# Second Law Analysis of Parallel Plate Ducts with Span Wise Periodic Triangular Corrugations at one Wall

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1 INTERNATIONAL JOURNAL OF MULTIDISCILINARY SCIENCES AND ENGINEERING, VOL., NO. 7, OCTOBER 011 Second La Analysis of arallel late Ducts it Span Wise eriodic Triangular Corrugations at one Wall Alireza Falaat Department of Mecanics, Masar Branc, Islamic Azad University, Masar, Iran Abstract In tis study, entropy eration for ydro dynamically and termally developing laminar flo in a parallel plate ducts it span ise periodic triangular corrugations at one all at constant eat flux is investigated. Entropy eration is obtained for various aspect ratio (α, various corrugation angle (Ф, various number of corrugation (n and various Reynolds number. It is found tat it te increasing aspect ratio (α and various number of corrugation (n values and decreasing corrugation angle (Ф, total entropy eration decreases, it increasing aspect ratio (α and corrugation angle (Фvalues and decreasing number of corrugation (n, pumping poer decreases. Keyords Second La, Corrugation Duct, Laminar Flo and Aspect Ratio M I. INTRODUCTION any studies in engineering area involve fluid flo and eat transfer inside a duct. To analyze te energy transfer in a termal system, te first la of termodynamics is alays used. Hoever, te investigation of exergy or irreversibility of a termal system requires te second la analysis, relating to an entropy eration. In fluid flo and eat transfer processes, te total entropy eration consists of te entropy eration due to viscous friction beteen te all and te fluid, and tat due to eat transfer across finite temperature differences beteen te all and te fluid. For internal flo, tere are to conditions, constant all temperature condition and constant all eat flux condition. Tese are often investigated in te entropy eration studies. arallel plate ducts it span ise periodic triangular corrugations are used in liquid gas eat excangers. Entropy eration due to eat transfer and fluid flo as been investigated by many researcers. Bejan [1] [3] analyzed eat transfers from ducts it constant eat flux for flat plates, cylinders in cross flo and rectangular ducts. erez-blanco [4] integrated te entropy eration rate along te entire surface of te eat excanger, and ten evaluated te effect of te eat transfer augmentation tecnique on te total entropy-eration rate. Sain [5] presented te second la analysis for different saped duct suc as triangular, sinusoidal etc, in laminar flo and constant all temperature boundary conditions. He made a comparison beteen tese ducts to find an optimum sape. He found tat te circular duct geometry is te favorable one among tem. He made anoter study in order to investigate te constant eat flux effects on tese cross-sectional ducts itout taking into account te viscosity variation in te analysis [6]. Viscosity variation as considered by Sain [7] for turbulent flo condition for circular ducts [8]. Recently, Oztop [9] made a study on entropy eration in semicircular ducts. Dagtekin et al. [10] investigated te problem for circular duct it different saped longitudinal fins for laminar flo using te similar metods of Sain [6]. Oztop et al. [11] made a study on entropy eration in rectangular ducts it semicircular ends ducts it to boundary conditions: constant all temperature and constant all eat flux and Jarungtammacote [1] investigated entropy eration for exagonal duct subjected to constant eat flux. Te main aim of tis study is to investigate entropy eration troug parallel plate ducts it span ise periodic triangular corrugations at one all at constant eat flux. To te best of te autor's knoledge te entropy eration in parallel plate ducts it span ise periodic triangular corrugations it constant eat flux as not yet been investigated. Te duct is assumed to be infinite in te span ise direction. Terefore, te end effects due to te sort bounding alls are neglected. Te corrugated all is subjected to te termal boundary condition, ile te flat all is considered to be adiabatic. Te present paper reports an analytical study of entropy eration in laminar flo. Te effect of aspect ratio, corrugation angle, number of corrugation and Reynolds number on entropy eration and pumping poer are analyzed. II. DEFINITION OF HYSICAL MODEL Te pysical model of parallel plate ducts it span ise periodic triangular corrugations at one all elliptical duct is depicted in Fig. 1. Te ydraulic diameter of any duct given by (1 D 4A p c [ISSN: ].ijmse.org 1

2 INTERNATIONAL JOURNAL OF MULTIDISCILINARY SCIENCES AND ENGINEERING, VOL., NO. 7, OCTOBER 011 ere Ac is cross-sectional area and is perimeter. Te ydraulic diameter for annular sector cross-sectional area can be ritten as: D n(1 α tanφ 1+ sinφ n(1 α 1+ cosφ ( A c Fig.. control volume for entropy eration Integrating Eq. 3 along te duct lengt L and by using Eq. 4-7, te dimensionless total entropy eration becomes Fig. 1. Cross section of parallel plate ducts it span ise periodic triangular corrugations at one all III. ENTROY GENERATION Te total entropy eration itin a control volume of tickness dx, son in Fig., along te duct can be ritten as follos: [( 1+ 4Stτλ( 1+ τ /( 1+ τ + 4Stτλ ] Ns ln (9 f Ec + ln 1 8St ( + 4Stτλ In tese equations some parameters can be made dimensionless as follos: Nu (10 St ρ UC Re r ds& δq& m& ds T and δ Q& mc & dt qp dx (4 For an incompressible fluid e ave (3 U Ec C ( T τ λ T T Ti ( q / T T L D i i (11 (1 (13 T ds C dt v d (5 ressure drop in Eq. 8 is given in te folloing equation. d fρu D dx Te bulk temperature variation of fluid along a duct can be ritten as follos 4q T T0 + ρudc x Te non-dimensional entropy eration number Ns can be defined as: S& S& Ns Q& / T mc & (6 (7 (8 Te fully developed ( f Re and Nu values obtained by Sparro and Carmci [13] for variety of duct geometries. IV. REQUIRED UMING OWER Te poer required to overcome te fluid friction in te duct in dimensionless form is Ac U R Q & (14 For constant all eat flux boundary conditions, te pumping poer to eat transfer ratio for fully developed laminar flo becomes µ ( f Re R Re 8ρ D q (15 [ISSN: ].ijmse.org

3 INTERNATIONAL JOURNAL OF MULTIDISCILINARY SCIENCES AND ENGINEERING, VOL., NO. 7, OCTOBER 011 V. RESULT AND DISCUSSION In tis section, te entropy eration due to eat transfer and viscous friction is investigated for fully developed laminar flo in te parallel plate ducts it span ise periodic triangular corrugations at one all at constant eat flux for ater. Te termo-pysical properties used are son in Table 1: Table 1: Termo-pysical properties of ater SYMBOL QUANTITY C ( J / kg K r (K T µ ( Ns / m ρ ( kg / m A. Effect of Aspect Ratio Fig. 3 sos dimensionless entropy eration for different aspect ratio (α of parallel plate ducts it span ise periodic triangular corrugations at one all at different Reynolds number values. In tis figure, total entropy eration decreases considerably ile te Reynolds number is increased. As te value of aspect ratio (α is increased total entropy eration decreased for fixed Reynolds number. Fig. 4 sos variation of pumping poer for different aspect ratio (α and Reynolds numbers. As aspect ratio (α is increased pumping poer to eat transfer ratio decreases. Wit increasing of Reynolds number pumping poer to eat transfer ratio values also increase. For a fixed Reynolds number as aspect ratio (α values are increased pumping poer to eat transfer ratio values are decreased, especially for iger values of Reynolds number. Tese results indicate tat for larger aspect ratio friction losses are smaller tan tat of loer aspect ratio as expected. 4 Fig. 4. Variation of pumping poer for different α values and Reynolds number (Φ600, τ0. 1, n3 B. Effect of Corrugation Angle Fig. 5 sos dimensionless entropy eration for different corrugation angle (Ф of parallel plate ducts it span ise periodic triangular corrugations at one all at different Reynolds number values. As te corrugation angle (Фis increased total entropy eration increases for fixed Reynolds number, especially for loer values of Reynolds number. Wit increasing of Reynolds number total entropy eration values also decrease. Fig. 6 sos variation of pumping poer for different corrugation angle (Ф and Reynolds numbers. As te corrugation angle (Ф is increased pumping poer to eat transfer ratio decreases. Wit increasing of Reynolds number pumping poer to eat transfer ratio values also increase. For a fixed Reynolds number as corrugation angle (Ф are increased pumping poer to eat transfer ratio values are decreased, especially for iger values of Reynolds number. Tese results indicate tat for larger corrugation angles (Ф friction losses are smaller tan tat of loer sector angels (Ф as expected. Fig. 5. Variation of dimensionless entropy eration for different corrugation angles values and Reynolds number (α 0.3, τ0. 1, n3 Fig. 3. Variation of dimensionless entropy eration for different α values and Reynolds number (Φ600, τ0. 1, n3 [ISSN: ].ijmse.org 3

4 INTERNATIONAL JOURNAL OF MULTIDISCILINARY SCIENCES AND ENGINEERING, VOL., NO. 7, OCTOBER 011 Fig. 6. Variation of pumping poer for different corrugation angles values and Reynolds number (α 0.3, τ0. 1, n3 Fig. 8. Variation of pumping poer for different number of corrugation values and Reynolds number (α 0.3, Φ600, τ0. 1 C. Effect of Number of Corrugation Fig. 7 sos te effects of number of corrugation on entropy eration at different Reynolds numbers for a fixed aspect ratio (α 0.3 and corrugation angle (Ф600, namely, for a fixed cross sectional area. Entropy eration is influenced by number of corrugation. As Reynolds number is increased, te dimensionless entropy eration decreases. Tus, loer entropy eration is obtained for smaller value of number of corrugation. Te decrease of total entropy eration depends on te decrease of number of corrugation as expected. Fig. 8 sos variation of pumping poer to eat transfer ratio for various number of corrugation and Reynolds numbers. Increasing Reynolds number yields iger pumping poer to eat transfer ratio values for fixed number of corrugation. As te number of corrugation is increased pumping poer to eat transfer ratio values increases for fixed Reynolds number, especially for iger values of Reynolds number. Fig. 7. Variation of dimensionless entropy eration for different number of corrugation values and Reynolds number (α 0.3, Φ600, τ0. 1 VI. CONCLUSION In tis study second la analysis of laminar flo subjected to constant all eat flux as been obtained for parallel plate ducts it span ise periodic triangular corrugations at one all. Some conclusions can be given as follos: As Reynolds number is increased total entropy eration is decreasing. Wit increasing value of aspect ratio (α and decreasing corrugation angle (Ф are decreased total entropy eration for fixed Reynolds number. Te pumping poer ratio decreases as te aspect ratio (α, and decreases as corrugation angle (Ф are increased. Wen number of corrugation is increased total entropy eration and pumping poer ratio are increasing for fixed Reynolds number. A a b C c D Ec f k L m& n Ns Nu p r R q NOMENCLATURE cross-sectional area of duct, m igt of duct, m igt of duct, m specific eat, J / kg K ydraulic diameter, m Eckert number Darcy friction factor eat transfer coefficient, W / m K termal conductivity of fluid, W / m K Lengt of duct, m mass flo rate, kg / s number of corrugation dimensionless entropy eration Nusselt number ressure, a erimeter of duct, m randtl number pumping poer to eat transfer rate ratio eat flux, W / m [ISSN: ].ijmse.org 4

5 INTERNATIONAL JOURNAL OF MULTIDISCILINARY SCIENCES AND ENGINEERING, VOL., NO. 7, OCTOBER 011 Q & Re St s S & T T i T U x Total eat flux, W Reynolds number Stanton number entropy, Greek alpabets T α ρ Φ τ µ λ W / K entropy eration rate, Temperature, K Inlet fluid temperature, K W / K Wall temperature of te duct, K velocity in coil tube, axial distance, m m / s increase of fluid temperature, K Total pressure drop, Aspect ratio, density, a / b 3 kg / m alf of corrugation angle N / m dimensionless temperature difference viscosity, a s dimensionless axial distance Communications in Heat and Mass Transfer, vol, 48, 005, pp [11] Ozotop, HF., Dagtekin, I., Sain, AZ., Second la analysis of fully developed laminar flo for rectangular ducts it semicircular ends, International Communications in Heat and Mass Transfer, vol 36, 009pp [1] Jarungtammacote, S., Entropy eration analysis for fully developed laminar convection in exagonal duct subjected to constant eat flux, Journal of Energy, vol, 35, 010, pp [13] Sparro, E.M., Carmci, M., Heat Transfer and Fluid Flo Caracteristics of Span ise eriodic Corrugated Ducts, International Journal of Heat and Mass Transfer, vol, 3, 1980, pp Alireza Falaat Faculty Member of Department of Mecanical Engineering, Masar Branc, Islamic Azad University, Masar, Iran. Tel: REFERENCES [1] Bejan, A., Second-la analysis in eat transfer, International Journal of Energy,vol,5, 1980, pp [] Bejan, A., Second-la analysis in eat transfer and termal design, Advanced Heat Transfer, vol, 15, 198, pp [3] Bejan, A., Fundamentals of exergy analysis, entropyeration minimization, and te eration of flo arcitecture, International Journal of Energy Researc, vol, 6, 00, pp [4] erez, Blanco., Irreversibility in eat-transfer enancement. In: Second la aspects of termal design, Ne York: ASME, vol, 33, 1984, pp [5] Sain, AZ., A second la comparison for optimum sape of subjected to constant all temperature and laminar flo, Heat and Mass Transfer, vol, 33, 1998, pp [6] Sain, AZ., Irreversibilities in various duct geometries it constant all eat flux and laminar flo, Journal of Energy, vol, 3, 1998, pp [7] Sain, AZ., Second la analysis of laminar viscous flo troug a duct subjected to constant all temperature, Journal of Heat Transfer, vol, 10, 1998, pp [8] Sain, AZ., Entropy eration in turbulent liquid flo troug a smoot duct subjected to constant all temperature, International Journal Heat and Mass Transfer, vol, 43, 000, pp [9] Ozotop, HF., Effective parameters on second la analysis for semicircular ducts in laminar flo and constant all eat flux, International Communications in Heat and Mass Transfer, vol, 3, 005, p [10] Dagtekin, I., Ozotop, HF., Sain, AZ., An analysis of entropy eration troug a circular duct it different saped longitudinal fins for laminar flo, International [ISSN: ].ijmse.org 5

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