Natural Convection of Silicone Oil-Based Al2O3 Nanofluid

in a Cylindrical Enclosure

BAHA TULU TANJU KAMİL KAHVECİ Mechanical Engineering Department

Trakya University Mechanical Engineering Department, Trakya University, 22180 Edirne

TURKEY kamilk@trakya.edu.tr http://kamilkahveci.trakya.edu.tr

Abstract: - Natural convection heat transfer of silicone oil-based Al2O3 nanofluid in a cylindrical enclosure used as a control unit in the subsea hydrocarbon and injection wells is investigated in this study. The governing equations obtained with the Boussinesq approximation are solved using Comsol Multiphysics finite element analysis and simulation software. Computational results are obtained for nanoparticle solid volume fraction in the range of 0%-8% and for Rayleigh number in the range of 10

5-10

7. The results show that temperature inside

the enclosure decreases considerably when nanoparticles are used in the cylindrical electronic control. The results also show that temperature inside the enclosure decreases substantially with an increase in the Rayleigh number.

Key-Words: - Natural convection, nanofluid, Al2O3, cylinder, Rayleigh number, Nusselt number

1 Introduction Natural convection heat transfer in enclosures have received considerable attention due to numerous potential engineering applications such as energy transfer in buildings, cooling of electronic devices and solar collectors. Conventional heat transfer fluids have been used as working fluids in most of previous studies [1-3]. Conventional heat transfer fluids have low thermal conductivities. This is the main drawback in enhancing the performance and the compactness of many engineering devices. Therefore, there is a strong need for advanced heat transfer fluids with substantially higher thermal conductivities. The way to eliminate this need is to use solid particles within a base fluid. Micron-sized particles have been used in the past, but sedimentation and clogging were persistent problems in fluids with these particles. The introduction of nanofluids has eliminated these drawbacks. The presence of the nanoparticles causes an anomalous increase in the effective thermal conductivity of the fluid. Keblinski et al. [4] investigated four possible mechanisms for this anomalous increase. These mechanisms are: Brownian motion of the nanoparticles, molecular level layering of the liquid at the liquid-particle interface, the nature of heat transfer in the nanoparticles, and nanoparticle clustering. They also showed that the Brownian motion is a negligible contributor, and that liquid layering around the nanoparticles could cause rapid conduction.

The objective of this study is to investigate natural convection heat transfer of silicone oil-based Al2O3 nanofluid in a cylindrical enclosure used as a control unit in subsea hydrocarbon and injection wells.

2 Problem Formulation The basic configuration used in the analysis is shown in Fig. 1. The cylindrical enclosure of height H and diameter D has two small cylinders of diameter d in it, which dissipates heat from its surfaces.

Figure 1. Geometry and the coordinate system.

Electronic Control Unit

Electronic Control Module Electronic Control Module

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The following dimensionless variables are used to nondimensionalize the governing equations:

where u*, v*, w* are the dimensional velocity components in the x*, y* and z* directions, respectively, p* is the dimensional pressure, T* is

the dimensional temperature, is the density, and is the thermal diffusivity. The reference temperature

may be taken as

without

losing the generality while keeping the dimensionless heat flux equal to one. The term q is the heat flux from the surfaces of the inner cylinders.

The flow is assumed to be Newtonian, steady, and incompressible. The buoyancy effects are incorporated in the formulation by invoking the Boussinesq approximation. The viscous dissipation terms and the thermal radiation are assumed to be negligible. With the foregoing assumptions, the dimensionless governing equations can be given as follows:

where is the kinematic viscosity of the fluid, g is

the gravitational acceleration and T is the

coefficient of thermal expansion. T* is the temperature difference. The Prandtl and Rayleigh numbers are defined as:

f

fPr

,

ff

*3f,T TLg

Ra

, (7)

Nondimensional governing equations are subjected to the following boundary conditions:

The following approach proposed by Yu and Choi [15] was used for the thermal conductivity prediction of the nanofluid:

3

fsfs

3fsfs

feff )1)(kk(k2k)1)(kk(2k2kk/k , (12)

where is the ratio of the nanolayer thickness to the original particle radius. Yu and Choi [5] compared

their results for =0.1 with existing experimental results from previous studies and obtained reasonably good agreement.

Nanofluid viscosity is generally estimated using existing relations for a two-phased mixture. The following Brinkman model [6] was used as the relation for the effective viscosity in this study.

5.2feff )1/( (13)

Other properties of nanofluid that are present in the governing equations can be defined by the following equations:

spfpeffp CC)1(C (14)

sTfTeffT )1( (15)

where

sfeff )1( (16)

3 Problem Solution The solutions of the governing equations are obtained by Comsol Multiphysics finite element analysis and simulation software for Rayleigh numbers from 10

5 to 10

7. Al2O3 was taken as

nanoparticles and the ratio of the nanolayer thickness to the original particle radius was taken at a fixed value of 0.1. Silicone oil was used as the base fluid due to its low electrical conductivity. The thermo-physical properties of the fluid and solid

phase are shown in Table 1. is selected as convergence criteria, where err is relative error based on the Euclidean norm:

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where N is the number of degrees of freedom, Ei is

the error and is the dependent variable and S is the scale factor. Table 1. Thermophysical properties of base fluid and nanoparticle.

Property Silicone Oil (AK1000)

Al2O3

(kg/m3) 970 3970

Cp (J/kgK) 1550 765

k (W/mK) 0.15 40

x107 (m2/s) 1.0 131.7

Tx106 (1/K) 920 24

4 Conclusion The effect of Rayleigh number and nanoparticle usage on the flow and heat transfer in the electronic control unite can be seen in Figs. 2-7. As can be observed from the figures, the fluid particles move upward along the surfaces of the inner cylinders due to the buoyancy forces as a result of heat flux on their surfaces. The fluid particles rise until they reach near the top surface where they turn towards the surface of the outer cylinder and the separation wall. Then, they turn downward near those walls.Final1y, the restriction imposed by the bottom wall forces the fluid particles to turn towards the hot walls.The flow paths are completed as the colder fluid particles are entrained to the ascending flows. The other half of the outer cylinder, where there are no inner cylinders, separation wall serves as a heater. Therefore, fluid particles move upwards by the effect of bouncy forces. Then, fluid particles move toward the surface of the outer cylinder because of the restriction imposed by the top wall. The fluid particles cooled by the cold outer surface move downwards and then move toward the surface of the separation wall because of the restriction imposed by the bottom wall. For low values of Rayleigh number, circulation intensity is weaker in the region with inner cylinders compared to the region without inner cylinders due to the higher viscous forces and weak buoyancy forces. However, when the Rayleigh number increases, circulation becomes stronger in the region with inner cylinders as the buoyancy forces becomes dominant. As can be seen in the figures, as the Rayleigh number increases, the temperature in the electronic control

module decreases substantially as a result of stronger circulation depending on the higher buoyancy forces. The nanoparticle usage increases energy transport from heated surfaces to the nearby fluids because of the increase of thermal conductivity coefficient. This creates a positive effect on the circulation intensity. The nanoparticle usage also increases fluid viscosity, as seen from Eq. (13). This leads to an increase at viscous forces. Because this effect is stronger than the effect caused by thermal conductivity increase, a decrease is seen in the circulation intensity due to the usage of nanoparticles in the base fluid. As stated before, nanoparticle usage increases the thermal conductivity coefficient of the fluid significantly. Consequently, even though nanoparticle usage decreases the circulation intensity, an increase is seen in the heat transfer rate and therefore a significant decrease at the temperatures inside the electronic control unit.

Fig. 2 Temperature and velocity fields for Ra=10

5

and =0%.

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Fig. 3 Temperature and velocity fields for Ra=10

5

and =8%.

Fig. 4 Temperature and velocity fields for Ra=10

6

and =0%.

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Fig. 5 Temperature and velocity fields for Ra=10

6

and =8%.

Fig. 6 Temperature and velocity fields for Ra=107

and =0%.

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Fig. 7 Temperature and velocity fields for Ra=10

7

and =8%. Acknowledgment The authors acknowledge the financial support received from Trakya University Scientific Research Project Unit.

References: [1] Eastman, J.A., Choi, S.U.S., Yu, W.,

Thompson, L.J., Anomalously Increased Effective Thermal Conductivity of Ethylene Glycol-Based Nanofluids Containing Copper Nanoparticles, Appl. Phys. Lett., Vol. 78, 2001, pp. 718–720.

[2] Choi, S.U.S., Zhang, Z.G., Yu, W., Lockwood, F.E., Grulke, E.A., Anomalous Thermal Conductivity Enhancement in Nanotube Suspension, Appl. Phys. Lett., Vol. 79, 2001, pp. 2252–2254.

[3] Xuan, Y., and Li, Q., Heat Transfer Enhancement of Nanofluids, Int. J. Heat & Fluid Flow, Vol. 21, 2000, pp. 158-164.

[4] Keblinski, P., Phillpot, S.R., Choi, S.U.S., Eastman, J.A., Mechanisms Of Heat Flow In Suspensions of Nano-Sized Particles (Nanofluids), Int. J. Heat Mass Tran., Vol.45, 2002, pp. 855–863.

[5] Yu, W., Choi, S.U.S., The Role of Interfacial Layers in the Enhanced Thermal Conductivity of Nanofluids: A Renovated Maxwell Model, J. Nanopart. Res., Vol. 5, 2003, pp. 167–171.

[6] Brinkman, H. C., The Viscosity of Concentrated Suspensions and Solutions, J. Chemical Physics, Vol. 20, 1952, pp. 571–581.

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