On the Use of Thermodynamic Optimization Tools for Closed Systems working with Engineered Heat Transfer Fluids

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1 On the Use of Thermodynamic Optimization Tools for Closed Systems working with Engineered Heat Transfer Fluids Guillermo Soriano 1,*, Frank Porras 1, 2, Pablo Guevara 1, 2, Gabriel Bravo 1, 2. 1 Centro de Energías Renovables y Alternativas CERA- Escuela Superior Politécnica del Litoral ESPOL, Guayaquil-Ecuador 2 INER, Quito-Ecuador * Corresponding gsorian@espol.edu.ec ABSTRACT An assessment on the use of engineered heat transfer fluids on closed loop heat transfer systems is presented. A constant wall temperature system under turbulent regime is chosen as a first approximation to closed loop ground heat exchanger systems. An analysis on entropy generation and pumping power on the system working with different engineered heat transfer fluids is performed. Three types of fluids are considered: multiwalled carbon nanotube (MWCNT) based nanofluids, slurries with microencapsulated phase change materials (MPCM) and a mixture of both fluids. Specific heat, thermal conductivity and viscosity are modelled using theoretical and experimental relations available in the literature. Nanofluids in the system result on greater entropy generation and pumping power consumption when compared with base fluid. MPCMs slurries produce the minimum entropy generation and pumping power consumption. Mixtures are affected by the content of nanofluids resulting in a performance below of MPCMs slurries. The improvement on heat capacity of the fluid produced by Microencapsulated phase change material is the main factor in reducing entropy generation and pumping power consumption for the system. KEYWORDS Entropy, heat transfer, engineered fluids, MWCNT nanofluids, MPCM slurries. INTRODUCTION Several initiatives for the development of novel heat transfer fluids with improved thermophysical properties have been conducted in the last decades. The development of these new fluids have the potential of increasing energy efficiency and reduce capital cost with smaller systems (Choi et al. 2004; Alvarado et al. 2007). The most promising applications of these fluids are in closed loop heat transfer systems found on processing and power industries, district cooling, HVAC, refrigeration and microelectronics cooling. Geothermal heat pumps (GHPs) constitute a special kind of closed loop system used for heating and cooling applications. Since 1995, GHPs have experimented a significant growth especially in United States, Europe and Japan (Hepbasli andakdemir, 2004; ASHRAE, 2011). These systems may have potential to be used in tropical weathers as found in the Ecuadorian coast to replace evaporative cooling towers. The desirable properties of a heat transfer fluid used in closed systems are: high thermal conductivity, high heat capacity, low viscosity, stability, durability, non-toxic and chemically inert (Buongiorno et al., 2009; Saidur et al. 2011). Two trends have been explored to develop better engineered fluids: nanofluids and slurries of microencapsulated phase change materials. Page 1 of 8

2 Nanofluids exhibit a trade-off between thermal conductivity and viscosity (Das et al. 2008; Buongiorno et al. 2009), and slurries of microencapsulated phase change material a trade of between heat capacity and viscosity (Zhao and Zhang, 2011). Additionally, efforts to combine nanofluids and MPCMs slurries advantages have been done by Alvarado et al. (2007) and Tumuluri et al. ( 2011). The tradeoffs between properties make the selection of the appropriate fluid for a given application a complex task. A candidate methodology for selecting the appropriate fluid and system design is entropy generation minimization. This methodology was presented by Sahin ( 2000) to model simple systems like constant wall temperature and constant heat flux with water and glycerol. Singh et al. ( 2010) used entropy generation minimization methodology to study alumina based nanofluids and Bejan ( 1979,1995) developed the methodology for analyzing entropy generation in forced convective heat transfer withvarious geometries. The present work uses entropy generation analysis and pump power consumption to develop an optimum thermal design of the GHP system approximated as a constant temperature loop. This methodology allows for comparison of mixtures containing Microencapsulated Phase Change Material (MPCM) and multiwalled carbon nanotube based nanofluid with a base fluid with the objective of developing a design tool for engineering applications. METHODS Density( ), specific heat( ), thermal conductivity( ), and dynamic viscosity ( ) are the main thermophysical properties required for analyzing a thermodynamic system. In a previous study (Porras et al. 2013) a mixture of water, octadecane based MPCMs and multiwalled carbon nanotubes NP was used to analyze the entropy generation of a heat exchanger with constant heat flux. In this work, a Ground Source Heat Exchanger (GHX) was approximated as internal flow on a tube under constant wall temperature. For the selected operation conditions eicosene (C 20 H 40 ) was chosen as the MPCM due to its phase change temperature 36.4 C (Thermal-FluidsPedia ) which allows an adequate temperature gradient for its operation. Blend Properties Model The blend is a mixture of MPCM slurry and MWCNT based nanofluid with fixed volume fractions. Equation (1) use simple mixing theory to define density. ( ) (1) For specific heat, Mulligan (Mulligan et al. 1996) derived equation (2) from an energy balance. ( ( ) ) (2) The thermal conductivity can be modeled using a linear blending rule for two components as given in equation (3). Other models have a deviation of less than 10% respect to this linear blending rule (Assael et al. 1992; 2004). Thermal conductivity of MPCM slurry is calculated using Maxwell s relation (Maxwell, 1881). Thermal conductivity of nanofluids is modeled using Hamilton and Crosser relationship (Hamilton and Crosser, 1962) Page 2 of 8

3 ( ) (3) In the case of viscosity, Drew and Passman (1999) proposed a linear equation for newtonian suspensions including a linear viscosity coefficient (Cμ) depending on the type of nanoparticle used. In the case of a mixture of NP and MPCM we expand Drew model to obtain the linear equation (4). ( ) (4) The MPCM and NP viscosity coefficients (, respectively) were chosen such that at certain concentrations of MPCM or NP the effective viscosity calculated from equation (4) matches experimental data reported in literature (Tumuluri et al. 2011). Ground heat exchanger (GHX) model The GHX can be approximated to a constant wall temperature model as shown in Figure 1. With inlet temperature and wall temperature, refrigeration thermal loads were considered and different temperature variations between the inlet and outlet were assumed. These values were chosen to represent commercially available equipment. Figure 1. Ground heat exchanger model According with commercial data sheets and in agreement with operating conditions a diameter of GHX was selected. For each cooling load and temperature variation a flow rate of the base fluid can be computed from equation (5). (5) The effective flow rates of the blend are computed by equating heat capacity rates of working fluid and base fluids as expressed in equation (6). (6) Considering the numerical values defined above for cooling load, the inlet, outlet and wall temperatures eported the length of GHX must be computed with equation (7) to satisfy the heat transfer phenomena. ( )( ) (7) Where St is the Stanton number and section. is the dimensionless length defined in the nomenclature Friction losses are computed with equation (8) (White, 1999). Page 3 of 8

4 (8) Entropy Model Assuming homogeneous mixture, incompressible flow, constant properties, no change in chemical composition, newtonian behavior and fully developed flow (hydrodynamic and thermally) under turbulent regime. An entropy generation rate expression (equation 9) for constant wall temperature under above mentioned condition was developed by Şahin (2000). { [ ] ( ) [ ]} (9) Where dimensionless temperature difference and Eckert number are defined by the expressions given in nomenclature. Darcy friction factor for smooth surfaces is used equation (10) (Incropera and De Witt, 1985) ( ( ) ) (10) Nusselt number at equation (11) (Incropera and De Witt, 1985) ( )( ) ( )( ) (11) Table 1. Thermophysical properties of components at 25 C Parameter Symbol Value Parameter Symbol Value Base Fluid Density 1000 NP Conductivity 80 ( ) NP Density 2100 MPCM Conductivity ( ) MPCM Density 0856 NP Conductivity Coefficient. 11 Base Fluid Specific MPCM Conductivity ( ) Heat Coefficient NP Especific Heat ( ) Base Fluid Viscosity 0.89E-3 MPCM Specific Heat ( ) NP Viscosity Coefficient 120 MPCM Latent Heat ( ) MPCM Viscosity Coefficient. 15 Base Fluid Conductivity ( ) RESULTS Figure 2 shows results of entropy generation for turbulent flow regime with a cooling load of 35 kw and temperature variation of 4 (case a) and 5 C (case b). Results show that for small temperature variations the entropy generation is reduced with MPCM slurry. For large temperature variation, water entropy generation is minimum. Figure 3 shows results of entropy generation with cooling loads of 106 kw (case a) and 176 kw (case b), both with temperature variation of 5 C. Results show that for larger cooling loads the use of MPCM provides a benefit from the entropy generation perspective. In all cases the use MWCNT increases entropy generated, which is not beneficial. Page 4 of 8

5 a) b) Figure 2. Entropy generated, cooling load 35 kw, 50.8mm diameter pipe, a) 4 ºC, b) 5 ºC fluid temperature variation between the inlet and outlet. a) b) Figure 3. Entropy generated, 5 ºC fluid temperature variation between the inlet and outlet and pipe diameter of 50.8mm, a) 106 KW, b) 176 kw. Figure 4 shows the tendencies of friction losses at different cooling loads and temperature variations versus MPCM volume fraction. For high cooling loads, an increase in MPCM reduces friction losses even at higher temperature variations. a) b) Page 5 of 8

6 Figure 4. Friction loss. Several temperature variations, 50.8mm diameter pipe, a) 35kW, b) 176kW DISCUSSIONS An analysis of equation (15) shows that heat transfer entropy generation due to heat transfer is kept constant (first and second terms), because operation conditions such as temperature variations and cooling load were set to constant values. Increasing volume fraction of MPCM and nanoparticle in the blend caused the dimensionless length to increase because advection in the fluid is reduced (lower Reynolds numbers and high viscosity), the Stanton number which represents the ratio between heat transfer due to convection and advection decreases in the same proportion. The amount remains constant despite having different concentrations of blend components. Since heat transfer entropy generation is constant the shape of Figure (2) and (3) is due to friction entropy generation. Use of MWCNT for this kind of applications is not recommended, as can be observed in Figures (2) and (3). The thermal conductivity of the fluid is improved when using nanoparticles, but this improvement becomes negligible because advection (important in turbulent flow) is reduced due to increase in viscosity which also increases friction losses. Use of MPCM increases the effective specific heat which depends on temperature variation (equation (4)). For high temperature variations adverse effects of viscosity overcome benefits of specific heat increment in the blend, this increase implies a mass flow reduction, equation (13). A consequence of adverse effect of viscosity is an increase in GHX length. Using MPCM friction losses are reduced (Figure (4)), which is attributed to flow rate reduction, although at high temperature variations greater than 5K this trend changes (Figure 4a). For cooling loads greater than 176 kw this trend can be maintained until temperature variations below 5K. The effect of friction loss reduction becomes negligible due to the increase in viscosity (Figure 4b). For temperature variations greater than 6K, the increase in effective specific heat does not make up the increase in viscosity, and losses due to friction increase almost linearly with increasing volume fraction of MPCM. CONCLUSIONS The constant temperature assumption can be improved to more realistic conditions. Soil stratification in which each layer has different thermal properties could be considered. Also the temperature variation as a function of depth and place could be modeled. Finally, effects of groundwater convective flows could be studied. For the considered assumptions, the effect of adding MPCM to the base fluid decreases friction losses for small temperature variations. This result is important because pumping power is diminished, despite increasing the length and therefore the initial costs and operational costs would decrease achieving a net savings over the life of the system. The method of entropy generation minimization (EGM) represents a first step in the analysis of a realistic thermal system as the analyzed GHX, the main difficulty of this tool is the development of an acceptable and representative model which helps to identify and quantify the irreversibilities found in the system in order to optimize its design and thermodynamic cycle in which it is operating. Further analysis is necessary to obtain experimental data for thermophysical properties and flow regimes which would result in more accurate models that help to represent in a better form the heat transfer phenomena. The first approach of newtonian fluid assumption helps to simplify the problem because results can be obtained quickly. This would serve as a reference Page 6 of 8

7 for comparison with subsequent works where the non-newtonian nature of the fluid is considered. NOMENCLATURE d GHX diameter Greek Symbols f Friction Factor Density Cp Especific Heat Volumetric Fraction H Latent Heat Phase Change Percentage T Temperature Viscosity Re Reynolds number, [ ( )] Dimensionless temperature,[( ) ] Pr Prandtl number, [ ] Dimensionless Length, [ ] Nusselt number, [ ] Subscrips Stanton number, [ ( )] np Nano Particles Eckert number, [ ( )] eff Effective Cooling Load mpcm Microencapsulated Phase Change Entropy Generation rate nf Nano Fluid Mass Flow bf Base Fluid L GHX lenth in Inlet Friction Loss Power w Wall Temperature Gradient K Termal Conductivity Viscosity Coefficient X Mass Fraction REFERENCES Alvarado, J.L., Marsh, C., Thies, C., Soriano, G. and Garg, P., Characterization of thermal properties and heat transfer behavior of microencapsulated phase change material slurry and multiwall carbon nanotubes in aqueous suspension, 2007, ASME. Alvarado, J.L., Marsh, C., Sohn, C., Phetteplace, G. and Newell, T., Thermal performance of microencapsulated phase change material slurry in turbulent flow under constant heat flux. International Journal of Heat and Mass Transfer, 50(9-10), pp ASHRAE, Chapter 34: Geothermal Energy ASHRAE HANDBOOK - HVAC Applications. Atlanta, Ga: ASHRAE, pp Assael, M., Chen, C., Metaxa, I. and Wakeham, W., Thermal conductivity of suspensions of carbon nanotubes in water. International Journal of Thermophysics, 25(4), pp Assael, M., Dymond, J., Papadaki, M. and Patterson, P., Correlation and prediction of dense fluid transport coefficients. III. n-alkane mixtures. International Journal of Thermophysics, 13(4), pp Bejan, A., A study of entropy generation in fundamental convective heat transfer. Journal of heat transfer, 101, pp Bejan, A., Entropy generation minimization: the method of thermodynamic optimization of finite-size systems and finite-time processes. CRC. Buongiorno, J., Venerus, D.C., Prabhat, N., McKrell, T., Townsend, J., Christianson, R., Tolmachev, Y.V., Keblinski, P., Hu, L. and Alvarado, J.L., A benchmark study on the thermal conductivity of nanofluids. Journal of Applied Physics, 106(9), pp Choi, S.U., Zhang, Z.G. and Keblinski, P., Nanofluids. Encyclopedia of Nanoscience and Nanotechnology, 6(1), pp Das, S.K., Choi, S.U., Yu, W. and Pradeep, T., Nanofluids: science and technology. Wiley-Interscience Hoboken, NJ. Page 7 of 8

8 Drew, D.A. and Passman, S.L., Theory of multicomponent fluids. Springer New York. Hamilton, R. and Crosser, O., Thermal conductivity of heterogeneous two-component systems. Industrial & Engineering chemistry fundamentals, 1(3), pp Hepbasli, A. and Akdemir, O., Energy and exergy analysis of a ground source (geothermal) heat pump system. Energy Conversion and Management, 45(5), pp Incropera, F.P. and De Witt, D.P., Fundamentals of heat and mass transfer. Maxwell, J.C., A treatise on electricity and magnetism. Clarendon Press. Mulligan, J., Colvin, D. and Bryant, Y., Microencapsulated phase-change material suspensions for heat transfer in spacecraft thermal systems. Journal of Spacecraft and Rockets, 33(2), pp Porras, F., Guevara, P. and Soriano, G., A Study for Entropy Generation of a Heat Transfer Fluid containing Multiwalled Carbon Nanotubes and Microencapsulated Phase Change Materials, Proceedings of Eleventh LACCEI Latin American and Caribbean Conference for Engineering and Technology (LACCEI 2013) Şahin, A.Z., Entropy generation in turbulent liquid flow through a smooth duct subjected to constant wall temperature. International Journal of Heat and Mass Transfer, 43(8), pp Saidur, R., Leong, K.Y. and Mohammad, H.A., A review on applications and challenges of nanofluids. Renewable and Sustainable Energy Reviews, 15(3), pp Singh, P.K., Anoop, K., Sundararajan, T. and Das, S.K., Entropy generation due to flow and heat transfer in nanofluids. International Journal of Heat and Mass Transfer, 53(21), pp Thermal-FluidsPedia Thermophysical Properties: Phase Change Materials Thermal-Fluids Central.Available: hysical_properties:_phase_change_materials [3/18/2013, 2013]. Tumuluri, K., Alvarado, J.L., Taherian, H. and Marsh, C., Thermal performance of a novel heat transfer fluid containing multiwalled carbon nanotubes and microencapsulated phase change materials. International Journal of Heat and Mass Transfer, 54(25), pp White, F.M., Fluid mechanics, WCB. Zhao, C. and Zhang, G.H., Review on microencapsulated phase change materials (MEPCMs): Fabrication, characterization and applications. Renewable and Sustainable Energy Reviews, 15(8), pp Page 8 of 8