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Computational Analysis of Three-Dimensional Unsteady Natural Convection and Entropy Generation in a Cubical Enclosure Filled with Water-Al2O3 Nanofluid

  • Research Article - Chemical Engineering
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Abstract

Effects of Rayleigh number, solid volume fraction and entropy generation on the natural convection heat transfer and fluid flow inside a three-dimensional cubical enclosure filled with water-Al2O3 nanofluid have been investigated numerically using the control volume finite difference method. The enclosure left sidewall is maintained at isothermal hot temperature, while the right one is maintained at isothermal cold temperature. The other enclosure walls are considered adiabatic. The second law of thermodynamics is applied to predict the nature of irreversibility in terms of entropy generation rate. Numerical computations are carried out for Rayleigh numbers from \({(10^{3} \leq {\rm Ra} \leq 10^{6})}\) , solid volume fraction from \({(0\% \leq \varphi\, \leq 20\%)}\) , while the Prandtl number of water is considered constant as (Pr = 6.2). Streamlines, isothermal lines, counters of local and total entropy generation and the variation of Bejan number, local and average Nusselt numbers are presented and discussed in detail. The results explain that the average Nusselt number increases when the solid volume fraction of nanoparticles and the Rayleigh number increase. Also, the Bejan and average Nusselt numbers have a reverse behavior to each other for the same range of Rayleigh number and solid volume fraction. In addition, the results show that the entropy generation rate due to heat transfer, friction and the total entropy generation increase as the solid volume fraction increases, while it increases highly when the Rayleigh number increases especially near the hot left sidewall.

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Abbreviations

Be:

Bejan number

C p :

Specific heat at constant pressure (J/kg K)

g :

Gravitational acceleration (m/s2)

k :

Thermal conductivity (W/m K)

l :

Enclosure width and height (m)

n :

Unit vector normal to the wall

N s :

Dimensionless local generated entropy

Nu:

Local Nusselt number

Pr:

Prandtl number

Ra:

Rayleigh number

\({S'_{{\rm gen}}}\) :

Generated entropy (kJ/kg K)

t :

Dimensionless time (t′·α/l 2)

T :

Dimensionless temperature \({[(T'-T'_{c})/(T'_{h}\,-\,T'_{c})]}\)

T′ c :

Cold temperature (K)

T′ h :

Hot temperature (K)

T o :

Bulk temperature \({[T_{o} = (T'_{c}+T'_{h}) / 2]}\) (K)

\({\vec {V}}\) :

Dimensionless velocity vector (\({\vec{{V}^{\prime}}\cdot l/\alpha )}\)

x, y, z :

Dimensionless Cartesian coordinates (x′/l,  y′/l,  z′/l)

α :

Thermal diffusivity (m2 /s)

β :

Thermal expansion coefficient (1 / K)

ρ :

Density (kg/m3)

μ :

Dynamic viscosity (kg/m s)

ν :

Kinematic viscosity (m2/s)

φ :

Nanoparticle or solid volume fraction

φ S :

Irreversibility coefficient

\({\vec{\psi}}\) :

Dimensionless vector potential (\({\vec{{\psi }^{\prime}}/\alpha )}\)

\({\vec {\omega }}\) :

Dimensionless vorticity (\({\vec{{\omega }^{\prime}}\,\alpha /l^{2})}\)

ΔT :

Dimensionless temperature difference

av:

Average

x, y, z :

Cartesian coordinates

fr:

Friction

f :

Fluid

m :

Mean or average

nf:

Nanofluid

s :

Solid

th:

Thermal

tot:

Total

\({^{{\prime}}}\) :

Dimensional variable

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Authors and Affiliations

  1. Unité de recherche de Métrologie et des Systèmes Energétiques, Ecole Nationale d’Ingénieurs, Université de Monastir, 5000, Monastir, Tunisia

    Lioua Kolsi, Mohamed Naceur Borjini & Habib Ben Aïssia

  2. Mechanical Engineering Department, College of Engineering, Babylon University, Babylon City, Hilla, Iraq

    Ahmed Kadhim Hussein

  3. Department of Thermofluids, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, UTM Skudai, 81310, Johor Bahru, Malaysia

    H. A. Mohammed

Authors
  1. Lioua Kolsi
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  2. Ahmed Kadhim Hussein
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  3. Mohamed Naceur Borjini
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  4. H. A. Mohammed
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  5. Habib Ben Aïssia
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Correspondence to Lioua Kolsi.

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Kolsi, L., Hussein, A.K., Borjini, M.N. et al. Computational Analysis of Three-Dimensional Unsteady Natural Convection and Entropy Generation in a Cubical Enclosure Filled with Water-Al2O3 Nanofluid. Arab J Sci Eng 39, 7483–7493 (2014). https://doi.org/10.1007/s13369-014-1341-y

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  • DOI: https://doi.org/10.1007/s13369-014-1341-y

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