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Heat convection in micropolar nanofluid through porous medium-filled rectangular open enclosure: effect of an embedded heated object with different geometries

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Abstract

A numerical investigation has been performed to analyze heat convection through a micropolar nanofluid in an open rectangular enclosure filled with a porous medium. The enclosure is embedded with a heated object and having a heated non-planar bottom wall. Three different shapes of the embedded heated object, diamond-shaped, L-shaped, and triangular-shaped, are considered, and their effects are compared numerically. Successive over-relaxation method coupled with Gauss–Seidel iteration technique are employed in order to numerically tackle the nonlinear model momentum and energy equations. The outcomes are discussed in terms of streamlines, isotherms, and isolines of microrotation, averaged Nusselt number on the heated wall for different values of intricated parameters. The calibrated parameters Darcy number, vortex viscosity, Rayleigh number, and volume fraction of nanoparticles, respectively, are taken in the range 0.0001 ≤ Da ≤ 0.1, 0.5 ≤ K ≤ 5.0, 104 ≤ Ra ≤ 106, and 0 ≤ φ ≤ 0.04. It reveals that in the absence of heated object, the non-planarity of the wall lessens the heat transfer rate by 12.95% (when compared to the planar wall). The impact of the shape of the embedded heated object on the heat transfer rate is estimated and found an enhancement of 15.34%, 11.63%, 13.51% for diamond-shaped, L-shaped, and triangular-shaped objects, respectively. Increasing the Darcy number boosts the heat transfer rate while an upsurge in the vortex viscosity parameter lessens the heat transfer rate. The Nusselt number in the enclosure with and without a heated object (depending on the volume fraction of nanoparticles) is also computed numerically.

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Abbreviations

\(c_{\text{p}}\) :

Specific heat capacity (J kg−1 K−1)

Da:

Darcy number (–)

H :

Height of the enclosure (m)

j :

Micro-inertia density (m−2)

k :

Coefficient of thermal conductivity (W m−1 K−1)

K :

Dimensionless vortex viscosity (–)

N* :

Angular velocity (s−1)

N :

Dimensionless angular velocity vector normal to the x–y plane (–)

Nu:

Nusselt number (–)

Pr:

Prandtl number (–)

Ra:

Rayleigh number (–)

\(T^{*}\) :

Dimensional temperature (K)

\(u^{*}\), \(v^{*}\) :

Dimensional velocity component along x and y-axis (m s−1)

u, v :

Dimensionless velocity component along x and y-axis (–)

\(u_{\text{in}}\) :

Inlet velocity (m s−1)

\(x^{*} ,y^{*}\) :

Dimensional Cartesian coordinates (m)

x, y :

Dimensionless Cartesian coordinates (–)

\(\alpha\) :

Thermal diffusivity (m2 s−1)

\(\beta\) :

Coefficient of volumetric thermal expansion (K−1)

\(\xi ,\eta\) :

Coordinates of the computational domain in the dimensionless form (–)

\(\theta\) :

Dimensionless temperature (–)

κ :

Vortex viscosity (m−1 s−1)

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\rho\) :

Density (kg m−3)

\(\upsilon\) :

Kinematic viscosity (m2 s−1)

\(\varphi\) :

Volume fraction of nanoparticle (–)

\(\chi\) :

Material parameter (–)

\(\omega\) :

Dimensionless vorticity (–)

ave:

Average

f:

Base fluid

nf:

Nanofluid

p:

Particle, pressure

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Authors and Affiliations

  1. Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, 125001, India

    Endalkachew Getachew Ushachew & Mukesh Kumar Sharma

  2. Department of Mathematics, Wolkite University, Wolkite, Ethiopia

    Endalkachew Getachew Ushachew

  3. Faculty of Military Science, Stellenbosch University, Stellenbosch, South Africa

    O. D. Makinde

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  1. Endalkachew Getachew Ushachew
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Ushachew, E.G., Sharma, M.K. & Makinde, O.D. Heat convection in micropolar nanofluid through porous medium-filled rectangular open enclosure: effect of an embedded heated object with different geometries. J Therm Anal Calorim 146, 1865–1881 (2021). https://doi.org/10.1007/s10973-020-10118-x

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