Neural Computing and Applications

, Volume 29, Issue 10, pp 695–703 | Cite as

Analysis of magnetohydrodynamic flow and heat transfer of Cu–water nanofluid between parallel plates for different shapes of nanoparticles

  • Umar Khan
  • Naveed Ahmed
  • Syed Tauseef Mohyud-Din
Original Article


The present study analyzes the heat transfer in the flow of copper–water nanofluids between parallel plates. For effective thermal conductivity of nanofluids, Hamilton and Crosser's model has been utilized to examine the flow by considering different shape factors. By employing the suitable similarity transformations, the equations governing the flow are transformed into a set of nonlinear ordinary differential equations. The resulting set of equations is solved numerically with the help of Runge–Kutta–Fehlberg numerical scheme. The graphical simulation presents the analysis of variations, in velocity and temperature profiles, for emerging parameters. A comprehensive discussion also accompanies the graphical results. Moreover, the effects of relevant parameters, on skin friction coefficient and Nusselt number, are highlighted graphically. It is noticed that the velocity field is an increasing function of all the parameters involved. Furthermore, the temperature of the fluid is maximum for the platelet-shaped particles followed by the cylinder- and brick-shaped particles.


Nanofluids MHD Numerical solution Hamilton and Crosser's model Nusselt number 



Component of velocity in x direction


Component of velocity in y direction


Temperature of the fluid




Density of nanofluid


Viscosity of the fluid


Thermal diffusivity of the fluid


Electrical conductivity of the nanofluid


Conductivity of the base fluid


Conductivity of the nanoparticles


Dimensionless temperature


Volume fraction of nanoparticles


Shape factor of nanoparticles


Density of base fluid


Density of nanoparticles

\({\left( {\rho {C_{\text{p}}}} \right)_{\text{f}}}\)

Heat capacity of base fluid

\({\left( {\rho {C_{\text{p}}}} \right)_{\text{s}}}\)

Heat capacity of nanoparticles


Electrical conductivity of the base fluid


Electrical conductivity of the nanoparticles


Dimensionless variable


Dimensionless velocity along the x direction


Dimensionless velocity along the y direction


Dimensionless temperature


Skin friction coefficient


Nusselt number


Compliance with ethical standards

Conflict of interest

The authors of this manuscript declare that there is no conflict of interest regarding the publication of this manuscript.


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Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  • Umar Khan
    • 1
  • Naveed Ahmed
    • 1
  • Syed Tauseef Mohyud-Din
    • 1
  1. 1.Department of Mathematics, Faculty of SciencesHITEC UniversityTaxila CanttPakistan

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