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Numerical Simulation of Natural Convection of a Nanofluid in an Inclined Heated Enclosure Using Two-Phase Lattice Boltzmann Method: Accurate Effects of Thermophoresis and Brownian Forces.

Ahmed M, Eslamian M - Nanoscale Res Lett (2015)

Bottom Line: The effects of thermophoresis and Brownian forces which create a relative drift or slip velocity between the particles and the base fluid are included in the simulation.The effect of thermophoresis is considered using an accurate and quantitative formula proposed by the authors.Some of the existing results on natural convection are erroneous due to using wrong thermophoresis models or simply ignoring the effect.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Engineering, Assiut University, Assiut, 71516, Egypt.

ABSTRACT
Laminar natural convection in differentially heated (β = 0°, where β is the inclination angle), inclined (β = 30° and 60°), and bottom-heated (β = 90°) square enclosures filled with a nanofluid is investigated, using a two-phase lattice Boltzmann simulation approach. The effects of the inclination angle on Nu number and convection heat transfer coefficient are studied. The effects of thermophoresis and Brownian forces which create a relative drift or slip velocity between the particles and the base fluid are included in the simulation. The effect of thermophoresis is considered using an accurate and quantitative formula proposed by the authors. Some of the existing results on natural convection are erroneous due to using wrong thermophoresis models or simply ignoring the effect. Here we show that thermophoresis has a considerable effect on heat transfer augmentation in laminar natural convection. Our non-homogenous modeling approach shows that heat transfer in nanofluids is a function of the inclination angle and Ra number. It also reveals some details of flow behavior which cannot be captured by single-phase models. The minimum heat transfer rate is associated with β = 90° (bottom-heated) and the maximum heat transfer rate occurs in an inclination angle which varies with the Ra number.

No MeSH data available.


Related in: MedlinePlus

Isotherms at Ra = 104 and Ra = 106 at various inclination angles. Pr = 7.02 and ϕ = 0.05
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Fig3: Isotherms at Ra = 104 and Ra = 106 at various inclination angles. Pr = 7.02 and ϕ = 0.05

Mentions: We start presenting the results with investigation of the relative magnitude of the resultant gravitational, thermophoresis, Brownian, and drag forces applied on a 10-nm CuO particle at various inclination angles and Ra numbers. In all simulations, the direction of the gravitational acceleration remains downward; however, the components of each force are determined along the x and y directions, which may vary as β varies. Fig. 2 shows the resultant forces exerting on a 10-nm nanoparticle along the cavity, for various inclination angles, at a particle loading of 5 % and Ra = 106. The resultant gravitational forces remain unchanged, although their x and y components change. The Brownian force is a function of the fluid temperature and particle size and therefore does not change with a change in the inclination angle. Thermophoresis force significantly changes due to alteration in the shape of isotherms, and thus the local temperature gradients (shown in Fig. 3). The drag force is an induced force and is created as a result of the existence of a slip velocity on the particle surface. Therefore, it is inferred that the drag force changes as a result of a change in slip velocity, and the slip velocity is created by Brownian, gravitational, and thermophoresis forces. The smallest forces acting on a 10-nm particle are the gravitational (weight and buoyancy) and thermophoresis forces with an order of magnitude of 10−20 N. Brownian force is of the order of 10−15 N, and the induced drag force, which is the largest force, is of the order of 10−12 to 10−14 N. Since the drag force exerted on particles varies with inclination angle, one may expect a change in the heat transfer rate, as well, as the inclination angle changes.Fig. 2


Numerical Simulation of Natural Convection of a Nanofluid in an Inclined Heated Enclosure Using Two-Phase Lattice Boltzmann Method: Accurate Effects of Thermophoresis and Brownian Forces.

Ahmed M, Eslamian M - Nanoscale Res Lett (2015)

Isotherms at Ra = 104 and Ra = 106 at various inclination angles. Pr = 7.02 and ϕ = 0.05
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4508308&req=5

Fig3: Isotherms at Ra = 104 and Ra = 106 at various inclination angles. Pr = 7.02 and ϕ = 0.05
Mentions: We start presenting the results with investigation of the relative magnitude of the resultant gravitational, thermophoresis, Brownian, and drag forces applied on a 10-nm CuO particle at various inclination angles and Ra numbers. In all simulations, the direction of the gravitational acceleration remains downward; however, the components of each force are determined along the x and y directions, which may vary as β varies. Fig. 2 shows the resultant forces exerting on a 10-nm nanoparticle along the cavity, for various inclination angles, at a particle loading of 5 % and Ra = 106. The resultant gravitational forces remain unchanged, although their x and y components change. The Brownian force is a function of the fluid temperature and particle size and therefore does not change with a change in the inclination angle. Thermophoresis force significantly changes due to alteration in the shape of isotherms, and thus the local temperature gradients (shown in Fig. 3). The drag force is an induced force and is created as a result of the existence of a slip velocity on the particle surface. Therefore, it is inferred that the drag force changes as a result of a change in slip velocity, and the slip velocity is created by Brownian, gravitational, and thermophoresis forces. The smallest forces acting on a 10-nm particle are the gravitational (weight and buoyancy) and thermophoresis forces with an order of magnitude of 10−20 N. Brownian force is of the order of 10−15 N, and the induced drag force, which is the largest force, is of the order of 10−12 to 10−14 N. Since the drag force exerted on particles varies with inclination angle, one may expect a change in the heat transfer rate, as well, as the inclination angle changes.Fig. 2

Bottom Line: The effects of thermophoresis and Brownian forces which create a relative drift or slip velocity between the particles and the base fluid are included in the simulation.The effect of thermophoresis is considered using an accurate and quantitative formula proposed by the authors.Some of the existing results on natural convection are erroneous due to using wrong thermophoresis models or simply ignoring the effect.

View Article: PubMed Central - PubMed

Affiliation: Department of Mechanical Engineering, Assiut University, Assiut, 71516, Egypt.

ABSTRACT
Laminar natural convection in differentially heated (β = 0°, where β is the inclination angle), inclined (β = 30° and 60°), and bottom-heated (β = 90°) square enclosures filled with a nanofluid is investigated, using a two-phase lattice Boltzmann simulation approach. The effects of the inclination angle on Nu number and convection heat transfer coefficient are studied. The effects of thermophoresis and Brownian forces which create a relative drift or slip velocity between the particles and the base fluid are included in the simulation. The effect of thermophoresis is considered using an accurate and quantitative formula proposed by the authors. Some of the existing results on natural convection are erroneous due to using wrong thermophoresis models or simply ignoring the effect. Here we show that thermophoresis has a considerable effect on heat transfer augmentation in laminar natural convection. Our non-homogenous modeling approach shows that heat transfer in nanofluids is a function of the inclination angle and Ra number. It also reveals some details of flow behavior which cannot be captured by single-phase models. The minimum heat transfer rate is associated with β = 90° (bottom-heated) and the maximum heat transfer rate occurs in an inclination angle which varies with the Ra number.

No MeSH data available.


Related in: MedlinePlus