International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: Editor-in-chief: Mahammad Nurmammadov
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International Journal of Partial Differential Equations and Applications. 2014, 2(6), 96-104
DOI: 10.12691/ijpdea-2-6-1
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Study of MHD Nanofluid Flow over a Horizontal Stretching Plate by Analytical Methods

A. Vahabzadeh1, M. Fakour1 and D. D. Ganji2

1Department of Mechanical Engineering, Sari Branch, Islamic Azad University, Sari, Iran

2Department of Mechanical Engineering, Mazandaran University, Babol, Iran

Pub. Date: December 11, 2014

Cite this paper:
A. Vahabzadeh, M. Fakour and D. D. Ganji. Study of MHD Nanofluid Flow over a Horizontal Stretching Plate by Analytical Methods. International Journal of Partial Differential Equations and Applications. 2014; 2(6):96-104. doi: 10.12691/ijpdea-2-6-1


The nonlinear two-dimensional forced-convection boundary-layer magneto hydrodynamic (MHD) incompressible flow of nanofluid over a horizontal stretching flat plate with variable magnetic field including the viscous dissipation effect is solved using the Variational iteration method (VIM), homotopy perturbation method (HPM) and Adomian decomposition method (ADM). In the paper, our results of the VIM, HPM and ADM are compared with the numerical method (Runge-Kutta fourth-rate). Also the influence of physical factors such as m, Eckert number (Ec) and the percentage of nanoparticles (ϕ) on the velocity and temperature profiles have been investigated. The comparisons of the results show that the HPM has the capability of solving the nonlinear boundary layer MHD flow of nanofluid with sufficient accuracy. The results show with increasing of the parameter m, velocity decreases but for temperature the reverse trend is observed and also with increasing of nanoparticles volume, the temperature value decreases and the velocity value increases. Also with increasing of Eckert number, the temperature value increases.

magneto hydrodynamic (MHD) flow of nanofluid Adomian decomposition method (ADM) Variational iteration method (VIM) Homotopy perturbation method (HPM)

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[1]  Fisher E. G., Extrusion of Plastics, Wiley, New York, 1976.
[2]  Altan, T., Gegel, S. O. H., Metal Forming Fundamentals and Applications, American Society of Metals, Metals Park, OH, 1979.
[3]  Tadmor, Z., Klein, I., Engineering Principles of Plasticating Extrusion, Polymer Science and Engineering Series, Van Nostrand Reinhold, New York, 1970.
[4]  J. H. He, Non-perturbative methods for strongly nonlinear problems [Ph.D. thesis], de-Verlagim Internet GmbH, Berlin, Germany, 2006.
[5]  J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141-1199, 2006.
[6]  J.-H. He, “Homotopy perturbation method for solving boundary value problems,” Physics Letters A, vol. 350, no. 1-2, pp. 87-88, 2006.
[7]  J. H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solutions& Fractals, vol. 26, no. 3, pp. 695-700, 2005.
[8]  J.-H. He, “Approximate analytical solution for seepage flow with fractional derivatives in porous media,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 57-68, 1998.
[9]  J. H. He, “Approximate solution of nonlinear differential equations with convolution product nonlinearities,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 69-73, 1998.
[10]  J. H. He, “Variational iteration method-a kind of non-linear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699-708, 1999.
[11]  J.-H.He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257-262, 1999.
[12]  J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37-43, 2000.
[13]  J.-H. He and X.-H.Wu, “Construction of solitary solution and compacton-like solution by variational iteration method,” Chaos, Solitons & Fractals, vol. 29, no. 1, pp. 108-113, 2006.
[14]  J.-H. He, “Periodic solutions and bifurcations of delay-differential equations,” Physics Letters A, vol. 347, no. 4-6, pp. 228-230, 2005.
[15]  J. H. He, “Limit cycle and bifurcation of nonlinear problems,” Chaos, Solitons & Fractals, vol. 26, no. 3, pp. 827-833, 2005.
[16]  A. Majidian, M. Fakour, A. Vahabzadeh, Analytical investigation of the Laminar Viscous Flow in a Semi-Porous Channel in the Presence of a Uniform Magnetic Field, International Journal of Partial Differential Equations and Applications, Vol. 2, No. 4, pp. 79-85, 2014.
[17]  A. Vahabzadeh, M. Fakour, D.D. Ganji, I.Rahimi Petroudi, Analytical accuracy of the one dimensional heat transfer in geometry with logarithmic various surfaces, Cent. Eur. J. Eng., vol. 4, pp. 341-355, 2014.
[18]  M. Fakour, A. Vahabzadeh, D.D. Ganji, Scrutiny of mixed convection flow of a nanofluid in a vertical channel, International journal of Case Studies in Thermal Engineering, (2014).
[19]  D. D. Ganji, M. Fakour, A. Vahabzadeh, S.H.H. Kachapi, Accuracy of VIM, HPM and ADM in Solving Nonlinear Equations for the Steady Three-Dimensional Flow of a Walter’s B Fluid in Vertical Channel, Walailak Journal of Science and Technology, Vol. 11, No 7, pp. 593-609, 2014.
[20]  J. Singh, P. K. Gupta, K. N. Rai, and CIMS-DST, “Homotopy perturbation method to space-time fractional solidification in a finite slab,” Applied Mathematical Modeling. Simulation and Computation for Engineering and Environmental Systems, vol. 35, no. 4, pp. 1937-1945, 2011.
[21]  S. O. Ajadi and M. Zuilino, “Approximate analytical solutions of reaction-diffusion equations with exponential source term: homotopy perturbation method (HPM),” Applied Mathematics Letters, vol. 24, no. 10, pp. 1634-1639, 2011.
[22]  D. Slota, “The application of the homotopy perturbation method to one-phase inverse Stefan problem,” International Communications in Heat and Mass Transfer, vol. 37, no. 6, pp. 587-592, 2010.
[23]  M M Rashidi, G Domairry and S Dinarvand. Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method Original Research Article. Communications in Nonlinear Science and Numerical Simulation, 14, pp. 708-717, 2009.
[24]  AA Soliman. A numerical simulation and explicit solutions of KdV-Burgers’ and Lax’s seventh-order KdV equations. Chaos, Solitons Fractals, vol. 29, pp. 294-302, 2006.
[25]  S Momani and S Abuasad. Application of He’s variational iteration method to Helmholtz equation. Chaos, Solitons Fractals, vol. 27, pp. 1119-1123, 2006.
[26]  M. Fakour, D.D. Ganji, M. Abbasi, Scrutiny of underdeveloped nanofluid MHD flow and heat conduction in a channel with porous walls, International journal of Case Studies in Thermal Engineering, (2014).
[27]  S. M. Aminossadati and B. Ghasemi, “Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure,” European Journal of Mechanics, B, vol. 28, no. 5, pp. 630-640, 2009.
[28]  T. C. Chiam, “Hydromagnetic flow over a surface stretching with a power-law velocity,” International Journal of Engineering Science, vol. 33, no. 3, pp. 429-435, 1995.
[29]  S. P. A. Devi and M. Thiyagarajan, “Steady nonlinear hydromagnetic flow and heat transfer over a stretching surface of variable temperature,” Heat and Mass Transfer, vol. 42, no. 8, pp. 671-677, 2006.