THERMAL SCIENCE

International Scientific Journal

Hossein Yahyazadeh

,

Davood Domairry Ganji

,

Arash Yahyazadeh

,

Mohammad Taghi Khalili

,

Payam Jalili

,

Mohsen Jouya

EVALUATION OF NATURAL CONVECTION FLOW OF A NANOFLUID OVER A LINEARLY STRETCHING SHEET IN THE PRESENCE OF MAGNETIC FIELD BY THE DIFFERENTIAL TRANSFORMATION METHOD

ABSTRACT
In the present study, the convective flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of a magnetic field are investigated. The governing partial differential equations with the auxiliary conditions are reduced to ordinary differential equations with the appropriate corresponding conditions via scaling transformations. The semi-analytical solutions of the resulting ordinary differential equations are obtained using differential transformation method coupled with Pade approximation. Comparison with published results is presented which reveals that the applied method is sufficiently accurate for engineering applications.
KEYWORDS
nanofluid, magnetic field, stretching sheet, natural convection, scaling transformations, differential transformation method
PAPER SUBMITTED: 2012-08-12
PAPER REVISED: 2012-09-01
PAPER ACCEPTED: 2012-09-07
DOI REFERENCE: https://doi.org/10.2298/TSCI1205281Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE Issue 5, PAGES [1281 - 1287]
REFERENCES
  1. Congedo, P. M., Collura, S., Congedo, P. M., Modeling and Analysis of Natural Convection Heat Transfer in Nanofluids, Proc. ASME Summer Heat Transfer Conf., 3, 2009, pp. 569-579
  2. Ghasemi, B., Aminossadati, S. M., Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid, Numer. Heat Transfer; Part A: Applications, 55 (2009), 8, pp. 807-823
  3. Ho, C. J., Chen, M. W., Li, Z. W., Numerical Simulation of Natural Convection of Nanofluid in a Square Enclosure: Effects Due to Uncertainties of Viscosity and Thermal Conductivity, Int. J. Heat Mss Transfer, 51 (2008), 17-18, pp. 4506-4516
  4. Ho, C. J., Chen, M. W., Li, Z. W., Effect of Natural Convection Heat Transfer of Nanofluid in an Enclosure Due to Uncertainties of Viscosity and Thermal Conductivity, Proc. ASME/JSME Thermal Engng. Summer Heat Transfer Conf. - HT, 1, 2007, pp. 833-841
  5. Zhou, J. K., Differential Transform and Its Application for Electrical Circuits. Huarjung University Press, Wuhan, China, 1986
  6. Jang, M. J., Chen, C. L., Liu, Y. C., Analysis of the Response of a Strongly Nonlinear Damped System using a Differential Transformation Technique, Applied Mathematics and Computation 88 (1997), 2-3, pp. 137-151
  7. Odibat, Z., Momani, S., Approximate Solutions for Boundary Value Problems of Time-Fractional Wave Equation, Applied Mathematics and Computation, 181 (2006), 1, pp. 1351-1358
  8. Kachapi, S. H., Ganji, D. D., Nonlinear Equations: Analytical Methods and Applications, Springer, 2012
  9. Ganji, D. D., A Semi-Analytical Technique for non-Linear Settling Particle Equation of Motion, Journal of Hydro-environment Research, doi:10.1016/j.jher.2012.04.002
  10. Khaki, M., Taeibi-Rahni, M., Ganji, D. D., Analytical Solution of Electro-Osmotic Flow in Rectangular Nano-Channels by Combined Sine Transform and MHPM, Journal of Electrostatics, 70 (2012), 5, pp. 451-456
  11. Oztop, H. F., Abu-Nada, E., Numerical Study of Natural Convection in partially Heated Rectangular Enclosures Filled with Nanofluids, Int. J. Heat Fluid Flow, 29 (2008), 5, pp. 1326-1336
  12. Aminossadati, S. M., Ghasemi, B., Natural Convection Cooling of a Localized Heat Source at the Bottom of a Nanofluid-Filled Enclosure, European J. Mech. B/Fluids, 28 (2009), 5, pp. 630-640
  13. Ibrahim, F. S., Mansour, M. A., Hamad, M. A. A., Lie-Group Analysis of Radiation and Magnetic Field Effects on Free Convection and Mass Transfer Flow past a Semiinfinite Vertical Flat Plate, Elect. J. of Diff. Eqns., 2005 (2005), 39, pp. 1-17
  14. Mukhopadhyay, S., Layek, G. C., Samad, S. A., Study of MHD Boundary Layer Flow over a Heated Stretching Sheet with Variable Viscosity, Int. J. Heat Mass Transfer, 48 (2005), 21-22, pp. 4460-4466
  15. Hamad, M. A. A., 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, 38 (2011), 4, pp. 487-492
  16. Rashidi, M. M., Laraqi, N., Sadri, S. M., A Novel Analytical Solution of Mixed Convection about an Inclined Flat Plate Embedded in a Porous Medium Using the DTM-Pade, International Journal of Thermal Sciences, 49 (2010), 12, pp. 2405-2412
  17. He, J.-H., Homotopy Perturbation Method with an Auxiliary Term, Abstract and Applied Analysis, 2012 (2012), DOI:10.1155/2012/857612 , pp. 1-7
  18. Ganji, D. D., Rahimi, M., Rahgoshay, M., Determining the Fin Efficiency of Convective Straight Fins with Temperature Dependent Thermal Conductivity by Using Homotopy Perturbation Method, International Journal of Numerical Methods for Heat & Fluid Flow, 22 (2012) pp. 263-272
  19. Hedayati, et al., An Analytical Study on a Model Describing Heat Conduction in Rectangular Radial Fin with Temperature-Dependent Thermal Conductivity, International Journal of Thermophysics, 33 (2012), 6, pp. 1042-1054
  20. Sheikholeslami, M., Ganji. D. D., Ashorynejad, H. R., et al., Analytical Investigation of Jeffery-Hamel Flow with high Magnetic Field and Nanoparticle by Adomian Decomposition Method, Applied Mathematics and Mechanics, 33 (2012), pp. 25-36
PDF VERSION [DOWNLOAD]
Evaluation of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field by the differential transformation method

© 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