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Control of combined convection in a nanofluid-filled lid-driven closed space via rectangular bar in the presence of magnetic field

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Abstract

In the present study, a computational work has been done to see the heat transfer, fluid flow and temperature distribution in a lid-driven cavity due to an adiabatic rectangular bar with different dimensions and locations. The closed cavity is heated from the bottom wall and cooled from the top while, vertical walls are adiabatic and magnetic field is affected in horizontally. The governing partial differential equations are discretized via monolithic Galerkin finite element method of higher order. The resulting system of nonlinear algebraic equations are linearized at the discrete solution which have been computed utilizing the efficient geometric multigrid linear solver. The influences of various physical parameters on the flow, in specific ranges such as the nanoparticle volume fraction \(\phi = 0.04\), length and location of the insulated bar, Reynolds number \(1 \le Re \le 200\), Hartmann number \(0\le Ha \le 100\) and Richardson number, \(0\le Ri \le 10\) are investigated. It is found that the location of the bar is a good control parameter for heat and fluid flow inside the cavity. Vertical bar position becomes more effective on heat and fluid than that of horizontal bar position, and the presence of the bar becomes insignificant for the lower values of Richardson numbers.

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Abbreviations

\(d_{\rm s}\) :

Diameter of nanoparticle (nm)

k :

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

g :

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

Gr :

Grashof number, \(\beta \hbox {g}\Delta \hbox {TL}^3/\nu ^2_{\rm f}\)

\(C_{\rm p}\) :

Specific heat (\(\hbox {J\,kg}^{-1}\,\hbox {K}^{-1}\))

L :

Length of closed cavity (m)

Pr :

Prandtl number, \(\nu _{\rm f}/\alpha _{\rm f}\)

Ha :

Hartmann number, \(B_{0}L\sqrt{\dfrac{\sigma _{\rm f}}{\mu _{\rm f}}}\),

Ri :

Richardson number, \({Gr}/{Re}^2\)

Re :

Reynolds number, \(\frac{U_0 L}{\nu _{\rm f}}\)

Nu :

Nusselt number (local)

\(Nu_{{\rm avg}}\) :

Average Nusselt number

\(U_0\) :

Velocity of wall

x, y :

Dimensional space coordinates (m)

X, Y :

Dimensionless space coordinates

p :

Pressure (\(\hbox {N\,m}^{-2}\))

P :

Dimensionless pressure

T :

Temperature in dimensional form (K)

u, v :

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

U, V :

Dimensionless velocity components

\(T_{\rm h}\) :

Hot lower wall temperature (K)

\(T_{\rm c}\) :

Cold upper moving wall temperature (K)

\(\nu\) :

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

\(\mu\) :

Dynamic viscosity (\(\hbox {kg\,m}^{-1}\,\hbox {s}^{-1}\))

\(\beta\) :

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

\(\rho\) :

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

\(\alpha\) :

Thermal diffusivity (\(\hbox {m}^2\,\hbox {s}^{-1}\))

\(\theta\) :

Dimensionless temperature

\(\phi\) :

Volume fraction of the nanoparticles

c:

Cold

h:

Hot

f:

Fluid

p:

Nanoparticles

nf:

Nanofluid

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Acknowledgements

Calculations have been carried out on the LiDOng cluster at Technische Universität, Dortmund, Germany. The support by the LiDOng team at the ITMC at TU Dortmund is gratefully acknowledged. We would like to thank the LiDOng cluster team for their help and support. We also used FeatFlow (www.featflow.de) solver package and would like to acknowledge the support by the FeatFlow team. Second and last authors extend their appreciation to the International Scientific Partnership Program (ISPP) at King Saud University for funding this research work through ISPP#131.

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Authors and Affiliations

  1. Department of Mathematics, Capital University of Science and Technology, Islamabad, Pakistan

    Shafqat Hussain & Khalid Mehmood

  2. Institut für Angewandte Mathematik (LS III), Technische Universität, Dortmund, Germany

    Shafqat Hussain

  3. Department of Mechanical Engineering, Technology Faculty, Firat University, Elazig, Turkey

    Hakan F. Öztop

  4. Department of Mechanical Engineering, King Saud University, Riyadh, Saudi Arabia

    Mohamed E. Ali

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  1. Shafqat Hussain
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  2. Hakan F. Öztop
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  4. Mohamed E. Ali
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Correspondence to Shafqat Hussain.

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Hussain, S., Öztop, H.F., Mehmood, K. et al. Control of combined convection in a nanofluid-filled lid-driven closed space via rectangular bar in the presence of magnetic field. J Therm Anal Calorim 137, 289–306 (2019). https://doi.org/10.1007/s10973-018-7914-3

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