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The present work demonstrates the natural convection of two layers filled the space between inner circular cylinder located within wavy enclosure using finite element scheme. The right layer is filled with Ag nano-fluid while the left layer is filled saturated porous media and the same nanofluid. The governing equations of fluid flow and heat trans...
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... of the computational domain which has been considered in the present work is presented in Figure 1. It consists of a circular internal cylinder placed within wavy vertical walled enclosure. ...
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... that, for constant magnitude of Rayleigh number, increasing the nano-fluid volume fraction from φ=0 to φ=0.1, the local Nusselt number profile will increase also which leads to the enhancement of heat transfer characteristics. With respect to impact of Darcy's number on local Nusselt number profile as presented in Figure 10. Increasing Darcy number yields in enhancing the amount of heat transfer. ...
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... reason behind that is that when Darcy's number increases, the buoyancy force and natural convection increase and mode of heat transfer changes from conduction mode at low Darcy number into convection mode in the high Darcy number. Figure 11 depicts the impact of number of undulations on local Nusselt number profile at Ra=10 6 , Da=10 -3 . It is noted that the flat vertical wall (N=0) gives the highest local Nusselt's number profile. ...
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... impact of Rayleigh and Darcy's numbers and nanofluid volume fraction on mean of Nusselt number is obtainable in Figure 12. This indicates that increasing Rayleigh and Darcy number as well as the concentration of nano-fluid will augment the average Nusselt number, which leads to remarkable enhancements in the amount of heat transfer. ...
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... example when Rayleigh's number increases from [10 4 ] to [10 6 ], the average Nusselt number improved from Nu=5.97 to Nu=11.4, respectively at constant nanofluid volume fraction equal to φ=0.1 as illustrated in Figure 12 (a). With respect to the impact of Darcy number when the nanofluid volume fraction stayed constant, it is seen that Darcy number increases from Nu=8.56 at [Da=10 -5 ] into Nu=12.43 ...
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... respect to the impact of Darcy number when the nanofluid volume fraction stayed constant, it is seen that Darcy number increases from Nu=8.56 at [Da=10 -5 ] into Nu=12.43 at [Da=10 -1 ] as illustrated in Figure 12(b). in addition to that, when the Rayleigh number stays constant at Ra=10 4 and the nanofluid volume fraction increases from φ=0.05, into φ=0.05, ...
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... Nu will increase from Nu=5.1 into Nu=5.97. Figure 13 explains the impact of the vertical location of internal cylinder in the mean of Nusselt number. When internal cylinder moves from the center of wavy enclosure (δ=0) vertically downward (δ=-0.2), the mean of the Nusselt number profile will increase, which enhances the heat transfer. ...
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... in case where the cylinder moves in upper direction (from δ=0 to δ=+0.20), the Nusselt's number mean will reduce, which reduces the amount of heat transfer. Finally, the impact of the number of undulations on the Nusselt number's mean is discussed in Figure 14 for a different number of Rayleigh. At low number of Rayleigh magnitude (Ra=10 3 ) as in Figure 14 (a), it has been noted that the increase in the number of undulation increases the mean of Nusselt number that leads to augmenting the amount of heat transfer. ...
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... the impact of the number of undulations on the Nusselt number's mean is discussed in Figure 14 for a different number of Rayleigh. At low number of Rayleigh magnitude (Ra=10 3 ) as in Figure 14 (a), it has been noted that the increase in the number of undulation increases the mean of Nusselt number that leads to augmenting the amount of heat transfer. Where the best amount of heat transfer is for N=3 and minimum is at N=0. ...
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... the best amount of heat transfer is for N=3 and minimum is at N=0. This behavior is quite reverse when Rayleigh's number increases into 10 5 as in Figure 14 (b) where the best amount of heat transfer is for N=0 and lowest is at N=3. At very high magnitude of Rayleigh's number (10 7 ) as in Figure 14 (c), when the number of undulations is N=1 gives the best amount of heat transfer in comparison with a flat vertical wall and others undulations number. ...
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... behavior is quite reverse when Rayleigh's number increases into 10 5 as in Figure 14 (b) where the best amount of heat transfer is for N=0 and lowest is at N=3. At very high magnitude of Rayleigh's number (10 7 ) as in Figure 14 (c), when the number of undulations is N=1 gives the best amount of heat transfer in comparison with a flat vertical wall and others undulations number. In this way, it is recommended that for better amount of heat transfer to move the internal cylinder with radius (R=0.2) vertically downward (δ=-0.20) ...
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Citations
... Although the discussion on wavy wall is a typical issue in natural and forced convection [8][9][10][11][12][13][14][15] , the case on double-sided undulation on mixed convection still lacks attention. In 2013, 16 was the first to design two wavy surfaces in a filled vertical rectangular cavity for the purpose of examining the type of nanofluids, nanoparticle fraction and other parameters. ...
Two dimensional wavy walls rectangular cavity with inclined magnetohydrodynamic has been examined in mixed convection configurations. Triple fins arranged in the upwards ladder were filled within alumina nanoliquid in the cavity. Vertical sinusoidal walls were heated, and the other side was kept cold while both horizontal walls were kept adiabatic. All walls were motionless except the top cavity that was driven to the right. The diversified range of control parameter in Richardson number, Hartmann number, number of undulations, length of the cavity has been performed in this study. The analysis was simulated using finite element method by employing the governing equation formula, and the results were delineated in the form of streamlines, isotherms, heatlines, and comparisons on several relationships between the local velocity in the y -axis line of 0.6, local and average Nusselt number along the heated surface and dimensionless average temperature. The findings revealed that high concentration nanofluids boost the rate of heat transfer without the need to apply any magnetic field. Results found that the best heat mechanisms are natural convection with significant-high Richardson number as well as constructing two waves on the vertical walls in the cavity.
... The study shows that the number of mesh and its quality plays a significant role to predict the accurate results for the Nu in natural convection. Majdi, Abdulkadhim [41] presented a CFD study for a circular body immersed in a porous media. The results show that the increasing of Rayleigh number (Ra) and volume fraction of the nanofluid enhance the floe strength and heat transfer. ...
... Their studies revealed that the rate of heat transmission increased as the temperature rose. In an enclosure with two cold-wavy vertical sides and insulated bottom-to-top walls, Majdi et al. [18] analyzed numerically the convection heat transfer from a heated cylinder. A porous medium is present in the left side of the domain and a nanofluid is present inside the cavity. ...
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Laminar natural-convection flow and entropy production within a vertical porous annulus filled with nanofluids are examined. The vertical walls of the external and internal cylinders are maintained at different temperatures TH and TC (TH > TC), respectively. In contrast, the bottom and top of the annulus are adiabatic. Equations of continuity, momentum, energy, and entropy are resolved using the finite volume approach. Our FORTRAN-language programming code is well-validated with other works. The effects of porosity 0.2 ≤ ε ≤ 0.99, nanoparticles 0 ≤ ϕ ≤ 0.08, nanofluid types, Rayleigh 10³ ≤ Ra ≤ 10⁵ and Darcy 10⁻⁴ ≤ Da ≤ 10⁻¹ numbers on the flow, heat transfer, and entropy production are examined. We find that nanoparticles' inclusion improves heat transfer and increases total entropy production St. Da and ε affect flow structure, thermal field, and entropy generation. Besides, increasing Da and ε, St, the average Nusselt Nu¯in,out, and Bejan Be numbers increase. However, in the opposite case, St and Be decrease. For Ra = 10⁵, the best Nusssetl number is maximum for the Ag-water nanofluid, which increases up to 9.50%. Adding TiO2 nanoparticles, on the other hand, results in a lower Nu¯in,out value. The increase of the inner cylinder size reduces Nu¯in,out and St.
