Mohammad Ali Abdous *, Shahriyar Ghazanfari Holagh, Masood Shamsaiee, Mohsen khoshzat and Hamid Saffari

Transcription

1 Conference Proceedings Paper An Ealuation of Heat ransfer Enhancement echnique in Flo Boiling Conditions Based on Entropy Generation Analysis: Micro-Fin ube Mohammad Ali Abdous *, Shahriyar Ghazanfari Holagh, Masood Shamsaiee, Mohsen khoshzat and Hamid Saffari School of Mechanical Engineering, Iran Uniersity of Science and echnology, ehran , Islamic Republic of Iran * Correspondence: el.: ; Fax: Abstract: he flo boiling heat transfer is one of the common phenomenon happening in the industries. he micro-fin tubes are one of the geometries idely used to enhance heat transfer rate in boiling condition. he entropy eration analysis is presented ith its formulation to find precisely the best operating conditions in micro-fin tubes in terms of geometrical parameters and flo conditions. his analysis shos important aspects of losses in fluid systems undergoing boiling. he losses include thermal loss related to the heat transfer and hydraulic one related to the pressure drop. he releant terms are described for both of these losses. he optimum tube diameter under specified conditions is found. he effect of different flo conditions such as mass elocity, inlet apor quality on contribution of pressure drop and heat transfer in entropy eration is discussed. It is discoered that there is a desirable set of conditions of fluid flo and micro-fin geometrical shape for hich the minimum entropy eration is reached. Keyords: entropy eration analysis (EGA; flo boiling; enhanced heat transfer; micro-fined tube; pressure drop 1. Introduction Various researchers hae conducted studies on the entropy eration in heat exchangers. Manjunath and Kaushik (2014 performed a reie on the importance of first and second la of thermodynamics in entropy eration analysis. Also, the application of the entropy eration analysis in design and optimization of engineering systems as reieed by Sciacoelli et al. (2015. Naphon (2011 presented experimental results as ell as theoretical formulations for entropy eration and exergy destruction in a tubular heat exchanger. hey included the effect of fluid temperature ariations along the length of the heat exchanger. heir results indicated that for a constant hot ater mass flux, the entropy eration number increases for higher inlet temperatures. Ye and Lee (2012 inestigated a numerical model for fin-and-tube condensers ith complex refrigerant circuit based on entropy eration. Compared to the condensers ith simple refrigerant path, there as an appreciable enhancement in heat transfer performance. Manjunath and Kaushik (2015 conducted an analytical analysis on an unbalanced heat exchanger based on the second la of thermodynamics. hey aried the length-to-diameter ratio for both counter flo and parallel flo configurations. heir results shoed that the dimensions for optimum heat exchanger design, namely length-to-diameter ratio, can be found. Some studies hae been published ith the focus on the entropy eration analysis in tophase flos in heat exchanger. Kaushik and Manjunath (2011 analyzed a single pass double pipe to phase flo heat exchanger. Based on the second la, they mainly considered three to-phase he 4th International Electronic Conference on Entropy and Its Applications (ECEA 2017, 21 Noember 1st December 2017;

2 flo regimes. hey reported their results of entropy eration number by arying parameters such as diameter, mass elocity, all superheat, and quality. Fe efforts hae been made to inestigate entropy eration in to-phase flos in tubes and channels. he local entropy eration for diabatic to-phase flo as studied by Reellin et al. (2009. hey performed a study on local entropy eration of to-phase diabatic flos. In order to analyze the entropy eration in saturated flo boiling in pipes, they deeloped to models, namely separated flo model and mixture model. Entropy eration in the eaporator of a apor compression refrigeration cycle as inspected by ürkakar and Okutucu-Özyurt (2015 by studying the ariations of channel height and idth, the heat flux, the mass flo rate and seeral other parameters. hey concluded that increasing heat flux increases the entropy eration. Abdous et al. (2015 conducted a comprehensie study on using of entropy eration analysis in a helically coiled tube in flo boiling condition under a constant heat flux. hey inestigated changing of important flo parameters such as saturation temperature, heat flux and apor quality on entropy eration. he optimum coil diameter as found based on their analysis. he main goal of this study is to find the optimum diameter of the micro-fin tube by means of entropy eration analysis. hen, ariation of flo conditions such as apor quality and mass elocity is studied on entropy eration and contribution of pressure drop and heat transfer one. 2. Mathematical Modeling Suppose a mixture of liquid and apor in saturated conditions enters a tube under constant all heat flux. he mathematical model of saturated to-phase flo is based on the second la of thermodynamics. For a finite control olume of length dl, the total entropy eration per unit length S can be ritten as: S here m is the total mass flo rate, Q m d( xs + (1 x sl = dl denotes the channel all temperature, Q is the rate of heat transfer into the control olume and s is the entropy. he apor quality can be defined as Equation (2: m x = (2 m + m he entropy eration per unit length ( And, the alues of dh and S l becomes: Q S d z= m ( sldx+ xd s + (1 xd sl (3 dhl are: dh = ds + dp (4 dh = ds + dp (5 l l l l l (1 2

3 herefore, in Equation (3, the alues of ds and ds l are obtained from Equations (4 and (5. h = =, dp = dp l l and sl = in saturated flo boiling, the entropy Assuming l sat eration per unit length ( sat S can be reritten as: m Q mx ( + (1- x l Sd z = ( hldx+ xdh + ( 1- x dhl - - dp 3 sat (6 m Q m Using the first la of thermodynamics Q is obtained as: dp dz = dh (7 sat sat S Q = mh d (8 Simplifying Equation (7 by using Equation (8, the final term for the entropy eration per unit length is S m d z sat sat d z dh 1 1 dp = (9 o contributions can be understood of the entropy eration per unit length ( sat S in Equation (9. he heat transfer contribution [(Equation (10], and the pressure drop contribution [Equation (11]; dh 1 1 = (10 S,ht m d z sat S m,pd = st a dp ( dz (11 being the to-phase pressure drop of tube coering graitational and acceleratie pressure drops. he relationship beteen apor quality and oid fraction is obtained from (Woldesemayat and A. J. Ghajar, 2003; = (1 +cos(. ( sin (12 here, and are the superficial liquid and gas elocity, respectiely, is the graitational acceleration and the is tube inclination angle. and are respectie densities of apor and liquid. is the fluid surface tension. In the case of a micro-fin tube, is the tube hydraulic diameter. is the atmospheric pressure and the is the system pressure. 3. Results and Discussions Figure 1 shos a schematic of a tube-in-tube straight heat exchanger designed by Wongsangam et al. of a micro-fin tubes for obtaining correlations of heat transfer coefficient and frictional pressure drop. HFC-134a flos in the inner tube, hile heating ater flos in the annulus in counter direction.

4 Figure 1. he schematic figure of the micro-fin tube-in-tube heat exchangers [Wongsa-ngam et al., 2002] he Geometrical Parameters of the Micro-Fin ube First, the geometry of micro-fin must be demonstrated here by some details. Important Parameters height (, the bottom idth (, the bottom thickness ( and the angle are shon in Figure 2. Symbol ( denotes the number of fins for the micro-fin tube. Figure 2. he cross sectional ie of the micro-fin tube (Wongsa-ngam et al., S is the distance beteen to tips of fins (Wongsa-ngam et al., 2002; S =B + 2e cos(α (137 he cross sectional tube all area per fin A and cross sectional flo area A are defined as follo; he hydraulic diameter is; he alpha angle (α in Figure 2 is: A =e tan(α + (2e tan(α +B B A = πd (148 4 NA (19 D = 4A cos(β NS (20 πd α=tan ( N B (21 2e he flo conditions are constant and presented in able 1. able 1. he assumed flo parameters. ( ( (

5 he increase in the alue of the mass flo rate is directly proportional to the square of tube outer diameter (D. In the micro-fin tube, the mass flo rate ( =A aries ith A (Equation (19. In addition, at constant heat flux, the alue of total heat rate entering the micro-fin tube is proportional to the tube outer diameter (D. herefore, the apor quality decreases hich leads to increase in the alue of mixture density. Consequently, at constant mass elocity, the mixture elocity and pressure drop decrease. At lo alues of tube outer diameter (D, the decrease in pressure drop causes a reduction in pressure drop contribution. Gradually, the increase in the alue of tube outer diameter (D, leads to an increase in pressure drop contribution. herefore, at this region the increase in the alue of mass flo rate becomes the dominant parameter in increasing the pressure drop contribution as shon in Figure 3. Consequently, the minimum point appears in the pressure drop contribution for the micro-fin one. Finally, the tube ith 5 mm outer diameter is recognized as an optimum for mentioned conditions. Figure 3. he entropy eration, pressure drop contribution and the heat transfer one for the microfin tube ith flo conditions (able 1 and geometrical parameters (able 2. able 2. he assumed geometrical parameters hen the tube outer diameter ( changes from 4 mm to 14 mm. (mm (mm (mm (m Change in Flo Conditions In this section, the geometrical parameters for the micro-fin tube are assumed to match ith the study of Wonsagam et al. as mentioned in able 3. able 3. he geometrical parameters for the micro-fin tube. (mm (mm (mm (mm (m

6 Assuming the geometrical parameters in able 4, the effect of changing in the flo conditions such as mass elocity (, inlet apor quality ( is studied. he ariation of entropy eration, and the respectie pressure drop and heat transfer contributions are plotted ersus mass elocity ( in Figure 4 for micro-fin tube. At constant heat flux, as the alue of mass elocity ( increases, the heat transfer coefficient rises (Wongsangam et al., herefore, the heat transfer contribution in entropy eration decreases (Equation (10. Moreoer, the increase in results in an increase in the frictional losses in both tubes. hus, the pressure drop contribution in entropy eration increases. Figure 5 illustrates the effect of ariation of inlet apor qualities ( on total entropy eration and its components for the micro-fin tube (able 3. able 4. he assumed flo conditions hen the alue of mass elocity ( changes from. ( ( Figure 4. he ariation of entropy eration, pressure drop contribution and heat transfer one ersus mass elocity ( for the micro-fin tube geometrical parameters (able 3 ith assumed flo conditions (able 4 he flo conditions are presented in able 5. he reduction in to-phase mixture density at constant mass elocity (450 kgm 2 s 1, is the result of increasing the inlet apor quality from 0.1 to 0.5. herefore, the mixture elocity and pressure drop contribution increasing gradually. he rising the alue of inlet apor quality results in higher heat transfer coefficients (Wongsangam et al., his means that for higher the heat transfer contribution is loer. able 5. he flo conditions hen inlet apor quality ( changes from

7 ( ( ( Figure 5. he ariation of entropy eration, pressure drop contribution and heat transfer one ersus inlet apor quality ( for the micro-fin tube geometrical parameters (able 3 ith assumed flo conditions (able Conclusions Enhancement of heat transfer rate is possible using arious passie methods. Creating microfins in the tube is one of the passie methods to augment the heat transfer coefficient. o ealuate this method, the entropy eration analysis is used in flo boiling. By using entropy eration analysis, the tube optimum diameter is found for specified flo conditions. he ariation of flo parameters such as mass elocity and apor quality is considered. It is shoed that, by increasing both of these factors, the contribution of pressure drop increases hile the heat transfer one decreases. Conflicts of Interest: he authors declare no conflict of interest. Nomenclature A Cross section (m 2 Cross sectional flo area (m 2 Cross sectional tube all area per fin (m 2 Be Bejan number ( Bottom thickness (m Bottom idth (m d Element discretization (m D Hydraulic diameter (m D ube outer diameter (m Fin height (m e 7

8 2 1 G Mass elocity ( kgm s 1 H Specific enthalpy ( Jkg L Length (m 1 Mass flo rate ( kgs N Number of fins( N s Entropy eration number ( P Pressure (Pa P Perimeter (m 2 Q Heat flux ( Wm Q Heat rate (W 1 S Specific entropy ( JK S Entropy eration per unit length ( Wm K emperature ( C U Conectie heat transfer coefficient ( Wm K Liquid superfacial elocity ( Gas superfacial elocity ( Greek symbols Void fraction ( Fin angle (deg. 3 Density ( kgm Fin spiral angle (deg. Specific olume (m 3 1 kg Subscripts ht Heat transfer in Inlet l Liquid pd Pressure drop sat Saturation o-phase Vapor Wall x Vapor quality References Abdous, M.A.; Saffari, H.; Aal, H.B.; Khoshzat, M. Inestigation of entropy eration in a helically coiled tube in flo boiling condition under a constant heat flux. Int. J. Refrig. 2015, 60, Kaushik, S.C.; Manjunath, K. Second la analysis of condenser by using ne heat transfer and pressure drop model based on flo regimes. Int. J. Exergy 2011, 9, Manjunath, K.; Kaushik, S.C.; 2014b. Second la thermodynamic study of heat exchangers: A reie. Rene. Sustain. Energy Re. 2014, 40, Manjunath, K.; Kaushik, S.C. Second la efficiency analysis of heat exchangers. Heat ransf. Res. 2015, 44, Naphon, P. Study on the exergy loss of the horizontal concentric micro-fin tube heat exchanger. Int. Commun. Heat Mass ransf. 2011, 38, , doi: /j.icheatmasstransfer Reellin, R.; Lips, S.; Khandekar, S.; Bonjour, J. Local entropy eration for saturated to-phase flo. Energy 2009, 34, Sciacoelli, A.; Verda, V.; Sciubba, E. Entropy eration analysis as a design tool A reie. Rene. Sustain. Energy Re. 2015, 43,

9 8. ürkakar, G.; Okutucu-Özyurt,. Entropy eration analysis and dimensional optimization of an eaporator for use in a microscale refrigeration cycle. Int. J. Refrig. 2015, 56, Woldesemayat, M.A.; Ghajar, A.J. Comparison of oid fraction correlations for different flo patterns in horizontal and upard inclined pipes. Int. J. Multiph. Flo 2007, 33, Wongsa-ngam, J.; Nualboonrueng,.; Wongises, S. Performance of smooth and micro-fin tubes in high mass flux region of R-134a during eaporation. Heat Mass ransf. 2002, 40, Ye, H.-Y.; Lee, K.-S. Refrigerant circuitry design of fin-and-tube condenser based on entropy eration minimization. Int. J. Refrig. 2012, 35, by the authors. Licensee MDPI, Basel, Sitzerland. his article is an open access article distributed under the terms and conditions of the Creatie Commons Attribution (CC BY license (ht://creatiecommons.org/licenses/by/4.0/. 9