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

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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.

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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

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Correspondence to Syed Tauseef Mohyud-Din.

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Khan, U., Ahmed, N. & Mohyud-Din, S.T. Analysis of magnetohydrodynamic flow and heat transfer of Cu–water nanofluid between parallel plates for different shapes of nanoparticles. Neural Comput & Applic 29, 695–703 (2018). https://doi.org/10.1007/s00521-016-2596-x

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