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Chin. Phys. B, 2014, Vol. 23(4): 048203    DOI: 10.1088/1674-1056/23/4/048203

Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid

Sadegh Khalilia, Saeed Dinarvandb, Reza Hosseinib, Hossein Tamimc, Ioan Popd
a Young Researchers and Elite Club, Saveh Branch, Islamic Azad University, Saveh, Iran;
b Mechanical Engineering Department, Amirkabir University of Technology, 424 Hafez Avenue, Tehran, Iran;
c Department of Mechanical Engineering, Saveh Branch, Islamic Azad University, Saveh, Iran;
d Department of Mathematics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
Abstract  In this article, the unsteady magnetohydrodynamic (MHD) stagnation point flow and heat transfer of a nanofluid over a stretching/shrinking sheet is investigated numerically. The similarity solution is used to reduce the governing system of partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using the fourth-order Runge-Kutta method with shooting technique. The ambient fluid velocity, stretching/shrinking velocity of sheet, and the wall temperature are assumed to vary linearly with the distance from the stagnation point. To investigate the influence of various pertinent parameters, graphical results for the local Nusselt number, the skin friction coefficient, velocity profile, and temperature profile are presented for different values of the governing parameters for three types of nanoparticles, namely copper, alumina, and titania in the water-based fluid. It is found that the dual solution exists for the decelerating flow. Numerical results show that the extent of the dual solution domain increases with the increases of velocity ratio, magnetic parameter, and permeability parameter whereas it remains constant as the value of solid volume fraction of nanoparticles changes. Also, it is found that permeability parameter has a greater effect on the flow and heat transfer of a nanofluid than the magnetic parameter.
Keywords:  nanofluid      Navier-Stokes equations      MHD      dual solutions      porous media  
Received:  19 June 2013      Revised:  13 October 2013      Accepted manuscript online: 
PACS:  82.70.-y (Disperse systems; complex fluids) (Navier-Stokes equations)  
  52.30.Cv (Magnetohydrodynamics (including electron magnetohydrodynamics))  
  02.60.Cb (Numerical simulation; solution of equations)  
Corresponding Authors:  Saeed Dinarvand     E-mail:,
About author:  82.70.-y; 47.10.Ad; 52.30.Cv; 02.60.Cb

Cite this article: 

Sadegh Khalili, Saeed Dinarvand, Reza Hosseini, Hossein Tamim, Ioan Pop Unsteady MHD flow and heat transfer near stagnation point over a stretching/shrinking sheet in porous medium filled with a nanofluid 2014 Chin. Phys. B 23 048203

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