Main Article Content

Davood Domiri GANJI Hossein YAHYAZADEH Arash YAHYAZADEH Mohammad Taghi KHALILI Mohsen JOUYA Payam JALILI


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 semianalytical 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.

Article Details

How to Cite
GANJI, Davood Domiri et al. EVALUATION OF NATURAL CONVECTION FLOW OF A NANOFLUID OVER A LINEARLY STRETCHING SHEET IN THE PRESENCE OF MAGNETIC FIELD BY THE DIFFERENTIAL TRANSFORMATION METHOD. Thermal Science, [S.l.], v. 16, n. 5, p. 1281-1287, dec. 2016. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/808>. Date accessed: 19 sep. 2017. doi: https://doi.org/10.2298/TSCI1205281Y.
Received 2016-12-28
Accepted 2016-12-30
Published 2016-12-30


[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

Most read articles by the same author(s)