Impact of Wall Waviness on the Convection Patterns Inside a Horizontal Porous Annulus

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Jabrane Belabid
Keyword(s):  
Boussinesq Approximation ◽  
Darcy Law ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Convective Instabilities ◽  
Alternating Direction ◽  
Alternating Direction Implicit Scheme ◽  
Convection Patterns ◽  
The Mathematical Model ◽  
Hydrodynamics Equations

Abstract A numerical simulation of natural convection in a horizontal porous annulus with an internal wavy surface has been carried out. Governing equations include the heat equation and the hydrodynamics equations under Darcy law and Boussinesq approximation. The mathematical model formulated with the temperature-stream function is solved numerically using the finite difference method with the alternating direction implicit scheme. Results show that the heat transfer and the convective instability depend strongly on the waviness of the inner cylinder. Last, streamlines and isotherms are presented for different waviness parameters of the internal wall for better understanding of the influence of amplitude and number of undulations on the thermo-convective instabilities.

Influence of Gravitational Modulation on Natural Convection in a Horizontal Porous Annulus

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Jabrane Belabid ◽  
Karam Allali
Keyword(s):  
Mathematical Model ◽  
Natural Convection ◽  
Boussinesq Approximation ◽  
System Of Equations ◽  
Convective Stability ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
The Mathematical Model ◽  
Hydrodynamics Equations

The influence of gravitational modulation on natural convection in a horizontal porous annulus is investigated in this paper. The mathematical model describing the phenomenon consists of the heat equation coupled by the hydrodynamics equations under the Boussinesq approximation. The derived system of equations with the stream function–temperature formulation is obtained and solved numerically using the alternating direction implicit method. It is shown that the convective stability of the fluid can be gained for small amplitudes of the vibration, while it will be lost for large ones. It was also observed that increasing the frequency has a destabilizing effect.

Comparative Numerical Simulation of Natural Convection in a Porous Horizontal Cylindrical Annulus

2014 ◽  
Vol 670-671 ◽  
pp. 613-616 ◽  
Author(s):  
Jabrane Belabid ◽  
Abdelkhalek Cheddadi
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Saturated Porous Medium ◽  
Published Data ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Cylindrical Annulus ◽  
Alternating Direction ◽  
Concentric Cylinders ◽  
Good Agreement

This work presents a numerical study of the natural convection in a saturated porous medium bounded by two horizontal concentric cylinders. The governing equations (in the stream function and temperature formulation) were solved using the ADI (Alternating Direction Implicit) method and the Samarskii-Andreev scheme. A comparison between the two methods is conducted. In both cases, the results obtained for the heat transfer rate given by the Nusselt number are in a good agreement with the available published data.

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