In this paper the second law analysis of thermodynamic irreversibilities in pseudo-plastic non-Newtonian nanofluids through a circular duct under uniform wall temperature thermal boundary have been carried out for laminar flow condition. This nanofluid consists of sodium carboxymethyl cellulose (CMC)–water and two different types of nanoparticles; namely, CuO and Al2O3. Entropy generation is obtained for various Power law number, various volume concentration of nanoparticles, various dimensionless temperature and various Reynolds number. It is found that with the decreasing Power law number and duct length values, total entropy generation at fixed Reynolds number decreases and with increasing wall temperature values, total entropy generation increases, also entropy generation decreases with increasing volume concentration of nanoparticles

falahat, alireza

saffarian, mohammadreza

shabani, mohsen

Universiti Teknikal Malaysia Melaka: UTeM Open Journal System

    ISSN: 2180-1053         Vol. 10 No.1       January – June 2018                         1  ENTROPY GENERATION OF PSEUDO-PLASTIC NON-NEWTONIAN NANOFLUIDS IN CIRCULAR DUCT UNDER CONSTANT WALL TEMPERATURE  A. Falahat1, M. Shabani2*, M. R. Saffarian3 1Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Iran 2Production technology research institute (ACECR), Ahvaz, Iran 3Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Iran   ABSTRACT  In this paper the second law analysis of thermodynamic irreversibilities in pseudo-plastic non-Newtonian nanofluids through a circular duct under uniform wall temperature thermal boundary have been carried out for laminar flow condition. This nanofluid consists of sodium carboxymethyl cellulose (CMC)–water and two different types of nanoparticles; namely, CuO and Al2O3. Entropy generation is obtained for various Power law number, various volume concentration of nanoparticles, various dimensionless temperature and various Reynolds number. It is found that with the decreasing Power law number and duct length values, total entropy generation at fixed Reynolds number decreases and with increasing wall temperature values, total entropy generation increases, also entropy generation decreases with increasing volume concentration of nanoparticles.   KEYWORDS: Entropy generation; Non –Newtonian fluid; Power law number; Laminar flow.  1.0 INTRODUCTION  Improvement of convective heat transfer is very important for many thermo-fluid systems. The heat convection can passively be enhanced by fluid thermo physical properties. One way of improving the thermal conductivities of fluids is to suspend small solid particles in the fluid. Pak and Cho (1998) presented an experimental investigation of the convective turbulent heat transfer characteristics of Al2O3 nanofluids. The heat transfer for the nanofluids increases with the increase of volume concentration and Reynolds number.  Masuda et al. (1993) showed that the viscosity and the thermal conductivity of liquids are changed by dispersing very-fine particles of some nanoparticles like Al2O3, SiO2 and TiO2 .                                                   *Corresponding author e-mail: M-shabani@phdstu.scu.ac.ir  Journal of Mechanical Engineering and Technology 2                              ISSN: 2180-1053         Vol. 10 No.1       January – June 2018  Das et al. (2003) have investigated the increase of thermal conductivity with temperature for water- Al2O3 and     water-CuO nanofluids by the temperature oscillation technique.  Entropy generation or exergy destruction is very important for design of thermo-fluid devises and for optimization, entropy generation must be decreased. For minimizing the entropy generation inside a duct has been extensively studied (Bejan, 1996, 1972, 1996a, 1996b).  Oztop et al. (2009) have investigated the entropy generation in rectangular ducts with semicircular ends cross section with two boundary conditions: constant wall temperature and constant wall heat flux. Ozotop et al.  (2009) investigated the entropy generation in for hexagonal duct ducts with constant heat flux boundary condition. Also, entropy generation in ducts with various cross sectional geometries under constant wall heat flux and laminar flow investigated by Sahin, (1996, 1998a, 1998b). Falahat and Vosough (2012) computed entropy generation in a coiled tube under constant heat flux for both laminar and turbulent regimes using alumina–water nanofluids. They found that by adding 1% volume fraction of nanoparticles to the base fluid, entropy generation decreases about 3% in laminar flow. Also, they obtained an optimal Reynolds number for the turbulent flow for which the entropy generation was minimized. Falahat (2011) made a study on entropy generation in s confocal elliptical ducts under constant heat flux. Moghaddami et al. (2011) obtained optimum Reynolds number which minimized entropy generation for water–Al2O3 and ethylene glycol- Al2O3 nanofluids using a circular tube under constant heat flux.  The main aims of this work to investigate a second law analysis for forced convection of non-Newtonian nanofluids in circular cross section duct with constant wall temperature boundary condition. This base fluid is CMC–water with two different types of nanoparticles: CuO and Al2O3.The effects of power-law nanofluids viscosity, Reynolds number, nanoparticles volume fraction, dimensionless temperature and length of pipe on entropy generation are investigated.    2.0 METHODOLOGY  2.1  Physical model and thermo physical properties of non-Newtonian    nanofluids  A geometrical configuration of the present problem has been shown in Figure 1. The geometries consist of circular duct with constant wall temperature. The flow in this work is considered laminar, steady, fully developed and incompressible.    Figure 1. Geometrical configuration Entropy Generation of Pseudo-Plastic Non-Newtonian Nanofluids in Circular Duct Under Constant Wall Temperature ISSN: 2180-1053         Vol. 10 No.1       January – June 2018                         3   The nanofluid in this channel is non-Newtonian and assumed that the fluid phase and nanoparticles are in the thermal equilibrium state and they flow with the same velocity. The CMC–water with low concentration (0.1–0.4%) is used as a base fluid of the nanofluid. The viscous properties of the CMC–water are given in Table 1. Jin et al. (2000) have shown that the thermo physical properties of the CMC–water (<6%) is similar to water. n is the Power-law number of the non-Newtonian base fluid. For Newtonian fluid, n equals 1, n < 1 is descriptive of the pseudo-plastic fluid while n > 1 describes the Dilatant fluid.  Table 1. Viscous properties of CMC–water (Jin et al., 2009)  Physical property n m CMC-water (0.0%) 1.00 0.000855 CMC-water (0.1%) 0.91 0.006319 CMC-water (0.2%) 0.85 0.017540 CMC-water (0.3%) 0.81 0.0313603 CMC-water (0.4%) 0.76 0.0785254    Thermo physical properties of the nanofluid are obtained from the flowing relations is available in the literature, as discussed by  Khanafer et al. (2003).  (1 )nf bf p        (1) ( ) (1 )( ) ( )c c cp nf p bf p p        (2) 2 2 ( )2 ( )k k k k knf p bf bf pk k k k kbf p bf bf p     (3) 2.5(1 )bfnf (4)   Table 2. Thermophysical properties of pure fluid and nanoparticles (Santra et al, 2008; Raptis et al, 2004)  Physical properties CMC-water (0.0-0.4%) Al2O3 CuO CP(J/kg K) 4179 765 535.6 𝜌 (kg/m3) 997.1 3970 6500 k (W/m K) 0.613 40 20    2.2  Mathematical Modeling  On the basis of average heat transfer and fluid friction, the equation of entropy generation rate is presented by Sahin (1998) as follows:  Journal of Mechanical Engineering and Technology 4                              ISSN: 2180-1053         Vol. 10 No.1       January – June 2018  (5)  1ln8)1(1.1ln.4.4.4 LLL NStNStNStpgeneStEcfeeCGS   Where, the non-dimensional entropy generation number Ns  can be defined as  (6)                      PgengenCGSTQSNs/  In above equations some dimensionless parameters can be defined as (7)                       PUChSt  (8)                        )(2iwP TTCUEc  (9)                       T Tw iTw  (10)                          LNL d   For Power-Law model, average velocity, friction factor, Reynolds number (Coulson, and Richardson, 1999) and Nusselt number (Chhabra and Richardson, 2008) are defined as (11)                       22.41312 ddUfmdnnUn (12)                    Re64f  (13)                      2Re3 1184n nU dnnn mn     (14)                        1133 1 31.754GCn PnfNun K Lnf             3.0 RESULTS AND DISCUSSIONS  The effect of the Power-law Number, volume concentration of nanoparticles, Reynolds number and length of duct for different nanofluids on the dimensionless entropy generation are investigated in circular duct under constant wall temperature. The surface temperature of duct is 350K.   The present results was also validated against the results of Sahin, 2008. Figure 2 shows the total dimensionless entropy generation of water with respect to Reynolds number. It Entropy Generation of Pseudo-Plastic Non-Newtonian Nanofluids in Circular Duct Under Constant Wall Temperature ISSN: 2180-1053         Vol. 10 No.1       January – June 2018                         5  can be seen from the comparison that both solutions are in a good agreement with each other. Two reasons for the discrepancies are due to different thermo physical properties and different Nusselt number. Sahin (2008) used Nusselt number for tube under constant wall temperature (Nu=3.66) but the present study utilized the Equation (14).       Figure 2.  Comparing the present results with the results of Sahin 2008   (n=1, θ=0.01 and φ=0)  The effect of Power-law Number and volume concentration of Al2O3 nanoparticles on dimensionless entropy generation have been shown in Figure 3. It can be seen that dimensionless entropy generation decreases with decrease of Power-law Number in fixed volume concentration of nanoparticles and also it decreases with increase of volume concentration of nanoparticles.    Figure 3.  The effect of n and volume concentration of Al2O3 on dimensionless entropy generation (θ=0.08, Re=500)  Journal of Mechanical Engineering and Technology 6                              ISSN: 2180-1053         Vol. 10 No.1       January – June 2018  Figure 4 shows the effect of dimensionless temperature and volume concentration of nanoparticles on dimensionless entropy generation. As the dimensionless temperature increases, the dimensionless entropy generation increases for each volume concentration of nanoparticles. Also, entropy generation decrease with increase of volume concentration of nanoparticles for each dimensionless temperature.     Figure 4.  The effect of dimensionless temperature and volume concentration of Al2O3 on dimensionless entropy generation (n=0.85, Re=500)  Figure 5 shows the effect of Reynolds number and nanoparticles volume fraction on dimensionless entropy generation. It can be seen that dimensionless entropy generation decreases with the increase of Reynolds number for each nanoparticles volume fraction.       Figure 5.  The effect of Reynolds number and volume concentration of Al2O3 on dimensionless entropy generation (n=0.85, θ=0.08) Entropy Generation of Pseudo-Plastic Non-Newtonian Nanofluids in Circular Duct Under Constant Wall Temperature ISSN: 2180-1053         Vol. 10 No.1       January – June 2018                         7  Figure 6 shows the effect of different nanoparticles types (Al2O3 and CuO) and volume concentration of nanoparticles on dimensionless entropy generation. When volume concentration of nanoparticles is increased, the dimensionless entropy generation decreases in two nanoparticles types. The CuO /CMC-Water nanofluid with higher volume fraction of nanoparticles and higher volume of CMC may be a good choice as a working fluid because of their dimensionless entropy generation rate is lower than the Al2O3/CMC-Water nanofluids.     Figure 6. The effect of Power law number and volume concentration of Al2O3 and CuO on dimensionless entropy generation (Re=500, θ=0.08)   Figure 7 shows the effect of length of duct and nanoparticles types on dimensionless entropy generation for fixed volume concentration of nanoparticles. It can be seen that dimensionless entropy generation increases with the increase of duct length for each type of nanoparticles, because by increasing of length of duct thermal irreversibility increases.     Journal of Mechanical Engineering and Technology 8                              ISSN: 2180-1053         Vol. 10 No.1       January – June 2018    Figure 7.  The effect of length of duct and nanoparticles types on dimensionless entropy generation (n=0.85, θ=0.08, φ=2% and Re=500)   4.0 CONCLUSIONS  In this study second law analysis of laminar flow of pseudo-plastic non-Newtonian nanofluids has been obtained for circular duct under uniform wall temperature thermal boundary. Some conclusions can be given as follows:  Dimensionless entropy generation decreases with increasing of volume concentration of nanoparticles and Reynolds number.  As the Power-law Number decreased, dimensionless entropy generation decreases for each volume concentration of nanoparticles.  Dimensionless entropy generation increases with the increase of dimensionless temperature and increase of duct length for each type of nanoparticles.  Dimensionless entropy generation of CuO /CMC-Water nanofluids is lower than the Al2O3/CMC-Water nanofluids.  Dimensionless entropy generation increases with the increase of duct length for each type of nanoparticles.               Entropy Generation of Pseudo-Plastic Non-Newtonian Nanofluids in Circular Duct Under Constant Wall Temperature ISSN: 2180-1053         Vol. 10 No.1       January – June 2018                         9  5.0 REFERENCES  Bejan, A. (1979). A study of entropy generation in fundamental convective heat transfer. 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NOMENCLATURE   CP specific heat , kJ/kg K Greek symbols d diameter, m   viscosity of the fluid, Pa.s f friction factor   density, 3/ mkg  G mass flow rate, kg/s   nanoparticles volume fraction h heat transfer coefficient, W/m2 K   dimensionless temperature k thermal conductivity of the fluid, W/m K subscripts L length of coiled tube, m bf  base fluid m Power law consistency nf  Nanofluid n Power law index p  particles Nu Nusselt number w  Wall NL Dimensionless length   Pr Prandtl number   Re Reynolds number   S specific entropy, kJ/kg K   T temperature, K   x local position along the flow direction, m     

Entropy generation of pseudo-plastic non-Newtonian nanofluids in circular duct under constant wall temperature

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Entropy generation of pseudo-plastic non-Newtonian nanofluids in circular duct under constant wall temperature

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