Proceedings of CHT-12 ICHMT International Symposium on Advances in Computational Heat Transfer July 1-6, 2012, Bath, England CHT12-MN03 DOI: 10.1615/ICHMT.2012.CHT-12.530
ISBN: 978-1-56700-303-1 ISSN: 961-91393-0-5
HEAT TRANSFER ENHANCEMENT USING CuO/WATER NANOFLUID Meriem AMOURA*,§, Amar MAOUASSI** and Noureddine Zeraibi** * Université des Sciences et de la technologie Houari Boumedienne, Faculté de Physique, Dépt. Energétique. B.P. 32 El-Alia, 16111 Bab-Ezzouar, Alger, Algeria ** Université de Boumerdes, Faculté des hydrocarbures, Dépt. Transport et Equipements, Avenue de l’indépendance, 35000 Boumerdes, Algeria § Correspondence author. Fax: +(213) 21 247 344 Email:
[email protected]
ABSTRACT The flow and heat transfer is an important phenomenon in engineering systems due to its wide application in electronic cooling, heat exchangers, double pane windows etc.. The enhancement of heat transfer in these systems is an essential topic from an energy saving perspective. The lower heat transfer performance when conventional fluids, such as water, engine oil and ethylene glycol are used hinders improvements in performance and a consequent reduction in the size of such systems. The use of solid particles as an additive suspended into the base fluid is a technique for heat transfer enhancement. Therefore, the heat transfer enhancement in a horizontal circular tube that is partially heated under laminar regime has been investigated numerically. Nanofluid was made by dispersion of CuO nanoparticles in pur water. Results illustrate that the suspended nanoparticles increase the heat transfer with an increase in the nanoparticles volume fraction and at any given Reynolds number. NOMENCLATURE Cp D L q Re r T u, v x, r
Specific heat (J/kg K) Diameter (m) Length of cylinder (m) Heat flux (W/m2) Reynolds number Radius Temperature Velocity components Axial and radial coordinates
Greek symbols Nanoparticle fraction Dynamic viscosity (kg/m s) Density (kg/m3) Subscripts f fluid nf nanofluid
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INTRODUCTION One of the most important needs of modern industries is high performance heat transfer equipment. In the past few decades many techniques for heat transfer enhancement have been proposed. One idea involves improving the performance of heat transfer fluids by the addition of solid particles [Choi 2001, Das 2003]. Suspensions of nano-sized (< 100 nm) particles in conventional heat transfer fluids (such as water, ethylene glycol, and engine oil) were named nanofluid by Choi [1995]. To understand and describe various features of flow and heat transfer behavior of nanofluids, numerous investigations have been carried out [Godson 2009]. Almost all previous investigations show that the thermal conductivity of nanofluids increases significantly over that of the base fluid [Godson 2009, Yu 2008, Li 2009]. Oxide nanoparticles [Pak 1998, Wen 2004, Heris 2006, He 2007, Nguyen 2007], carbon nanotubes [Ding 2006, Garg 2009] and other types on nanoparticles [Xuan 2003, Yang 2005, Yu 2009, Torii 2009] have been used in the preparation of nanofluids. Conventional heat transfer fluids such as water, ethylene glycol and transformer oil have been employed as base fluid. All investigators have studied convective heat transfer of nanofluids in circular tubes. Results of these investigations show that the heat transfer coefficient of nanofluids is considerably higher than that of the base fluid and the enhancement of heat transfer coefficient increases with nanoparticle concentration and nanofluid flow rate. Convective heat transfer characteristics of nanofluid CuO/water in horizontal circular tube with constant wall heat flux in the laminar flow regime were studied numerically. A computational code by use of the finite volume method is developed [Patankar 1988]. Laminar model was used to simulate the flow and heat transfer using the SIMPLE scheme for pressure-velocity coupling. This code is validated by comparison with results reported in the literature. PROBLEM FORMULATION The geometry under investigation is shown in Fig. 1. We consider a horizontal circular tube with a finite length and a diameter D. The flow will be considered as axi-symmetric and therefore it is two dimensional so that it can be represented by the axial and radial coordinates only. The tube contains water and CuO nanoparticles. These particles are assumed to be in the same size and shape. In addition, the solid particles are in thermal equilibrium with the base fluid and they are the same velocity. D Entrance of fluid L
Figure 1. Geometry of the problem.
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The physical properties of the nanofluid are assumed to be independent of temperature but of course are functions of the volume fraction of the suspended nanoparticles. The buoyancy effects are neglected. The thermophysical properties such as density, thermal conductivity of the base fluid and nanoparticle and viscosity are summarized in Table 1. The governing equations for nanofluid in axi-symmetric cylinder are the continuity, momentum, and energy equations with their density, thermal conductivity, and viscosity modified for nanofluid application. The continuity written in cylindrical coordinate for an axi-symmetric geometry is:
nf u 1 nf rv 0 x r r Momentum equations in the axial and radial directions are:
nf nf
uu x uv x
(1)
nf
1 rvu P u 1 u nf r nf r x x x x r r r
(2)
nf
1 rvv P v 1 v v nf r nf nf 2 r r r x x r r r r
(3)
The axi-symmetric form of energy equation is:
nf
uT x
nf
1 rvT knf T 1 knf T r r r x c pnf x r r c pnf r
(4)
As mentioned before, nanofluid properties are combinations of base fluid and particle properties. The effective density of nanofluid is predicted by mixing theory: (5)
Specific heat is also defined by mixing theory: (6)
Table 1 Material properties of fluid and nanoparticle [Jang 2007, Abu-Nada 2010] Water 3
Density (kg/m ) Thermal conductivity (W/m K) Specific heat capacity (J/kg K Dynamic viscosity (Ns/m2) x 10-3
1000 0.6 4183 1.003
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CuO 6350 69 535 -
The thermal conductivity of nanofluid was evaluated from the model proposed by Maxwell [1873] namely: (7)
The effective viscosity of fluid containing small particules is given by Brinkman [1952] as (8) The dimensionless fom of the governing equations can be obtained by use of dimensioness variables defined as: (9) The problem is characterized by the following parameters of similarity: the Reynolds number:
(10)
the Prandtl number:
(11)
the Peclet number: Pe=Re Pr
(12)
The Nusselt number of the nanofluids is expected to depend on a number of factors such as thermal conductivity and specific heat capacity, the volume fraction of the suspendes particles, the flow structure and the viscosity of the nanofluid. The Nusselt number of the nanofluid can be expressed as:
Shah[1975]
(13)
The mean temperature of the fluid for an axi-symmetric case at any cross-section of the tube is: D/ 2
2C pTurdr
Tmean
0 D/ 2
2urdr
2 U mean( D / 2 )2
D/2
T ( r , x )u( r , x )rdr 0
0
where T is the temperature at a distance r from the axis where the axial velocity is u. The boundary conditions in this geometry are summarized in figure 2 and table 2.
872
(14)
Zone N°2
Zone N°1
Zone N°3
Entrance
Exit
U=f (r)
r Symetric axe x Figure 2. Boundary conditions
Table 2 Boundary conditions The condition Axial velocity U Radial velocity V Temperature T
Entrance U0
Re D
Zone N°1 Zone N°2 Zone N°3 Symetric axe 0 x 1m 1 x 1,5m 1,5m x 5m 1m U 0 U=0 U=0 U=0
V=0
V=0
T0= 288 K
T= Twall
V=0 q=900W/m2
V=0 T 0 r
r V 0 r T 0 r
The numerical simulation is based on the finite volume formulation. The governing equations are integrated over each control volume to obtain a set of linear algebraic equations. These equations were solved by employing SIMPLE algorithm for the pressure correction processes, and convective and diffusive terms were discretized by upwind and central difference schemes, respectively. Second order discretization scheme were employed for all simulation. For cylinder’s diameter less than 2mm and a length equal to 5 m, a grid independence study was carried out with three different (301x31, 401x31 and 421x31) grid sizes. These studies are performed for 10% volume fraction of CuO. Mean temperature profiles along of the cylinder are plotted for Reynolds number equal at 25 as shown in Fig. 3. From Fig. 3 it is very clear that grid size 401x31 and 421x31 gave same results. The 401x31 and non-uniform grid is chosen for computation, allowing fine grid spacing near the wall of cylinder and in the second zone (starting about a quarter of the way and ending about half way) (Figure 4).
873
320
315
310
Tmean
Frame 001 14 May 2011 title
301 by 31 401 by 31 421 by 31
305
300
295 0
1
2
3
4
5
x
Figure 3. Temperature profiles at Re=25 for 10% volume fraction of CuO.
r
Figure 4. : Schematic of grid.
x
The convergence of the numerical solution is based on residuals of governing equations that were summed over all cells in the comutational domain. Convergence was achieved when the summation of residuals decreased to less than 10-8 for all equations. Furthemore, in order to validate the numerical code used for the present study, the steadystate solutions obtained as time-asymptotic solutions for an vertical square cavity with differentially heated sidewalls and adiabatic top and bottom walls, have been compared with the results of Hadjisophocleous [1998], Tiwari [2007] and Kuang [2010]. In particular, the average Nusselt numbers, the maximum horizontal and vertical velocity components obtained at Rayleigh numbers in the range between 103 and 106 are summarized in the table 3. A very agreement has been obtained.
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Table 3 Comparison between present study and results reported in the literature Hadjisophocleous [1998]
Tiwari [2007]
Kuang [2010]
Present study
3.544 0.814 3.586 0.186 1.141
3.642 0.804 3.702 0.178 1.087
3.597 0.819 3.669 0.181 1.118
3.643 0.818 3.690 0.179 1.108
15.995 0.814 18.894 0.103 2.29
16.144 0.822 19.665 0.110 2.195
16.185 0.819 19.648 0.112 2.243
16.164 0.821 19.665 0.111 2.228
37.144 0.855 68.91 0.061 4.964
34.30 0.856 68.77 0.059 4.450
36.732 0.858 68.288 0.063 4.511
36.720 0.857 68.260 0.060 4.489
66.42 0.897 226.4 0.0206 10.39
65.59 0.839 219.73 0.04237 8.803
66.47 0.869 222.34 0.03804 8.758
66.48 0.890 219.55 0.0399 8.765
Ra=103
umax y vmax x Ra=104
umax y vmax x Ra=105
umax y vmax x Ra=106
umax y vmax x
RESULTS The heat transfer performance has been investigated for the Reynolds number range 25
