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Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux



F. Khoddamrezaee, R. Motallebzadeh and D. Jajali Vahid
 
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ABSTRACT

In this study, the characteristics of (EG+AL2O3) nanofluid and (EG) fluid which cross a rectangular arrangement of tubes in a shell and tubes heat exchanger have been investigated. The stagnation point, separation point, heat transfer coefficient and shear stress in both of nanofluid and purefluid have been determined and compared with each other. The heat transfer and velocity simulation of two phase flow have been done by mixture model. Results show that by using of nanofluid, the stagnation and separation points of flow were postponed and the amount of heat transfer coefficient and shear stress increased but the effect of shear stress increase can be neglected in compare of unusual heat transfer rising.

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  How to cite this article:

F. Khoddamrezaee, R. Motallebzadeh and D. Jajali Vahid, 2010. Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux. Journal of Applied Sciences, 10: 500-505.

DOI: 10.3923/jas.2010.500.505

URL: https://scialert.net/abstract/?doi=jas.2010.500.505
 

INTRODUCTION

Using a fluid with better heat performance is an effective parameter to increase heat transfer rate in the heat exchangers. Previously to increase heat transfer in the heat exchanger, engineers used suspension of fluid and solid particle with the micron and millimeter diameter. But using this kind of particle causes sedimentation and decrease the flow rate. Pipe scrubbing and great pressure loss in the pipelines are the disadvantages of using large particles in basefluid.

The difference of density between the base fluid and the rigid particles causes sedimentation or buoyancy lift of particles. In sedimentation case, when the gravity force on the rigid particle become equivalent to the Archimedes force, the summation of two forces becomes zero and the particle move downward with the constant velocity. The particles sediment when they reach the nonmoving surface, where, the fluid velocity is also zero.

Sedimentation velocity of the particles in the fluid is calculated by Stocks low:

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux

In this relation (ρ21) is the density difference between base fluid and the suspended particles. If the particles density is less than the fluid density the particles move upward with the constant velocity Vs and if the particles density is more than the fluid density they move downward and sediment. When the fluid density and particles density are near to each other the sedimentation velocity decreases. Also, decreasing in the sedimentation velocity occurs by decreasing the particles radius. Sedimentation velocity of the particles has a vise versa relation with the kinetic viscosity of the fluid. However, suspension stability increases by increasing the kinetic viscosity of the fluid. So, researchers suggest using of the particle with the nanometer size in the base fluid (especially water, oil and ethylene glycol) to decrease the sedimentation velocity. Using the particles with the nanometer size not only causes the better stability of the suspension but also causes an exaggerating increase in heat transfer performance. According to the recent studies, increasing in conduction coefficient of nanofluids is the major reason of increasing the convection heat transfer rate in nanofluids.

Xuan and Li (2003) studied experimentally the convection heat transfer and friction coefficient characters of nanofluid in both of laminar and turbulent flow. Their results show that heat transfer coefficient of the nanofluid is more than the base fluid in the same conditions. This coefficient changes with the changing the flow velocity and volumetric ratio of nano particles. Yang et al. (2005) studied the convection heat transfer coefficient of graphite nano particles in laminar flow in a horizontal heat exchanger experimentally. This study has considered the result of changing the Reynolds number, volume ratio, temperature and type of fluid on the heat transfer coefficient.

Lee and Choi (1996) studied force convection heat transfer in parallel channels by using a special nanofluid and found that the heat resistant decreases with the ratio of 0.5. Wen and Ding (2004) studied the experimental result of (Al2O3-water) nanofluid convection heat transfer along a copper tube with 4.5 mm diameter and 970 mm length. They find that nanofluid heat transfer coefficient increases by increasing the Reynolds number and the volumetric ratio of particles. Also, heat transfer coefficient increasing in the entrance part is more than the other. Despite of better heat transfer characters, nano particles movement causes non steady temperature and viscosity counter occur. Heris et al. (2006) studied laminar flow of CuO-water and (Al2O3-water) in a copper tube with 1 m length, 6 mm diameter and 0.5 mm thickness. The copper tube is positioned inside a stainless steel tube with internal diameter of 32 mm. To obtain constant temperature boundary condition on the copper tube, saturated vapor flows inside the stainless steel tube. The results show that heat transfer coefficient increases by increasing the particles volumetric ratio and Peclet number.

Hong et al. (2006) investigated the effect of the clustering of nanoparticles on the thermal conductivity of nanofluids. The results show that thermal conductivity of nanofluids is directly related to the agglomeration of nanoparticles and increases nonlinearly with increasing volume concentration. Leong et al. (2006) proposed a new model for predicting thermal conductivity of nanofluids by considering the effects of the interfacial layer at the solid-liquid interface. Zhang et al. (2007) showed that the thermal conductivity of some nanofluids indicated no anomalous enhancements.

Timofeeva et al. (2007) studied the thermal conductivity and viscosity of Alomina nanoparticles dispersed in water and ethylene glycol. Results showed that the measured thermal conductivity of nanofluids was less than the predicted values of the effective medium theory. He et al. (2007) showed that the thermal conductivity of nanofluids increases with increasing volume fraction in a nonlinear trends. Lee et al. (2007) showed that viscosity of nanofluids significantly decreases with increasing temperature. Murshed et al. (2008) investigated the thermal conductivity and viscosity of nanofluids. The results showed that the measured thermal conductivity and viscosity of nanofluids are higher than those of base fluids and increase with increasing particle volume concentration.

In this study, the velocity profile, heat transfer coefficient and shear stress of (EG+AL2O3) nanofluid through the shell and tube heat exchanger with rectangular arrangement of tubes have been considered and compared with the base fluid (EG).

MATERIALS AND METHODS

Mixture method is used to solve the governing equations. In this method nanofluid acts like a pure fluid. There is no velocity difference between fluid and the particles. The fluid and the particles have heat equilibrium. Continuity, momentum and energy equations for one phase fluid are used for the nanofluid. The effect of nano particles enters in the nanofluid physical characteristics. The distribution of the particles is assumed to be steady in the base fluid because the diameter of the particles is less than 100 nm.

Eastman et al. (1997) studied that, the Ethylene Glycol and Alumina nanofluids have better stability than the other nanofluids.

Governing equations: Continuity, momentum and energy are the governing equations. They are defined for solving the multi phase fluid with mixture method for two phase flow as follow:

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(1)

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(2)

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(3)

where, Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux is mass transfer rate between two phases or mass production resource. Vm and ρm are the mean velocity and mean density of nanofluid. n is number of phases. α is volume percentage of each phases. Vk and ρk are the phases velocity and density.

The momentum equation for mixture is:

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(4)

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(5)

In this relation F is the body force and the Einstein equation is used to estimate the viscosity of suspension.

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(6)

The energy equation of mixture phase is:

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(7)

where, Se is applied to all kind of heat sources.

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux

For compressible flow Ek = H and for incompressible flow Hk is sensible enthalpy of k phase.

For EG-Al2O3 nanofluid without mass resource, above equations simplified to continuity, momentum and energy equations of single phase fluid flow. The effect of nano particles enters in the physical characteristics of fluid. Therefore:

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(8)

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(9)

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(10)

where, in the above equations:

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(11)

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(12)

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(13)

where, P indices stand for the particles characters; b stand for the base fluid characters and nf stands for nanofluid characters. Cp is the specific heat. α is volume percentage of nano particles in base fluid.

In this study, ratio of conduction coefficient of nanofluid to base fluid is calculated from experimental results of Hamilton and Crosser (1962).

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(14)

where, n (n = 3/ψ) is geometry coefficient.

ψ is the ratio of area between a sphere with the same volume of particle and particle real body area. It is called spherical coefficient.

Boundary conditions and geometry: To solve the Eq. 8 through 10, boundary conditions are:


Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
Fig. 1:

Heat exchanger with rectangular arrangement of tubes schematic

Constant velocity V0 = 1 (m sec-1) and constant temperature T0 = 273 (k) is applied to inlet.

Velocity of nanofluid on the outer wall is assumed to be zero. The heat flux through the surface of each tube is assumed to be q = 10241 (w m-2). As shown in the Fig. 1 Sr = 40 cm, SL = 40 cm and D = 20 cm. Four tubes with 20 cm diameters are positioned with the central distance of 40 cm from each other. Heat flux is q = 10241 (w m-2) from the tube walls and is assumed to be constant. Nanofluid (Ethylene Glycol+Alumina) flow vertical to tubes axes. The tubes are arranged rectangular. It is assumed that the alumina particles with the diameter of 1 have a stable suspension in ethylene glycol base fluid.

Numerical methodology: To solve the Eq. 8-10 with the illustrated boundary conditions; finite volume method, non organized triangle mesh and simple algorithm is used.

Validation: It is needed to compare the results of calculations with the experimental or numerical study by the other researcher to ensure about the methodology and calculations. The results are predicated by simulation of the nanofluid (EG+Al2O3) with zero nano particle volume ratio is studied and compared with the (Zukauskas, 1972) experimental results. The predication must be as above because there is no other experimental or theoretical results about nanofluid flow around the tubes. Zukauskas (1987) found the relation between heat transfer ratio and ReD, Pr, ST/D.

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(15)

where, for gases n = 0 and for fluids n = 0.25.

In Eq. 15 Prw is Prandtl number in the wall temperature Tw. The other characters are calculated with reference to fluid temperature. The function f(ReD) is defined by Reynolds number and tubes arrangement.


Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
Fig. 2:

Correction factor diagram of heat transfer coefficient for the different columns


Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
Fig. 3:

Validation results diagram

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
(16)

With inserting the value of ST, SL and D in Eq. 15 and 16:

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux

By using the correction factor from Fig. 2:

For the first row Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux = 739 and for the second row Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux= 844.

The simulated diagram is shown in Fig. 3. Note to the inlet velocity in relation 16 it is found that the maximum values in the diagram are consonant to the results from (Zukauskas, 1987) relations. By using the mean velocity, which is assumed to be half of the inlet velocity, the values which are calculated from Eq. 15 and 16 decreases.

RESULTS AND DISCUSSION

Velocity profile comparison: With reference to (EG+Al2O3) velocity profile in Fig. 4, for tubes 1 and 3 the velocity becomes maximum on β = 80° and the flow separation happens on β = 100°.


Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
Fig. 4:

Velocity counters of nanofluid in heat exchanger with rectangular arrangement


Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
Fig. 5:

Velocity counters of pure fluid in heat exchanger with rectangular arrangement

Therefore, by increasing in β the backward flow happens. On the other tubes column (walls 2 and 4) flow separation degree increases and reach to β = 120°. The velocity profiles shows that nanofluid has more velocity in the area between tube rows therefore, the convection heat transfer is more than the other areas.

As it is seen, nanofluids flow becomes turbulent after the separation and the backward flow has high velocity. Stagnation point is on β = 0° for the walls 1 and 3. For walls 2 and 4 the stagnation points are on β = 80°.

In Fig. 5, the velocity profile of the pure Ethylene Glycol fluid on the rectangular arrangement of tubes is shown. Note to this profile the separation point happens on β = 90° for all the walls. According to the diagram stagnation points on the walls 1 and 3 are on β = 0° and for the walls 2 and 4 are on β = 60°.

Heat transfer coefficient comparison between (EG+Al2O3) nanofluid and (EG) pure fluid: In Fig. 6 the diagram shows that the heat transfer coefficients of walls 1 and 3 are coincided on each other for the pure fluid (EG). This matter also happens for walls 2 and 4.


Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
Fig. 6:

Heat transfer coefficient of pure fluid in heat exchanger with rectangular arrangement


Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
Fig. 7:

Heat transfer coefficient of nanofluid in heat exchanger with rectangular arrangement

Heat transfer coefficient on first column of tubes (walls 1 and 3) is the same as the second column (walls 2 and 4). Therefore, by increasing the number of tubes vertically or horizontally heat flux from each tube has one value.

In Fig. 7 the diagram shows that heat transfer coefficients of walls 1 and 3 are approximately coincided on each other for nanofluid. This matter also happens for walls 2 and 4. But the heat transfer coefficient on the first column of tubes (walls 1 and 3) is different from the second column (walls 2 and 4). The maximum heat transfer coefficient happens on the first column. The value of the heat transfer coefficient on first column is 785 w m-2 k. The second column heat transfer coefficient is 760 w m-2 k. The heat transfer coefficient decreases in comparison with the first column by increasing number of the columns. This coefficient becomes constant after the flow becomes fully develop.

By using nanofluid (EG+Al2O3) heat transfer coefficient increases by the ratio of 3.25 on the first column and 3.16 on the second column.

Shear stress comparison between nanofluid (EG+Al2O3) and pure fluid (EG): Theoretical relations and experiments show that shear stress of flow increases in the tube by using nanofluid in comparison with pure fluid.


Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
Fig. 8:

Shear stress on the walls of nanofluid in heat exchanger with rectangular arrangement


Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux
Fig. 9:

Shear stress on the walls of pure fluid in heat exchanger with rectangular arrangement

Figure 8 shows the shear stress on the walls when the nanofluid (EG+Al2O3) is external flow on the tubes. Shear stress value on the first column of tubes is less than 35 Pa. The shear stress value on the second column is about 40 Pa.

Figure 9 shows the shear stress on the walls when the pure fluid (EG) flow on the tubes. Figure 9 shows that the shear stress on the first column is approximately the same as nanofluid. But on the second column the value of the shear stresses on the walls are 35 Pa which are different from the value on the second column when the nanofluid flows on the walls.

It can be estimated from the above that the shear stress in external flow with nanofluid increases due to the increasing in viscosity of the nanofluid in comparison with the pure fluid. The increasing ratio of shear stress is about 1.19. However, this increasing happens only on the second column and the shear stress does not have great difference between nanofluid and pure fluid on the first column.

The effect of the increasing in shear stress in comparison with the extreme increasing of heat transfer coefficient is negligible.

NOMENCLATURES

Image for - Simulation of (EG+Al2O3) Nanofluid Through the Shell and Tube Heat Exchanger with Rectangular Arrangement of Tubes and Constant Heat Flux

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