INVESTIGATION OF TiO 2 -WATER NANOFLUID BEHAVIOR THROUGH A WAVY CORRUGATED PIPE IN TERMS OF HEAT TRANSFER AND PUMPING POWER

Transcription

1 INVESTIGATION OF TiO 2 -WATER NANOFLUID BEHAVIOR THROUGH A WAVY CORRUGATED PIPE IN TERMS OF HEAT TRANSFER AND PUMPING POWER 1 M SALEHIN, 2 M MEHSAN, 3 A MEHMOOD, 4 M AWAIS, 5 M USMAN 1,2,3,4,5 Department of Mechanical and Chemical Engineering (MCE) Islamic University of Technology (IUT), Board bazar, Gazipur-1704, Bangladesh 1 musfequssalehin@iut-dhaka.edu, 2 ehsan@iut-dhaka.edu, 3 aqibmehmood@iut-dhaka.edu, 4 muhammadawais@iut-dhaka.edu, 5 mdusman@iut-dhaka.edu Abstract In sustainable energy, implementation of nanofluid as a working fluid is a novel method in many engineering and industrial applications. Nanofluid provides superior thermo-physical properties in terms of higher thermal conductivity for outstanding thermal performance of the working fluid. In the present article, numerical investigation of heat transfer and pumping power are performed for TiO 2 -water nanofluid through wavy corrugated pipe subjected to constant heat flux. The study is carried out for a wide range of Reynolds number 15,000-40,000 and nanoparticles volume concentration 1% to 5%. Finite volume method is applied in order to solve continuity, momentum and energy equations and realizable k-ε model with enhanced wall treatment is chosen for single phase analysis. By the addition of nanoparticles within a preferred volume fraction in base fluid water results higher heat transfer rate and reduced pumping power. Finally the optimum volume fraction of the nanofluid is determined up to which the requirement of pumping power per unit length is lower compared to base fluid. Index Terms Heat Transfer, Nanofluid, Pumping Power, Wavy Wall. I. INTRODUCTION In thermal engineering science, nanofluid is one of the effective working fluids in terms of intensified heat transfer performance employed in many engineering applications. Nanofluid is prepared by the stable and homogeneous dispersion of solid nanoparticles of size below 100 nm within a desired volume concentration in base fluid like water, oil, ethylene glycol etc. or in a mixture of two liquids [1]-[3].By the addition of nanoparticles, the thermo-physical properties of nanofluid are substantially enhanced which influences the thermal and hydrodynamic behavior of working fluid in terms of increased heat transfer rate [4]-[8]. Several numerical and experimental investigations have been performed with different types of nanofluids employed in corrugated geometries for many aspects of heat transfer applications. The flow of nanofluid through corrugated geometries causes the flow behavior to be disturbed due to recirculation, flow separation and turbulence at the near wall. The implementation of nanofluid and corrugation applied at the wall both potentially enhance the thermal and hydrodynamic behavior of working fluid [9]-[13]. Forced convection heat transfer behavior of water γal 2 O 3 andethylene glycol γal 2 O 3 nanofluidswere observed in a uniformly heated tube subjected to constant heat flux for both laminar and turbulent flow condition [14]. Heat transfer rate was increased with particles volume fraction and Reynolds number. Same nanofluids were employed in a parallel, coaxial and heated disk to observe a considerable augmentation of convective heat transfer coefficient and an empirical correlation was proposed for Nusselt number in terms of Reynolds and Prandtl number [15]. Cu-water nanofluid with 1% volume concentration was employed in a circular tube with constant heat flux and two phase model was adopted to investigate the improvement of heat transfer [16]. Laminar natural convection heat transfer enhancement was reported with Cu water nanofluid as a cooling mediumin a differentially heated square cavity and the study was performed for a range of Rayleigh number 10 4 to 10 7 and nanoparticles volume fraction 0.05% to 5% [17]. This nanofluid was also implemented in a two isothermally heated parallel plates for significant heat transfer enhancement considering the fluid as Newtonian and Non-Newtonian for Reynolds number 5 to 1500 and particles volume fraction up to 5% [18]. Experiments with horizontal double-tube counter flow heat exchanger suggested a significant heat transfer improvement and pressure drop characteristics with TiO 2 -water nanofluid and maximum 11% of enhancement in heat transfer compared to base fluid was achieved with a little penalty of pressure drop [19]. To explore the effect of Peclet number, nanoparticles types and volume fraction on to the heat transfer characteristics, γal 2 O 3 -water and TiO 2 -water nanofluid were used in a shell andtube heat exchanger under turbulent flow condition [20]. Fotukian and Esfahany [21] performed experimentation with dilutecuo/water nanofluid inside a circular tube to investigate the heat transfer performance and pressure drop. Convective heat transfer coefficient was increased by 25% with approximately 20% penaltyin pressure drop. Heat transfer enhancement for natural convection was shown with horizontalconcentric annuli using different types of nanoparticles such as Cu, Ag, Al 2 O 3 and TiO 2 submerged in water for Rayleigh number 10 3 to 10 5 [22]. Heidary and Kermani [23] studied numerical investigation on the effect of nanoparticles on forced convection heat 2

2 transfer augmentation in sinusoidal-wall channel of a range of Reynolds number 5 to 1500,volume fraction up to 20% and Cu-water nanofluid was employed. Maximum enhancement was 50% compared to base fluid and Nusselt number and skin friction coefficient were investigated. Laminar forced convection heat transfer improvement was reported Al 2 O 3 -water nanofluid in a circular tube fitted with twisted tape inserts [24]. This experimental study was performed for range of Reynolds number 700 to 2200 and particle volume concentration from 0 to 0.5%. Heat transfer and pressure drop characteristics were observed in an isothermally heated V-shape corrugated channel with Cu-water nanofluid [25]. Similar works were performed with laminar Cu-water nanofluid through a wavy wall where effect of nanoparticles volume fraction, wave amplitude and Reynolds number on the local skin friction coefficient and Nusselt number were shown [26]. The effect of cross-sectional area of the tube (circular, elliptical and flat) on the friction factor and heat transfer enhancement was performed by TiO 2 -water nanofluid up to volume fraction of 2.5% [27]. The horizontal flat plate showed highest heat transfer improvement compared to other two geometries for Reynolds number ranging from 5,000 to 20,000. Two phase mixture model was employed to explore the effect of nanoparticles volume fraction, wave amplitude and Reynolds number on the enhancement of turbulent forced convection heat transfer [28]. Al 2 O 3 -water nanofluid was used as working fluid results were compared with single phase model.sakrfadl conducted a comprehensive numerical investigation to investigate heat transfer performance with different corrugated surface shapes (trapezoidal, triangle and semicircular) subjected to constant wall heat flux [29]. Finite volume method was employed to solve the governing equations and among three geometries trapezoidaland triangle corrugated surface showed significant heat transfer enhancement for Reynolds number 700 to Different corrugated surface shapes like triangular square and arc were employed with different nanoparticles like Al 2 O 3, SiO 2, ZnO and CuO to investigate the overall improvement of thermal and hydrodynamic behavior [30]. Square rib groove channel provided the highest performance evaluation criterion (PEC) for Reynolds number varying from 30,000 to 50,000 and volume concentration 1% to 4%. Surface roughness were applied at the wall boundary with relative roughness 0.001, and 0.01 in order to enhance the convective heat transfer coefficient by a considerable amount [31]. Wall roughness contributed the enhancement of average nusselt number by 3.10%, 21.86% and 63.03% for relative roughness of the wall of 0.001, and 0.01 respectively. k-ω SSTturbulent model was considered for Reynolds number ranging from 10,000 to 30,000 and volume fraction 1% to 5%. Triangular shaped corrugated pipe imposed to constant wall heat flux was considered to explore the effect of Al 2 O 3 -water nanofluid on the enhancement of heat transfer and reduction of pumping power under turbulent flow condition[32].significant augmentation of convective heat transfer coefficient was reported through a trapezoidal corrugated channel with different wave-amplitude ratios by employing three types of nanoparticles Al 2 O 3, TiO 2, CuO dispersed in water for a range of volume fraction 1% to 5% for turbulent flow condition [33]. Numerical study on turbulent convective heat transfer enhancement was reported corrugated channels of different shapes such as sine shaped, rectangular and V-corrugation [34]. The study was performed for a range of Reynolds number 2,000-14,000, particle volume fraction 1%-5% and Al 2 O 3, TiO 2, Cu nanoparticles were employed. Most of the research articles emphasized on the enhancement of convective heat transfer coefficient using nanofluid in different corrugated geometries. In order to accomplish higher heat transfer rate nanofluid requires increased pumping power due to its improvement of thermo-physical properties. The justification of the implementation of nanofluid in terms of increased pumping power was not discussed elaborately in most of the research articles. So, the scope of our present work is to study the turbulent forced convection heat transfer enhancement using TiO 2 -water nanofluid employed in a sinusoidal corrugated tube. The study is conducted for a range of Reynolds number 15,000-40,000 and nanoparticles volume concentration up to 5%. Results are compared to simple pipe and finally the volume fraction with which nanofluid requires the minimum pumping power for optimum working condition is determined. II. NOMENCLATURE A C Cross-sectional area of pipe A W surface area of pipe C P Specific heat at constant pressure D Diameter of the pipe h C Average heat transfer coefficient k Thermal conductivity P Differential pressure Q Heat transfer Q Heat flux T Temperature U Velocity of flow at inlet W Pumping power Volume fraction µ Dynamic viscosity ν Kinematic viscosity ρ Mass density Nu Nusselt number Re Reynolds number Pr Prandtl number III. GOVERNING EQUATIONS The Reynolds number for the flow of nanofluid is expressed as 3

3 Re = (1) The rate of heat transferq nf to tube wall is assumed to be totally dissipated to nanofluid flowing through a corrugated tube, raising its temperature from inlet fluid bulk temperature T bi to exit fluid bulk temperature T bo. Thus, Q = m C (T T ) (2) Where m is the mass flow rate of nanofluid, C Pnf is the specific heat of nanofluid at constant pressure. The definition of bulk temperature T b is given by T = (3) The average heat transfer coefficient, h c is given by h = ( ) (4) Where A W is the surface area of circular tube and T m is the difference between the wall temperature and the average bulk temperature of the fluid. The average wall temperature T w is computed by T = T,dx (5) So the expression of average Nusselt number is defined as follows Nu = (6) The pumping power per unit length in turbulent flow is given by W = Where P is pressure difference P = (7) (8) d = / (13) Where M is the molecular weight of the base fluid, N is the Avogadro number, and ρ fo is the mass density of the base fluid calculated at temperature T o = 293 K. V. PHYSICAL MODEL AND BOUNDARY CONDITION A numerical investigation of turbulent forced convection through a sinusoidal corrugated tube is presented by employing commercial computational fluid dynamics software, ANSYS Fluent [38]. The length and diameter of the pipe are 300 mm and 10 mm respectively and an uniform constant heat flux of 5,000 W/m 2 is applied at the corrugate wall boundary shown in figure 1. IV. THERMOPHYSICAL PROPERTIES OF NANOFLUID The density and specific heat of TiO 2 -water nanofluid is found from the following equation [35] Density, ρ = ρ φ + ρ (1 φ) (9) Specific heat,c = (1 φ)c + φc (10) The thermal conductivity of the nanofluid is calculated using the correlation proposed by Koo and Kleinstreuer [36]. k = k + 2k + 2(k k )φ k + 2k (k k )φ k βφρ C K T f(t, φ) ρ D Where,f(T, )=( )T+( ) (11) The dynamic viscosity of nanofluid is calculated by using the following empirical correlation developed by Corcione [37] =... (12) Where d bf is the equivalent diameter of the base fluid molecule, and is given by Figure 1. Numerical domain of the circular corrugated pipe and corresponding mesh (not to scale) A 2D simulation with axisymmetric model is considered to reduce computational time and resource. The corrugation has amplitude of 3 mm and wavelength of 30 mm. Realizable k-ε turbulent model is employed with enhanced wall treatment for the single phase analysis.the pressure has been measured at two sections- 60 mm and 240 mm from the inlet respectively to measure the pressure drop ensuring the readings at fully developed region.nanofluid is allowed to flow with a uniform velocity and uniform temperature of 300 K at the inlet of the pipe with an assumption of no slip condition. Heat transfer parameter like convective heat transfer coefficient and average Nusselt number and fluid dynamics parameter like friction factor and pumping power are calculated under prescribed flow condition. VI. CODE VALIDATION AND GRID INDEPENDENCE TEST In order to carry out the code validation, water considered as working fluid allowed to flow in a circular pipe and average Nusselt number measured at fully developed region is compared with correlation proposed by Dittus and Boelter [39] with good 4

4 agreement, shown in figure 2. Grid independence test is carried out with water as working substance flowing through the corrugated channel for the flow Reynolds number 20,000 shown in figure 3. Beyond the grid size of 33,505 there is no significant change in average Nusselt number. So, for the present simulation 23,860 are taken as the optimum grid size of the fluid domain. B. Effect of corrugation on heat transfer and pumping power Figure 5. Use of corrugation for heat transfer enhancement Figure 2. Code validation test Figure 3. Grid independence test VII. RESULT AND DISCUSSION A. Effect of volume fraction of nanofluid on heat transfer The addition of nanoparticles in base fluid significantly improves the convective heat transfer coefficients with an increase of particles volume fraction and flow Reynolds number as shown in figure 4. At Reynolds number 30,000, convective heat transfer coefficient for TiO 2 -water nanofluid of 5% volume fraction is 66.92% higher than water. The improvement is higher at higher volume fraction of nanoparticles and at higher flow Reynolds number. The implementation of corrugation at the wall boundary contributes noticeable amount of enhancement in heat transfer coefficient shown in figure 5. At Reynolds number 30,000,for corrugated pipe, heat transfer rate is enhanced by 26.15% compared to plain pipe. The working substance is considered as water. Similar trend is observed for nanofluid of all volume fractions flowing through the corrugated pipe. The required pumping power for corrugated pipe is more than that of plain pipe due to its near wall turbulence at the wall boundary in terms of flow circulation, separation and vortex formulation. In figure 6, the requirements for pumping power per unit length of pipe for both plain pipe and corrugated pipe is shown. Pumping power requirement also increases with the nanoparticles volume fraction due to the superior thermo-physical properties of nanofluid in terms of increased viscosity shown in figure 7. The requirement is higher at higher Reynolds number and at higher volume fractions of nanofluid. Justification of this increased pumping power for its higher viscosity is discussed in the next section. Figure 4. Improvement of heat transfer coefficient with particles volume fraction. Figure 6.Requirements of pumping power for corrugated and plain pipe. 5

5 methods for intensifying heat transfer performance in many aspects of heat transfer applications. Now, the implementation of corrugation increases the heat transfer rate but at the same time it requires higher amount of pumping power. The reduction of pumping power could be achieved for a certain range of volume fraction with a goal of achieving same convective heat transfer coefficient. In the present study, minimum pumping power occurs at 2% volume fraction of nanofluid. On the other side the implementation of nanofluids have significantly augmented the heat transfer performance with an increase of Reynolds number and nanoparticles volume fraction. REFERENCES Figure 7. Requirements of pumping power for nanofluid of different volume fractions. C. Justification of increased pumping power The justification of the implementation of nanofluid in terms of increased pumping power compared to water is shown in figure 8. In order to achieve a constant heat transfer coefficients, nanofluid requires lesser amount of pumping power per unit length up to a certain volume fraction of nanoparticles. Figure 8. Comparison of pumping power for nanofluid with that for water at the same heat transfer coefficient (zoomed from h=11000 W/m 2 K to h=18000w/m 2 K). So, the use of nanofluid results reduction of pumping power for the same heat transfer rate. The pumping power requirement is lowest for 2% of volume fraction. The nanofluid with 4% of volume fractions requires almost same or little lesser amount of pumping power compared to water. At a volume fraction of 5%, the requirement of pumping power always greater than base fluid. So, for the present study, nanofluid with 2% volume fraction flowing through sinusoidal corrugated tube is the optimum working condition in order to accomplish same heat transfer coefficients. CONCLUSION The implementation of nanofluid in a corrugated channel is one of the inexpensive and innovative [1] Zhu, Hai-tao, Yu-sheng Lin, and Yan-sheng Yin. "A novel one-step chemical method for preparation of copper nanofluids." Journal of colloid and interface science (2004): [2] Wen, Dongsheng, and Yulong Ding. "Formulation of nanofluids for natural convective heat transfer applications." International Journal of Heat and Fluid Flow 26.6 (2005): [3] Prabhat, Naveen. Critical evaluation of anomalous thermal conductivity and convective heat transfer enhancement in nanofluids. Diss. Massachusetts Institute of Technology, [4] Lee, S., SU-S. Choi, S, and Li, and J. A. Eastman. "Measuring thermal conductivity of fluids containing oxide nanoparticles." Journal of Heat transfer (1999): [5] Eastman, Jeffrey A., S. U. S. Choi, Sheng Li, W. Yu, and L. J. Thompson "Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles." Applied physics letters 78.6 (2001): [6] Wang, Xinwei, XianfanXu, and Stephen U. S. Choi. "Thermal conductivity of nanoparticle-fluid mixture." Journal of thermophysics and heat transfer 13.4 (1999): [7] Xie, Huaqing, Jinchang Wang, Tonggeng Xi, Yan Liu, Fei Ai, and Qingren Wu. "Thermal conductivity enhancement of suspensions containing nanosized alumina particles." Journal of Applied Physics 91.7 (2002): [8] Xie, Huaqing, Jinchang Wang, Tonggeng Xi, Yan Liu, and Fei Ai. "Dependence of the thermal conductivity of nanoparticle-fluid mixture on the base fluid." Journal of Materials Science Letters (2002): [9] Paisarn, Naphon. "Study on the heat-transfer characteristics and pressure drop in channels with arc-shaped wavy plates." Journal of Engineering Physics and Thermophysics 83.5 (2010): [10] Elshafei, E. A. M., M. M. Awad, E. El-Negiry, and A. G. Ali. "Heat transfer and pressure drop in corrugated channels." Energy 35.1 (2010): [11] Das, Sarit Kumar, Nandy Putra, Peter Thiesen, and WilfriedRoetzel. "Temperature dependence of thermal conductivity enhancement for nanofluids." Journal of heat transfer (2003): [12] Guzmán, Amador M., Maria J. Cárdenas, Felipe A. Urzúa, and Pablo E. Araya."Heat transfer enhancement by flow bifurcations in asymmetric wavy wall channels." International Journal of Heat and Mass Transfer (2009): [13] Xuan, Yimin, and Qiang Li. "Heat transfer enhancement of nanofluids." International Journal of heat and fluid flow 21.1 (2000): [14] Maı ga, Sidi El Bécaye, Cong Tam Nguyen, Nicolas Galanis, and Gilles Roy. "Heat transfer behaviors of nanofluids in a uniformly heated tube." Superlattices and Microstructures 35.3 (2004): [15] Maiga, Sidi El Becaye, Samy Joseph Palm, Cong Tam Nguyen, Gilles Roy, and Nicolas Galanis. "Heat transfer 6

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