approximation for the Solution of the Generalized Fisher and Burger-Fisher Equations, Applied Mathematics and Computation, 154 (2004), 1, pp. 203-210
  25. Rashidi, M. M., et al., Entropy Generation in Steady MHD Flow due to a Rotating Porous Disk in a Nanofluid, International Journal of Heat and Mass Transfer, 62 (2013), pp. 515-525

© 2021 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, 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