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Thermal Analysis of Steady Simulation of Free Convection from Concentric Elliptical Annuli of a Horizontal Arrangement

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Abstract

A steady simulation of the laminar free convection heat transfer is carried out between two cylinders of different cross sections. The inner cylinder is elliptical with different values of aspect ratio, while the outer cylinder is maintained circular. The numerical simulations are considered in two dimensions within the laminar regime. The computer software ANSYS-CFX is used to solve numerically the principal equations that describe the conservation of mass, momentum, and energy. These equations are considered for different values of the Rayleigh number (Ra = 103, 104, and 105), the Prandtl number (Pr) is chosen between 0.701 and 100, and the aspect ratio (E) varies from 0.1 to 1. The computational results show the influence of the studied parameters on the motion of fluid induced by the thermal buoyancy force. Also, the rate of heat transfer is evaluated. The contours of isotherm and streamline are depicted to analyze the temperature distribution and fluid motion, respectively. Furthermore, the heat transfer rate between the surface of the inner cylinder and fluid is evaluated according to the average value of the Nusselt number. It was found that the elliptical form of the inner cylinder has a tendency to boost the rate of heat transfer more than the circular form. Also, a low value of the Prandtl number creates some counter-rotating zones in the lower part of the computed domain.

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Abbreviations

a :

Big elliptical radius,(m)

b :

Small elliptical radius, (m)

E :

Aspect ratio, (−)

g :

Gravitational acceleration, (m.s−2)

L :

Distance between cylinders, (m)

n s :

Normal vector, ( −)

Nu :

Nusselt number, ( −)

P :

Dimensionless pressure, (− 

Pr :

Prandtl number, ( −)

Ra :

Rayleigh number, ( −)

RR :

Radii ratio, ( −)

T :

Temperature, (K

α :

Thermal diffusivity, (m2. s−1)

β :

Thermal expansion coefficient, (K−1)

ϕ :

Angular angle, (degree)

Ɵ :

Dimensionless temperature, ( −)

µ :

Dynamic viscosity, (kg. m−1.s−1)

ρ :

Density, (kg. m−3

c:

Cold surface

h:

Hot surface

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Authors and Affiliations

  1. Laborarory of Sciences and Marine Engineering (LSIM), Faculty of Mechanical Engineering, USPTO-MB, BP 1505, El -Menaouer, 31000, Oran, Algeria

    Houssem Laidoudi

  2. Department of Technology, University Centre of Naama, P.O. Box 66, 45000, Naama, Algeria

    Houari Ameur

  3. Department of Mechanical Engineering, Savadkooh Branch, Islamic Azad University, Savadkooh, Iran

    S. A. R. Sahebi

  4. Department of Planning, Design, and Technology of Architecture, Sapienza University of Rome, Rome, Italy

    S. Hoseinzadeh

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  1. Houssem Laidoudi
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  2. Houari Ameur
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  3. S. A. R. Sahebi
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  4. S. Hoseinzadeh
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Correspondence to Houari Ameur or S. Hoseinzadeh.

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Laidoudi, H., Ameur, H., Sahebi, S.A.R. et al. Thermal Analysis of Steady Simulation of Free Convection from Concentric Elliptical Annuli of a Horizontal Arrangement. Arab J Sci Eng 47, 15647–15660 (2022). https://doi.org/10.1007/s13369-022-06717-5

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