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Natural convection of alumina-water nanofluid in a partially heated square cavity with isothermal blockage inside with uniform magnetic field and heat generation/absorption

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Abstract

Natural convection of \(\mathrm{Al}_2\mathrm{O}_3\)-water nanofluid in a square cavity with an isothermally heated square blockage and partially heated on the bottom wall is investigated numerically. The effect of uniform magnetic field and heat generation/absorption is also studied. The governing equations are discretized by the finite volume method using power law scheme and solved by semi-implicit method for pressure-linked equation algorithm. The study was first validated with published works and satisfactory agreement was obtained. The effect of thermophysical parameters such as Rayleigh number, Hartmann number, heat generation/absorption and solid volume fraction of nanoparticles on the flow and temperature fields is demonstrated. The results are presented graphically in the form of isotherms, streamlines, velocity and Nusselt number.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: All data included in this manuscript are available upon request by contacting the corresponding author.]

Abbreviations

B :

Blockage ratio

\(B_0\) :

Magnetic field strength

\({c_p}\) :

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

g :

Acceleration due to gravity, \(\mathrm{m}\ \mathrm{s}^{-2}\)

H :

Height of the cavity, m

Ha:

Hartmann number

k :

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

\({\mathrm{Nu}_\mathrm{avg}}\) :

Average Nusselt number

\({\mathrm{Nu}_\mathrm{loc}}\) :

Local Nusselt number

p :

Pressure \((\mathrm{kg}\ \mathrm{m}^{-1}\ \mathrm{s}^{-2})\)

P :

Dimensionless pressure

Pr:

Prandtl number

q :

Heat generation or absorption, \((\mathrm {W}\, \mathrm {m}^{-3}\,\mathrm {K}^{-1})\)

Q :

Dimensionless heat generation or absorption

\(\mathrm{Ra}\) :

Rayleigh number

t :

Dimensional time (s)

T :

Dimensional temperature (K)

u,v :

Velocity components \((\mathrm{m}\ \mathrm{s}^{-1})\)

U,V :

Dimensionless velocity components

x,y :

Dimensional coordinates (m)

X,Y :

Dimensionless coordinates

\(\alpha \) :

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

\(\beta \) :

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

\(\mu \) :

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

\(\nu \) :

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

\(\theta \) :

Dimensionless temperature

\(\rho \) :

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

\(\tau \) :

Dimensionless time

\(\varphi \) :

Volume fraction of the nanoparticles

\(\epsilon \) :

Dimensionless heat source length

\(\varPhi \) :

General transport variable

c:

Cold wall

h:

Hot wall

s:

Nanoparticles

f:

Fluid

nf:

Nanofluid

E,W,N,S:

Control volume nodes

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Acknowledgements

The author N. Suresh would like to acknowledge the Rajiv Gandhi National Fellowship (RGNF) (Grant No. F1-17.1/2016-17/RJNF-2015-17-SC-TAM-24774), India for their financial supports.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641046, India

    N. Suresh

  2. Department of Applied Mathematics, Bharathiar University, Coimbatore, 641046, India

    N. Nithyadevi

  3. Faculty of Engineering, Kuwait College of Science and Technology, 35004, Doha District, Kuwait

    A. J. Chamkha

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  1. N. Suresh
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  3. A. J. Chamkha
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Correspondence to N. Nithyadevi.

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Suresh, N., Nithyadevi, N. & Chamkha, A.J. Natural convection of alumina-water nanofluid in a partially heated square cavity with isothermal blockage inside with uniform magnetic field and heat generation/absorption. Eur. Phys. J. Plus 137, 400 (2022). https://doi.org/10.1140/epjp/s13360-022-02557-2

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