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Review of Natural Convection Within Various Shapes of Enclosures

  • Review--Mechanical Engineering
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Abstract

The previous studies related to the thermal-driven flow within enclosures had been summarized in the present work. Various geometries of enclosures like square, rectangular and triangular had been summarized. Besides, enclosures filled with different fluids had been taken into consideration like traditional and nanofluids as well as porous medium, Newtonian and non-Newtonian fluids and multilayer systems. The governing equations of heat transfer and fluid flows had been presented for different cases. Different numerical models like homogeneous, inhomogeneous and thermal non-equilibrium model, Darcy, Darcy extended–Forchheimer model, etc., had been summarized. The influence of various dimensionless parameters like Rayleigh, Darcy, Bejan and Hartmann number, nanofluid loading, diverse thermal cases of the applied boundary conditions, angle of inclination, the number for undulations, the existence of inner body and many others parameters acting and influencing hardly up on both of the entropy generation and the heat transfer was illustrated. The present review illustrates the physical mechanism behind the buoyancy thermally driven flow in terms of figures of contours as well as the Nusselt numbers profiles.

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Abbreviations

C p :

Specified heat at a steady pressure (kJ/kg.K)

g :

Acceleration of gravity (m/s2)

k :

Thermal conductivity (W/m.K)

P :

Pressure without dimension

p :

Pressure (Pa)

Pr:

Prandtl number (νf/αf)

R :

Radiation parameter

Ra:

Rayleigh number \( (g \beta_{f} L^{3} \Delta T / \nu _{f} \alpha _{f} )\)

Ha:

Hartmann number

T :

Temperature (K)

T c :

The cold surface’s temperature (K)

\( \varepsilon \) :

Porosity

L :

Length and height of enclosure

Y O :

Distance between original and wavy wall

\( \Omega \) :

Vorticity

d p :

Nanoparticle diameter

K r :

Thermal conductivity ratio

\(\delta \) :

Position of the inner body moved vertically

\(\zeta \) :

Position of the inner body moved diagonally

B :

Length of heat source

D :

Position of heat source

Q :

Internal heat generation/absorption coefficient

\(\Delta T\) :

Temperature difference

T * :

The temperature without dimension (T−Tc/Th−Tc)

μ :

Dynamic viscosity (kg/ms)

ρ :

Density (kg/m3)

T h :

The hot surface’s temperature (K)

u :

The component of velocity in x-axis (m/s)

y :

Cartesian coordinate in vertical axis (m)

V :

The component of dimensionless velocity in y-axis

v :

The component of velocity in y-axis (m/s)

X :

Dimensionless coordinate in horizontal axis

x :

Cartesian coordinates in horizontal direction (m)

Y :

Dimensionless coordinate in vertical direction

A :

Aspect ratio

U :

The component of the dimensionless velocity in x-axis (m/s)

Nul :

Localized number of Nusselt the hot

N :

Undulation number

AR :

Aspect ratio

Nuave :

Average Nusselt number

F :

Frequency

LTNE:

Local thermal non-equilibrium model

\(\psi \) :

Dimensionless stream function

\(\Psi \) :

The function of dimensional stream (m2/s)

β :

Thermal expansion volumetric coefficient (K−1)

φ :

Nanofluid volume fraction

λ :

Amplitude

\(\phi\) :

Inclination angle

α :

The diffusivity of heat (m2/s)

ν :

Kinematic viscosity (μ /ρ)(m2s−1)

γ :

Phase deviation

\(\Gamma\) :

Basis function

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Acknowledgements

The authors would like to thank Babylon University (http://en.uobabylon.edu.iq/) for giving them the opportunity, time and scientific support for completing this work, and the first author is grateful to Al-Mustaqbal University College (https://mustaqbal-college.edu.iq/) for the financial support.

Funding

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Saudi Arabia, for funding this work through General Research Project under grant number GRP/31/42.

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Authors and Affiliations

  1. Mechanical Engineering Department, University of Babylon, Babylon Province, Iraq

    Ammar Abdulkadhim & Isam Mejbel Abed

  2. Air Conditioning and Refrigeration Techniques Engineering Department, Al-Mustaqbal University College, Babylon Province, Iraq

    Ammar Abdulkadhim

  3. Department of Physics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia

    Nejla Mahjoub Said

  4. LGM, Preparatory Institute for Engineering Studies, University of Monastir,, Monastir, Tunisia

    Nejla Mahjoub Said

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  1. Ammar Abdulkadhim
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  2. Isam Mejbel Abed
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  3. Nejla Mahjoub Said
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Correspondence to Nejla Mahjoub Said.

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Abdulkadhim, A., Abed, I.M. & Mahjoub Said, N. Review of Natural Convection Within Various Shapes of Enclosures. Arab J Sci Eng 46, 11543–11586 (2021). https://doi.org/10.1007/s13369-021-05952-6

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