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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

Abstract

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.

Keywords

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

Abbreviations

\(\check{u}\)

Component of velocity in x direction

\(\check{v}\)

Component of velocity in y direction

\(\check{T}\)

Temperature of the fluid

p

Pressure

\({\rho_{\text{nf}}}\)

Density of nanofluid

\({\mu_{\text{nf}}}\)

Viscosity of the fluid

\({\alpha_{\text{nf}}}\)

Thermal diffusivity of the fluid

\({\sigma_{\text{nf}}}\)

Electrical conductivity of the nanofluid

\({k_{\text{f}}}\)

Conductivity of the base fluid

\({k_{\text{s}}}\)

Conductivity of the nanoparticles

\(\theta\)

Dimensionless temperature

\(\phi\)

Volume fraction of nanoparticles

\(m\)

Shape factor of nanoparticles

\({\rho_{\text{f}}}\)

Density of base fluid

\({\rho_{\text{s}}}\)

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

\({\sigma_{\text{s}}}\)

Electrical conductivity of the base fluid

\({\sigma_{\text{f}}}\)

Electrical conductivity of the nanoparticles

\(\eta\)

Dimensionless variable

\(F\)

Dimensionless velocity along the x direction

\(F^{\prime}\)

Dimensionless velocity along the y direction

\(\varTheta\)

Dimensionless temperature

\({C_{\text{f}}}\)

Skin friction coefficient

\(Nu\)

Nusselt number

Notes

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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