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MHD Natural Convection Flow of CuO/Water Nanofluid in a Differentially Heated Hexagonal Enclosure with a Tilted Square Block

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Abstract

A numerical investigation has been performed to analyze the effect of magnetohydrodynamic natural convection flow in a differentially heated hexagonal enclosure having a tilted square block filled with CuO/water nanofluid. The horizontal walls of the cavity and tilted walls of the obstacle are uniformly heated of temperature \(\hbox {T}_\mathrm{h}\) while the inclined walls are kept at constant temperature \(\hbox {T}_\mathrm{c}\). The governing conservation equations of the physical problem have been solved using finite element method based on Galerkin weighted residual technique and obtained numerical results are presented graphically in terms of streamlines, isotherms, average Nusselt numbers, mid height horizontal and vertical velocities, average temperature and average velocity of nanofluid for a range of Rayleigh number (\(10^{3} \le { Ra} \le 10^{6}\)), Hartmann number (\(0 \le { Ha} \le 70\)) and solid volume fraction (\(0.1\% \le \phi \le 5\%\)) to show the flow structures and temperature characteristics. It is found that the flow fields and temperature distributions are influenced significantly for the effect of pertinent parameters. In addition, overall heat transfer rate enhanced due to higher values of Ra and \(\phi \) along with lower value of Ha. Comparisons of the present results with the previously published results on the basis of special cases are performed and found to be in good agreement.

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Abbreviations

\(C_p\) :

Specific heat at constant pressure (kJ kg\(^{-1}\) K\(^{-1}\))

g :

Gravitational acceleration (m s\(^{-2}\))

Ra :

Rayleigh number \(g\beta _f (T_h -T_c )L^{3}/\nu _f \alpha _f\)

L:

Length (m)

h :

Local heat transfer coefficient (W m\(^{-2}\) K\(^{-1}\))

k :

Thermal conductivity (W m\(^{-1}\) K\(^{-1}\))

Nu :

Nusselt number \(\textit{Nu} = hL/k_f\)

Pr :

Prandtl number \(\textit{Pr} = \nu _f /\alpha _f\)

p:

Dimensional pressure (N m\(^{-2}\))

P:

Dimensionless pressure

\(q_w\) :

Heat flux (W m\(^{-2}\))

T :

Dimensional temperature (K)

u, v :

Dimensional velocity components (m s\(^{-1}\))

U, V :

Dimensionless velocity components

x, y :

Dimensional coordinates (m)

X, Y :

Dimensionless coordinates

\(\alpha \) :

Fluid thermal diffusivity (m\(^{2}\) s\(^{-1}\))

\(\beta \) :

Thermal expansion coefficient (K\(^{-1}\))

\(\phi \) :

Volume fraction of nanoparticles

\(\theta \) :

Dimensionless temperature \(\theta = (T-T_c )/(T_h -T_c )\)

\(\mu \) :

Dynamic viscosity (N s m\(^{-2}\))

\(\nu \) :

Kinematic viscosity (m\(^{2}\) s\(^{-1}\))

\(\rho \) :

Density (kg m\(^{-3}\))

f :

Fluid

h :

Hot

c :

Cold

nf :

Nanofluid

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Acknowledgements

The authors wish to acknowledge the Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh and the Department of Mathematics, Jahangirnagar University, Savar, Dhaka-1342, Bangladesh for support and technical help throughout this research. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Department of Mathematics, Mawlana Bhashani Science and Technology University, Tangail, 1902, Bangladesh

    Mohammad Mokaddes Ali

  2. Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh

    Md. Abdul Alim

  3. Department of Mathematics, International University of Scholars, Dhaka, Bangladesh

    Rowsanara Akhter

  4. Department of Mathematics, Jahangirnagar University, Saver, Dhaka, 1342, Bangladesh

    Syed Sabbir Ahmed

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  1. Mohammad Mokaddes Ali
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Ali, M.M., Alim, M.A., Akhter, R. et al. MHD Natural Convection Flow of CuO/Water Nanofluid in a Differentially Heated Hexagonal Enclosure with a Tilted Square Block. Int. J. Appl. Comput. Math 3 (Suppl 1), 1047–1069 (2017). https://doi.org/10.1007/s40819-017-0400-y

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