numerical investigation of natural convective heat transfer and entropy

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NUMERICAL INVESTIGATION OF NATURAL CONVECTIVE HEAT TRANSFER AND ENTROPY GENERATION INSIDE A CLOSED CAVITY USING NANOFLUID Amina Benabderrahmane1*, Abdelwafi Messadi2 1

Faculty of Technology, Djilali Liabes University Sidi bel abbes 2 Faculty of Technology, Yahia Fares University Medea [email protected]

Abstract. Turbulent natural convection and entropy generation in a closed cavity saturated by a nanofluid is studied numerically. The horizontal walls are considered isothermal at different temperatures, however the others are adiabatic. The Navier-Stokes and energy equations are solved using the FLUENT computational fluid dynamics (CFD) software based on the finite volumes method (FVM). The boundaries of the domain are assumed to be impermeable and the fluid within the cavity is a water-based nanofluid having alumina nanoparticles for different volume fraction. The Boussinesq approximation is applicable. The results show that with using nanofluids the Nusselt number increases with increasing Rayleigh number contrary to the entropy. Keywords: Cavity, Nanofluid, Natural convection, Entropy generation, Heat transfer enhancement.

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Introduction

Natural convection flow in enclosures has many thermal engineering applications such as in double-glazed windows, solar collectors, cooling devices for electronic instruments, gas-filled cavities around nuclear reactor cores and building insulation. In most natural convection studies, the fluid within the cavity has low conductivity coefficient that limits heat transfer rate. For this reason researchers attention has been paid to the use of nanofluid; which is defined as the addition of a small solid particles of high thermal conductivity to common base or working fluids. Bouhalleb and Abbassi [1] reported a numerical investigation of the effect of CuO-water nanofluid on heat transfer and fluid flow in the case of natural convection in inclined cavity. The results show that the addition of CuO solid particle in water leads to enhancement of heat transfer. The average Nusselt number is influenced by the variation of aspect ratio and inclination angle. Hakan and Abu-Nada [2] performed a numerical study of natural convection in a partially heated enclosure filled with nanofluid. This study is done for nanofluids Al2O3, CuO and TiO2. The results show that the mean Nusselt number increases with increasing the solid volume fraction of nanoparticles for whole range of Rayleigh numbers. They have noticed that heat transfer at low aspect ratios is more pronounced than at high aspect ratios. Ghasemi and Aminossadati [3] presented a numerical study of heat transfer by natural convection in inclined enclosure filled with CuO-water nanofluid. The results show that the heat transfer depends on the Rayleigh number, the angle of inclination and the solid volume fraction of the nanoparticles and they show that adding nanoparticles into pure water improves its heat transfer performance. Arifin et al. [4] have studied a two dimensional laminar Marangoni boundary layer flow in a water based-nanofluid containing different types

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of nanoparticles: Cu, Al2O3 and TiO2. It was found that nanoparticles with low thermal conductivity, TiO 2, have better enhancement of heat transfer compared to Al2O3 and Cu. For a particular nanoparticle, when the solid volume fraction increases, the interface velocity and the heat transfer rate decreases. Natural convection in enclosure filled with Al2O3- water nanofluid has been investigated by Nasrin et al. [5]. Their results show that the heat transfer is most effective when increasing the concentration of solid particle and Prandtl number as well as decreasing aspect ratios. In recent decades, many scientists have been working on the second law of thermodynamics. Entropy has become a term used by biologists, mathematicians, sociologists, economists, architects, and especially by physicists. Entropy is an extensive quantity which quantitatively measures the degree of disorder of a system. It is defined by its variation during a reversible transformation and is equal to the amount of heat supplied to the system divided by the temperature of the same system. This notion first appeared in the field of studies of thermodynamics developed during the nineteenth century by Sadi Carnot, Rudolf Clausius, Ludwig Boltzmann and Josiah Willard Gibbs. It is a state function introduced in the context of the second principle of thermodynamics and concerns the estimation of heat, energy or order loss in a closed system. Contemporary thermodynamic analyzes of energy systems use a parameter called the entropy generation (or production) rate to measure irreversibilities related to heat transfer, friction, and other non-idealities in systems. Therefore, the minimization of entropy generation has become an option of great interest in thermo fluid processes. In recent years, the problem of entropy generation in nanofluid filled cavities was the interest of many researches; Oliveski et al. [6] investigated numerically the entropy generation in rectangular cavities that were submitted to the natural convection process due to the temperature difference between the vertical walls. Armaghani et al. [7, 8] studied the entropy generation and natural heat transfer of a nanofluid in Cshaped and baffled L-shaped cavities, respectively. Ismael et al. [9] investigated the entropy generation due to conjugate free convection in a square domain. They suggested a novel gauge for the evaluation of the thermal performance. Selimefendigil and Oztop [10] studied the natural convection and entropy generation of nanofluid filled cavity having different shaped obstacles with magnetic field effect. The current work presents a three dimensional numerical study of the impact of alumina/ water nanofluid on natural convection heat transfer and entropy generation inside a closed cavity under turbulent flow.

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Model description

The model is of three-dimensional natural convection inside a closed cavity of length (L=1m), high (h=0.75m) and width (l=0.5m) filled with alumina-water nanofluid. The horizontal walls are considered isothermal where the bottom side (T h) is heater than the top side (Tc); however the other walls are adiabatic. The model description and boundary conditions are shown in Fig.1.

Fig. 1 Cavity model description

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Governing equation

The conservation equations of mass, momentum, and energy for a three dimensional turbulent natural convection and steady incompressible flow with Boussinesq approximation were considered, the dimensionless governing equations are written as follow:



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Continuity equation:

U V W   0 X Y Z  Momentum equation :

U

(1)

  2U  2U  2U U V W P V W   Pr     X 2 Y 2 Z 2 X Y Z X 

  

   Ra Pr   2 2 2  W  W  W  U V W P U V W   Pr     X 2 Y 2 Z 2  X Y Z W   U

  2V  2V  2V U V W P V W   Pr    2 X Y Z Y Y 2 Z 2  X



U

(2)

Energy equation:

  2     2  2 V W     X 2 Y 2 Z 2 X Y Z 

Where α is the thermal diffusivity defined as:  

  

(3)

 C p

Ra and Pr are Rayleigh and Prandtl number respectively.

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Grid check independence study

To check the grid independency of the solution, the calculations were repeated for several grid sizes. The average Nusselt number for three grid sizes of 75x50x25, 100x75x50 and 150x120x90 are obtained for various values of Rayleigh number. The results are summarized in Table.1. As seen, the maximum deviation was less than 4% which means that the size grid has no influence on the results but only simulation takes time for converged, for this reason the grid size 75x50x25 was used in this study. Table.1. Grid size independency

Ra

70x50x25

Nu 100x75x50

150x120x90

 max

107 2x107 108 3x108

71.820 98.129 112.201 139.962

74.120 99.112 113.107 141.005

73.317 100.407 111.822 140.125

3.103 2.27 1.13 0.73

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Numerical procedures

The numerical simulation is performed using the finite volume method (FVM). The k-Ԑ turbulent model was used. Pressure based solver is used to solve the pressure based equation; Body force weighted scheme is used for pressure equation; for other equations of convection-diffusion, first order upwind is adopted. SIMPLE algorithm is used for pressure-velocity coupling.

6 Nanofluid properties The effective thermo-physical properties of the nanofluids are estimated by different formulas available in the literature. The formulas chosen for the thermo-physical properties of the nanofluid in this work are as follows:

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Density: Xuan and Roetzel [11]

nf  1     f   p

(4)

Specific heat: Pack and Cho [12]

C pnf  1    C p f  C p p

(5)

Thermal conductivity: Maxwell [13]

nf   f

 p  2 f  2   f   p   p  2 f     f   p 

(6)

Dynamic viscosity: Brinkman [14]

nf 

f

1   

(7)

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Thermal expansion coefficient: Kim et al. [15]

nf   f 1   

(8)

Thermo-physical properties of Al2O3 and H2O are presented in table.2 Table.2. Thermal properties of base fluid and nanoparticles used

Density (Kg/m3) Specific heat (J/kg K) Thermal conductivity (W/mK) Dynamic viscosity (Pa s) Thermal expansion coefficient (K-1)

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Base fluid (water) 988.2 4182 0.64 10-4 2.1 x 10-4

nanoparticles (alumina) 3880 773 36 6.3 x 10-6

Entropy generation rate

Due to conversion of thermal energy to other energy forms, like mechanical work in heat engine, and also spontaneous and unavoidable dissipation of all other energy forms to thermal energy via so called heat generation, additional issues and often confusions arise. The entropy generation, which is a measure of the imperfections of a system, is defined as a combination of the entropy produced by the viscous effects of the fluid and that produced by the thermal effects, as expressed by the following relation: S  Sheat  S friction

(9)

The 3D entropy balance equation in the absence of mass transfer and chemical reactions can be expressed in the Cartesian coordinates, by the following correlation:   2   2   2    U 2  V 2  W 2   V U 2  W V 2  U W 2   S               2                       x   y   z     x   y   z    x y   y z   z x     

(10)

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where:

T  

      L Th  Tc  

2

(11)

α is the thermal diffusivity and T is the mean temperature ( T 

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Th  Tc ) 2

Results and discussion

8.1. Effect of nanofluid on temperature distribution analysis Fig.2 presents the temperatures distribution of the adiabatic wall of the cavity with and without nanofluid, it can be seen clearly that the cavity’s walls temperature reduces with using 1% of Al 2O3 nanoparticles in water as base fluid. Fig. 3 shows the temperature distribution on the middle of the cavity (Z = 0.25m), it is observed that the use of nanofluid contributes to the increase of the temperature in the full region of the cavity; which means that the dispersion of nanoparticles in base fluid allows to the augmentation of fluid temperature and the decrease of wall temperatures which leads to the enhancement of convective heat transfer.

without nanofluids

with nanofluids (ϕ=1%)

Fig. 2. Temperature distribution of cavity’s adiabatic walls

without nanofluids

with nanofluids (ϕ=1%)

Fig. 3. Temperature distribution on the middle of the cavity

8.2. Effect of nanofluid on velocity field A qualitative comparison of the velocity distribution is presented in Fig.4; it is remarked that the velocity augments on the fully developed region with using nanofluid. The velocity contours are oriented towards the central region of the cavity and it is typically uniform over the entire cavity, there is also a slight increase in velocity close to the hot wall. This phenomenon is created by the fact that the fluid next to the hot wall receives heat and becomes lighter and rising due to the buoyancy. On the other hand, near the cold wall, it cools down and becomes heavier and downward which is the principal of natural convection.

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without nanofluids

with nanofluids (ϕ=1%)

Fig. 4. Velocity field on the middle of the cavity

8.3. Heat transfer characteristics using nanofluid Fig. 5 predicts a quantitative comparison of the average Nusselt number at the hot wall of the cavity when Rayleigh number varies from 107 to 3x108; it is recommended that Nu increases with increasing Ra due to the strengthened buoyant flow. From Fig.5 Nusselt number augments by using nanofluid and it slightly augments with the increase of nanoparticles volume fraction owing to the change of thermophysical properties of fluid. 8.4. Entropy generation The distribution of local entropy generation due to heat transfer and fluid friction irreversibility for pure fluid as well as nanofluid is shown in Fig. 6, in which the effect of nanoparticles volume fraction and Rayleigh number on entropy generation is studied. The results show that the increase of Rayleigh number produce an augmentation of the heat entropy generation; this is due to the rise of the buoyancy effect. Thus, the presence of nanoparticles plays a remarkable role in minimizing entropy; in the general sense, entropy can be considered as the measure of energy distribution, low entropy means that the energy is concentrated; high entropy means that energy is spread out. Fig.7 presents a qualitative comparison of entropy generation on the middle of the cavity, from this figure it is remarked that with adding 1% of alumina nanoparticles, entropy decreases on the fully developed region. In fact, nanofluid contributes to enhanced heat transfer and minimized entropy.

Fig. 5. Average Nusselt number for the cavity’s hot wall

Fig.6. Entropy generation variation inside the cavity

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without nanofluids

with nanofluids (ϕ=1%)

Fig.7. Qualitative comparison of entropy generation on the middle of cavity

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Conclusion

In the current paper, natural convection heat transfer performance and entropy generation of alumina/water nanofluid in three-dimensional enclosure is studied numerically using finite volume CFD method. Simulations were achieved for different Rayleigh numbers and volume fractions. The results show that the average Nusselt number increases with the increase of Rayleigh number and the nanoparticles volume fraction. Also, in the comparison with pure water, nanofluid presents higher average Nusselt number along the heating wall because the increased conductivity as a dominant parameter to increase heat transfer convection. The addition of nanoparticles into pure fluid decreases the entropy generation.

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2.

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