ENTROPY GENERATION ANALYSIS FOR A PULSATING HEAT PIPE

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1 Heat Transfer Research 44(1), 1 30 (2013) ENTROPY GENERATION ANALYSIS FOR A PULSATING HEAT PIPE Sejung Kim, 1 Yuwen Zhang, 1,* & Jongwook Choi 2 1 Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA 2 School of Mechanical and Aerospace Engineering, Sunchon National University, Jeonnam , Korea Address all correspondence to Yuwen Zhang zhangyu@missouri.edu The entropy generation is based on the second law of thermodynamics. In the present study, the entropy generation in a U shaped Pulsating Heat Pipe (PHP) is investigated numerically. The following five parameters, which are vapor mass, liquid temperature, latent heat, sensible heat, and friction, determine the entropy generation. The results show that the entropy generation is significantly affected by the initial temperature in the PHP. Particularly, variation of the vapor mass is a primary factor of entropy generation. On the other hand, the amplitude of the entropy generation is barely related to the pressure loss at the bend in the PHP. However, the frequency of entropy generation with the pressure loss is faster than that without the loss of pressure at the bend. KEY WORDS: pulsating heat pipe, entropy generation 1. INTRODUCTION In the past two decades, applications of heat pipes were focused on the purpose of cooling an electronic system. However, most electronic systems generate a lot of heat these days, because the systems are getting smaller and faster. The demand for the cooling function of the heat pipe is increasing, and it does not require the outside driving power. Also, the new ideas and designs for the heat pipe are still being investigated and developed to reduce the heat that could cause serious problems. The research on the heat pipe begun in 1960 s as several scientists started the invention of the conventional heat pipe. Trefethen (1962) grafted the idea of the heat pipe onto his space program. Grover et al. (1964) and Grover (1966) revealed that the sodium heat pipe is very effective in heat transport with a high performance. They presented experimental results for using the working fluids such as sodium, silver, and lithium in a stainless steel heat pipe with a screen wick. The /13/$ by Begell House, Inc. 1

2 2 Kim, Zhang, & Choi NOMENCLATURE A area, m 2 Q in,s,l sensible heat transfer into c p specific heat at constant liquid slug, W pressure, Q out,s,l sensible heat transfer out c v specific heat at constant of liquid slug, W volume, J/kg K R curvature radius of bend, mm d diameter of heat pipe, m R gas constant of vapor, g gravity, m/s 2 kj/kg K h(h lsen, h lv ) coefficient of convective heat Re Reynolds number transfer of liquid slug, W/m 2 K s specific entropy, kj/kg K k thermal conductivity, W/m K S entropy, kj/k K loss coefficient t time, s L length, m T temperature of liquid slug, K L p length of liquid slug, m v p velocity of liquid slug, m/s m mass of vapor plugs, kg x p displacement of liquid slug, m. m mass flow rate, kg/s Greek symbols Nu Nusselt number α thermal diffusivity, m 2 /s p vapor pressure, Pa γ ratio of specific heats Q heat capacity, kj Δ difference Q in,v1 evaporation heat transfer rate ρ density, kg/m 3 of left vapor plug, W τ p shear stress, N/m 3 Q out,v1 condensation heat transfer rate Subscripts of left vapor plug, W 0 initial condition Q in,v2 evaporation heat transfer rate B bend of right vapor plug, W l liquid Q out,v1 condensation heat transfer rate v vapor plug of right vapor plug, W W wall results produced the development of the heat pipe as the effective thermal device. Also, Leefer (1966) and Judge (1966) carried out the research on the heat pipe and showed that the maximum operating temperature of the heat pipe can be as high as 1650 o C. Several scientists began their researches with the heat pipe to dissipate heat from electronic devices. Akachi (1994) developed the Pulsating Heat Pipe (PHP) which was filled partially with a working fluid and it oscillated due to liquid vapor phase Heat Transfer Research

3 Entropy Generation Analysis for a Pulsating Heat Pipe 3 changes. The PHP could run with a small pressure difference, because the working fluid had no need to flow through the wick structure. Also, the PHP could reduce costs, because the wick structure was not required. Therefore, most of researchers used the PHP in which the working fluid moved back and forth between the evaporator and the condenser for heat transfer (Gi et al., 1999; Khandekar and Groll, 2001, 2003; Khandekar et al., 2003a; Zhang et al., 2004). Dobson and Harms (1999) described the motion of the working fluid in a PHP with an open end mathematically. They considered the heat transfer coefficient between the wall and vapor and ignored the effect of the surface tension and of the heat transfer from the surrounding liquid. Cai et al. (2002) visualized the processes of heat transfer and working fluid motion by using a plastic or glass PHP. They also showed that the pulsating motion improved if a working fluid had a low latent heat. Hosoda et al. (1999) computed the temperature and pressure of PHPs by solving the momentum and energy equations for a two-dimensional two-phase flow. Zhang and Faghri (2002) considered thin film evaporation and condensation and showed that the heat transfer of a PHP is dominated by the sensible heat regardless of the surface tension. Groll and Khandekar (2003) presented the generation and collapse of vapor bubbles at the total fixed volume of a PHP. The effects of various parameters on the PHP which include the diameter, number of turns, working fluid, and the inclination angle were studied by many researchers (Tong et al., 2001; Khandekar et al., 2002, 2003b; Charoensawan et al., 2003). The PHPs with working fluids such as water, methanol, ethanol, and R-123 were tested by inclining the pipes from 0 to 90 degrees. Consequently, the appropriate charge ratios (water: 30%, methanol: 60%, ethanol: 20% and R-123: 35%) were required for each working fluid in order to keep the maximum heat transfer of PHPs. On the other hand, the entropy is generated by the thermodynamic cycle when a working fluid moves in a PHP. The entropy generation is also caused by the friction loss and heat transfer of a working fluid (Khalkhali et al., 1999). Furthermore, the entropy generation is directly related to the irreversible process, and the quantity of the entropy generated is determined by the entropy and lost work during the process. Al-Zaharnah (2003) conducted a research on the effect of the wall temperature and Reynolds number on the entropy distribution in the pipe system. Moreover, Al-Zaharnah and Yilbas (2004) studied the effect of the fluid viscosity on the entropy generation for each different wall temperature. It was shown that the rate of entropy generation increased due to the high temperature of the pipe wall. Sahin and Ben-Mansour (2003) studied the effect of a developing laminar viscous fluid flow on the entropy generation in a circular pipe. They showed that the entropy generation increases near the wall and decreases gradually in the axial direction. In the present study, the entropy generation will be analyzed numerically considering two vapor plugs, a liquid slug, evaporation, and condensation in a PHP. The Volume 44, Number 1, 2013

4 4 Kim, Zhang, & Choi effects of initial temperature and pressure loss in the bend on entropy generation in a PHP will also be studied. 2. PHYSICAL MODEL A U-shaped PHP (Zhang et al., 2002) is shown in Fig. 1a, where two vapor plugs are located at both ends. The evaporator and condenser are divided by the center dotted line. In other words, the evaporator is located above the dotted line and the condenser below the dotted line. The U-shaped PHP can be converted to a linear pipe with a liquid slug located in the center of the pipe as shown in Fig. 1b. The following assumptions are made in order to investigate the entropy generation in the U-shaped PHP: 1) The pressure drop in the vapor due to the friction is neglected. 2) The vapor plug is assumed to be always in a saturated state and behave as an ideal gas. 3) The entropy is assumed to be generated by heat transfer and friction. 4) The liquid is assumed to be incompressible; subcooling in the liquid is considered. 2.1 Governing Equations for a Pulsating Flow The acceleration of the liquid slug is related to the pressure, gravity, and shear stress. Thus, the momentum equation is (Shao and Zhang, 2011) FIG. 1: Configuration of a pulsating heat pipe Heat Transfer Research

5 Entropy Generation Analysis for a Pulsating Heat Pipe 5 2 dxp p l v1 v2 b l p p p AL ρ = [( p p ) Δp ] A 2 ρ gax πdl τ, (1) 2 dt where Δp b is the pressure loss at the bend (Rohsenow et al., 1985): Δ p b 2 vp Kρ l vp > 0 2 = (2) 2 vp K ρ l vp < 0 2 and τ p is the shear stress: 16 / Re, Re 2200 c /2, c Re, Re τ p = lρυ l = 0.2 > (3) The energy equations of the two vapor plugs are dmct ( v1 v v1) dmv1 π dx 2 p = ct p d, p v1 v1 dt dt 4 dt (4) dm ( v2ct v v2) dmv2 π dx 2 p = ct p v2 + pv2 d. dt dt 4 dt The vapor plug can be assumed to be an ideal gas. Thus, the equation of state can be presented by π 2 pv1( Le+ xp) d = mv1rtv1, 4 π 2 pv2( Le xp) d = mv2rtv2. 4 Considering the initial conditions, the masses and temperatures of the two vapor plugs can be obtained: (5) (6) (7) 1 2 γ πd p 0 p v1 v1 = e+ p 4RT p 0 0 m ( L x ), 1 2 γ πd p 0 p v2 v2 = e p 4RT0 p0 m ( L x ), T p v1 v1 = T0 p0 ( γ 1) γ, (8) (9) (10) Volume 44, Number 1, 2013

6 6 Kim, Zhang, & Choi T p T v 2 v 2 = 0 p0 ( γ 1) where T 0 and P 0 are the initial temperature and pressure, respectively. γ, (11) 2.2 Latent and Sensible Heat Transfer The heat transfer in a PHP means that heat moves from the evaporator to condenser. There are two types of heat transfer in a PHP. One is the latent heat due to the phase change of a working fluid, and the other is the sensible heat because of heat transfer between the wall and liquid slug. The heat transfer rates in the two vapor volumes are related to the mass flux and can be obtained from Qin, v1 = m evp, v1hlv, (12) Qout,1 v = m con,1 v hlv, (13) Qin, v 2 = m e vp, v 2hlv, (14) Q = m h. (15) out, v 2 con, v 2 lv The temperature distribution in the liquid slug can be obtained by solving the energy equation 2 1 dtl d Tl hlsenπd = ( ). 2 T l T (16) w α dt dx k A l p l The initial and boundary conditions for Eq. (16) are T = T, t = 0, 0 < x < L, 0 p p (17) T = T, x = 0, v1 T = T, x = L. p v2 p p (18) (19) The sensible heat transfer to and from the liquid slug can be obtained by integrating heat transfer over the length of the liquid slug Q Q in,, s l out,, s l Lp πdh( Te Tl) dxl, xp > 0 Lp xp =, xp πdh( T T ) dx, x < 0 0 e l l p xp πdh( T T ) dx, x > 0 0 l c l p =, Lp πdh( Tl Tc) dxl, xp < 0 xp where the sensible heat transfer coefficient can be obtained from h = Nuk l /d. (20) (21) Heat Transfer Research

7 Entropy Generation Analysis for a Pulsating Heat Pipe Entropy Generation of Vapor Plugs The entropy is generated when a liquid slug is converted into a vapor plug due to evaporation in a PHP. According to the second law of thermodynamics, the rate of entropy generation due to a phase change can be calculated from ds dt The entropy generation in vapor plug 1 is since the change of specific entropy with respect to time is zero, i.e., ds v1 dt = 0. Thus, the entropy generation in vapor plug 1 is Similarly, the entropy generation in vapor plug 2 is v = ms m s. (22) in v out v Therefore, the equations of entropy generation in vapor plugs 1 and 2 can be rearranged as S = m s, (26) Also, because the entropy of the two vapor plugs is equal in the reference state, the above equations can be written as follows: S = m s, (28) Finally, the entropy generation in the two vapor plugs can be obtained from Δ S = ( m m ) s, (30) dms ( v1 v1) dmv 1 = sv1. (23) dt dt ds dt ds dt dm = (24) dt v1 v1 sv 1. dm = s (25) dt v2 v2 v2. v1 v1 v1 S = m s v2 v2 v2 v1 v1 0 S = m s. v2 v2 0 v1 v1 v1,0 0. (27) (29) Δ S = ( m m ) s. v2 v2 v2,0 0 (31) 2.4 Entropy Generation of Liquid Slug Since the liquid phase is incompressible, the following entropy equation is valid: Volume 44, Number 1, 2013

8 8 Kim, Zhang, & Choi Tds = c dt, p ds cp dt =. dt T dt (32) (33) Integrating Eq. (33) yields Tl sl = sl,0 + cpln. (34) T 0 The entropy generation in the liquid slug can be obtained by integrating Eq. (34) over the length of the liquid slug: ml π L 2 p Tl Sl = sdm l =ρ l d sl,0 cp ln dx, T π 2 L p Tl Sl S,0 l =ρl d cp ln dx, 4 0 T π L 2 p Tl Δ Sl =ρl d cp ln dx. 4 0 T (35) (36) (37) The friction by the liquid slug is related to the area, velocity, and shear stress. The entropy generation due to the friction on the liquid slug can be obtained from L p 1 Sf Sf,0 =Δ Sf = τπ l dvp dx. (38) 0 T l 2.5 Entropy Generation of Latent Heat and Sensible Heat in Heating and Cooling Sections When a working fluid is pulsating, the system is affected by the latent heat and sensible heat. By using the latent heat from Eqs. (12) (15), the entropy generation by the latent heat for evaporation and condensation can be presented as follows: Q Q Δ S = and Δ S =. elat, clat, elat, clat, Te Tc The entropy generation due to the sensible heat transfer is obtained by using the sensible heat from Qesen, Qcsen, Δ Sesen, = and Δ Scsen, =. (40) T T e c (39) Heat Transfer Research

9 Entropy Generation Analysis for a Pulsating Heat Pipe 9 As a result, the total entropy generation in a U-shaped PHP can be obtained by adding all the terms of the entropy generation: S =Δ S +Δ S +Δ S + ( ΔS + ΔS ) tot, gen v1 v2 l e, lat e, sen +( ΔS + Δ S ) +ΔS. clat, csen, f (41) 3. NUMERICAL APPLICATION The iteration method and implicit finite difference method are used to solve the physical model of vapor plugs and liquid slug numerically. Also, the equation of heat conduction is solved by the Tridiagonal Matrix Algorithm (TDMA) in order to get the temperature distribution of the liquid slug. The numerical procedures for obtaining the entropy generation are as follows: (1) The temperatures of the two vapor plugs, T v1 and T v2, are assumed, and the thermal and physical properties of the liquid slug are calculated according to T l. (2) The vapor pressures, p v1 and p v2, are solved by Eqs. (10) and (11). (3) The displacement of the liquid slug, x p, is calculated by Eq. (1). (4) The new masses of the two vapor plugs, m v1 and m v2, are obtained by accounting for the change in the vapor masses from Eqs. (8) and (9). (5) The pressures of the two vapor plugs, p v1 and p v2, are calculated by Eqs. (6) and (7). (6) The solutions for T v1 and T v2 are obtained from Eqs. (9) and (10). (7) The quantitites T v1 and T v2 are compared; they are obtained at step 6, with the values assumed at step 1. If the differences meet the small tolerance, go to step 8; otherwise, the above procedures are repeated at steps 2 6 until a converged solution is obtained. (8) The temperature distribution in the liquid slug is solved by Eq. (16), and then the sensible heat is calculated. (9) The latent heat is obtained by Eqs. (12) (15). (10) The entropy generations in vapor volumes 1 and 2, ΔS v1 and ΔS v2, are calculated by Eqs. (30) and (31). (11) The entropy generations by the liquid slug and friction, ΔS l and ΔS f, are calculated from Eqs. (37) and (38). (12) The entropy generations by the latent heat and sensible heat, ΔS e,lat, ΔS e,sen, ΔS c,lat and ΔS c,sen, are calculated from Eqs. (39) and (40). The sensible heat and latent heat are obtained from steps 8 and 9. (13) The total entropy generation by the U-shaped PHP is calculated from Eq. (41). Volume 44, Number 1, 2013

10 10 Kim, Zhang, & Choi 4. RESULTS AND DISCUSSION The following parameters are used in numerical calculations; they are taken from Zhang et al. (2002): L e = 0.1 m, L c = 0.1 m, L p = 0.2 m, d = 3.34 mm, T e = o C, T c = 20 o C, and h e = h c = 200 W/m 2 K, Δt = When the initial temperatures in a U-shaped PHP are 70 o C and 20 o C, respectively, the entropy generation is shown in Figs Figure 2a shows the entropy generation with time in vapor plugs 1. Although the value of the entropy generation is supposed to be positive, the entropy generation in vapor plug 1 has a negative value, because the initial mass is larger than the new mass. The entropy generation in vapor plug 1 with an initial temperature of 20 o C is characterized by a relatively large amplitude and a constant pattern with time. Unlike the initial temperature equal to 20 o C, the entropy generation in vapor plug 1 with an initial temperature of 70 o C presents a relatively small amplitude. Also, the amplitude and frequency of entropy generation in vapor plug 2 with an initial temperature of 20 o C are relatively larger than those with an initial vapor temperature of 70 o C, as shown in Fig. 2b. The reason for this phenomenon is that the difference between the initial and current masses at 20 o C is relatively larger than those at 70 o C. Figure 3 presents the entropy generation by the liquid slug with time when the initial temperatures are 70 o C and 20 o C. The entropy generation at initial temperatures of 70 o C and 20 o C is equal to about kj/k and kj/k, respectively. The entropy generation by a liquid slug is almost uniform without the difference in amplitudes and is not significantly affected by the initial temperature. The entropy generation due to the latent heat in vapor plugs 1 and 2, respectively, is shown in Figs. 4 and 5. Figures 4a and 5a present the entropy generation in evaporation; the entropy generation in vapor plugs 1 and 2 increase sharply with regular intervals at an initial temperature of 20 o C, because of the noticeable difference in temperatures. The amplitude and frequency at an initial temperature of 70 o C are steady, and the entropy generation with time is almost the same during the cycle. Also, the frequency at an initial temperature of 20 o C is longer than that at an initial temperature of 70 o C in the maximum entropy generation. Figures 4b and 5b show the entropy generation with time in vapor plugs 1 and 2, when a vapor plug enters into the cooling section. Unlike the evaporation process, the entropy generation at an initial temperature of 70 o C is higher than that at an initial temperature of 20 o C, because the difference between the cooling section s temperatures and an initial temperature of 70 o C is larger than that at an initial temperature of 20 o C. However, the frequency at an initial temperature of 20 o C is longer than that at an initial vapor temperature of 70 o C. Figure 6 shows the entropy generation due to the sensible heat at the initial temperatures of 70 o C and 20 o C. When a liquid slug pulsates, the entropy generation is related to the sensible heat as well as the latent heat. As seen from Fig. 6a, the graph at an initial temperature of 70 o C presents the entropy generation of constant period and shape, when the sensible heat is transfered into a liquid slug. However, Heat Transfer Research

11 Entropy Generation Analysis for a Pulsating Heat Pipe 11 FIG. 2: Entropy generation in two vapor plugs with different initial temperatures Volume 44, Number 1, 2013

12 12 Kim, Zhang, & Choi FIG. 3: Entropy generation in liquid slug with different initial temperatures Heat Transfer Research

13 Entropy Generation Analysis for a Pulsating Heat Pipe 13 FIG. 4: Entropy generation due to latent heat in vapor plug 1 Volume 44, Number 1, 2013

14 14 Kim, Zhang, & Choi FIG. 5: Entropy generation due to latent heat transfer in vapor plug 2 Heat Transfer Research

15 Entropy Generation Analysis for a Pulsating Heat Pipe 15 FIG. 6: Entropy generation due to sensible heat in a liquid slug Volume 44, Number 1, 2013

16 16 Kim, Zhang, & Choi FIG. 7: Entropy generation due to friction in a liquid slug Heat Transfer Research

17 Entropy Generation Analysis for a Pulsating Heat Pipe 17 FIG. 8: Total entropy generation at different initial temperatures Volume 44, Number 1, 2013

18 18 Kim, Zhang, & Choi the change in the entropy generation at an initial temperature of 20 o C gradually decreases with increasing time, because the sensible heat is sensitive to the temperature difference. On the other hand, the entropy generation in the cooling section at an initial vapor temperature of 70 o C is larger than that an the initial temperature of 20 o C, as shown in Fig. 6b. The amplitude of the entropy generation at an initial temperature of 70 o C gradually decreases, because the difference in the temperature is reduced with increasing time. However, there is a little change in the entropy generation at an initial temperature of 20 o C. Figure 7 presents the entropy generation due to the friction of a liquid slug at initial temperatures of 70 o C and 20 o C. There is a little difference in the entropy generation, because the velocity of a liquid slug is not nearly affected by the initial temperature. The values of the entropy generation due to the friction are very small; they have the order of approximately kj/k. Therefore, since the friction of a liquid slug does not affect the entropy generation, it can be ignored. Figure 8 shows the above-mentioned entropy generation at initial temperatures of 70 o C and 20 o C. The change in vapor plugs 1 and 2 is noticeably larger than in other quantities in entropy generation. In addition, the value of the entropy generation at the initial temperature of 20 o C is higher than that at an initial temperature of 70 o C. As a result, the initial vapor temperature has a significant effect on the change in entropy generation in a U-shaped PHP. Figures 9 19 demonstrate the effect of pressure losses at the bend on entropy generation. A pressure loss coefficient of 0.31 is used in calculations, when the curvature radius (r) of the bend is 5.83 mm, as shown in Fig. 1 (Ma et al., 2008). Figures 9 and 10 show entropy generation with and without pressure losses at the bend in vapor plugs 1 and 2, respectively. In the startup stage, the entropy generation in both cases has the same frequency. However, in the final stage, the frequency of entropy generation with a pressure loss is faster than that without a pressure loss. The reason is that the pressure drop prevents a liquid slug from moving in a PHP. Thus, the pressure loss at the bend has a significant effect on the frequency, while it does not affect the amplitude of the entropy generation. Unlike the cases with the two vapor plugs, Fig. 11 shows entropy generation by a liquid slug with time, and there is a little difference in the entropy generation with or without a pressure loss at the bend. The amplitude difference is about kj/k, and the frequency difference is almost constant. Figures show the cases of entropy generation due to evaporation and condensation with and without a pressure loss in vapor plugs 1 and 2, respectively. In other words, they present the effect of the latent heat on the entropy generation with and without a pressure loss. The frequencies of entropy generation due to evaporation and condensation in the two vapor plugs are similar to those shown in Figs. 4 and 5. The entropy generation in the startup stage is almost constant regardless of the existence of a pressure loss at the bend. However, the frequencies with a pressure loss are still faster than those without a pressure loss in the final stage. Heat Transfer Research

19 Entropy Generation Analysis for a Pulsating Heat Pipe 19 FIG. 9: Entropy generation with or without pressure loss at the bend in vapor plug 1 Volume 44, Number 1, 2013

20 20 Kim, Zhang, & Choi FIG. 10: Entropy generation with or without pressure loss at the bend in vapor plug 2 Heat Transfer Research

21 Entropy Generation Analysis for a Pulsating Heat Pipe 21 FIG. 11: Entropy generation with or without pressure loss at the bend in a liquid slug Figures 16 and 17 present the entropy generation due to the sensible heat of a liquid slug with or without a pressure loss in the heating section and cooling section, respectively. As shown in Figs , the frequencies of entropy generation with a pressure loss are faster than those without a pressure loss in the final stage. Figure 18 shows the entropy generation due to the friction of a liquid slug with or without a pressure loss at the bend. The entropy generation with the pressure loss is higher than that without a pressure loss. However, the difference in entropy generation due to friction is small. Therefore, the friction can be ignored in considering the entropy generation. Figure 19 presents the above-mentioned entropy generation with or without a pressure loss at the bend. The entropy generation is almost the same regardless of the pressure loss. However, the frequencies of a entropy generation with a pressure loss are quicker than those without a pressure loss at the bend. Volume 44, Number 1, 2013

22 22 Kim, Zhang, & Choi FIG. 12: Entropy generation due to evaporation with or without pressure loss in vapor plug 1 Heat Transfer Research

23 Entropy Generation Analysis for a Pulsating Heat Pipe 23 FIG. 13: Entropy generation due to condensation with or without pressure loss in vapor plug 1 Volume 44, Number 1, 2013

24 24 Kim, Zhang, & Choi FIG. 14: Entropy generation due to evaporation with or without pressure loss in vapor plug 2 Heat Transfer Research

25 Entropy Generation Analysis for a Pulsating Heat Pipe 25 FIG. 15: Entropy generation due to condensation with or without pressure loss in vapor plug 1 Volume 44, Number 1, 2013

26 26 Kim, Zhang, & Choi FIG. 16: Entropy generation due to transfer of sensible heat into a liquid slug with or without pressure loss Heat Transfer Research

27 Entropy Generation Analysis for a Pulsating Heat Pipe 27 FIG. 17: Entropy generation due to transfer of sensible heat from a liquid slug with or without pressure loss Volume 44, Number 1, 2013

28 28 Kim, Zhang, & Choi FIG. 18: Entropy generation due to friction in a liquid slug with or without pressure loss FIG. 19: Total entropy generation with or without pressure loss at the bend Heat Transfer Research

29 Entropy Generation Analysis for a Pulsating Heat Pipe CONCLUSIONS The entropy generation in a U-shaped PHP has been investigated with consideration of the initial temperatures and pressure losses at the bend. The entropy generation is calculated from variations of vapor mass, liquid temperature, latent heat, sensible heat, and friction. As a result, the entropy generation is sensitively affected by the initial temperature, and the variation of the vapor mass is the main cause of entropy generation. The amplitude of the entropy generation is irrelevant to the pressure loss at the bend. However, the frequency of entropy generation with a pressure loss is faster than that without a pressure loss. REFERENCES Akachi, H., Looped Capillary Heat Pipes, Japanese Patent, No. Hei697147, Al-Zaharnah, I. T., Entropy analysis in pipe flow subjected to external heating, Entropy, vol. 5, pp , Al-Zaharnah, I. T. and Yilbas, B. S., Thermal analysis in pipe flow: influence of variable viscosity on entropy generation, Entropy, vol. 6, no. 3, pp , Cai, Q., Chen, R., and Chen, C. L., An investigation of evaporation, boiling and heat transport performance in pulsating heat pipe, Proc. ASME Int. Mechanical Engineering Congress & Exposition, New Orleans, Louisiana, USA, Charoensawan, P., Khandekar, S., Groll, M., and Terdtoon, P., Closed loop pulsating heat pipe: Part A: Parametric experimental investigations, Appl. Thermal Eng., vol. 23, no. 16, pp , Dobson, R. T. and Harms, T. M., Lumped parameter analysis of closed and open oscillatory heat pipe, Proc. 11th Int. Heat Pipe Conf., Tokyo, Japan, pp , Gi, K., Sato, F., and Maezawa, S., Flow visualization experiment on oscillating heat pipe, Proc. 11th Int. Heat Pipe Conf., Tokyo, Japan, pp , Groll, M. and Khandekar, S., Pulsating heat pipe: Progress and prospects, Proc. Int. Conf. on Energy and the Environment, Vol. 1, Shanghai, China, pp , Grover, G., Evaporation-Condensation Heat Transfer Device, U.S. Patent , Grover, G., Cotter, T., and Erikson, G., Structure of very high thermal conductance, J. Appl. Phys., vol. 35, no. 6, pp , Hosoda, M., Nishio, S., and Shirakashi, R., Meandering closed loop heat transport tube (Propagation phenomena of vapor plug), Proc. 5th ASME/JSME Joint Thermal Engineering Conf., AJTE , San Diego, California, USA, Judge, J. F., RCA test thermal energy pipe, J. Missile Rockets, vol. 18, pp , Khalkhali, H., Faghri, A., and Zuo, Z. J., Entropy generation in a heat pipe system, Appl. Thermal Eng., vol. 19, pp , Khandekar, S., Charoensawan, P., Groll, M., and Terdtoon, P., (2003) closed loop pulsating heat pipes, part b: visualization and semi-empirical modeling, Appl. Thermal Eng., vol. 23, no. 16, pp , 2003a. Khandekar, S., Dollinger, N., and Groll, M., Understanding operational regimes of pulsating heat pipe: an experimental study, Appl. Thermal Eng., vol. 23, no. 6, pp , 2003b. Volume 44, Number 1, 2013

30 30 Kim, Zhang, & Choi Khandekar, S. and Groll, M., An insight into thermo-hydraulic coupling in pulsating heat pipe, Int. J. Thermal Sci. (Rev. Gen. Therm), vol. 43, no. 1, pp , Khandekar, S. and Groll, M., On the definition of pulsating heat pipes: An overview, Proc. 5th Minsk Int. Conf. (Heat Pipes, and Refrigerators), Minsk, Belarus, pp , Khandekar, S., Schneider, M., Kulenovic, P., and Groll, M., Thermofluiddynamic study of flat plate closed loop pulsating heat pipes, Microscale Thermophys. Eng., vol. 6, no. 4, pp , Leefer, B. I., Nuclear thermionic energy converter, Proc. 4th Intl. Heat Pipe Conf., London, UK, pp , Ma, H. B., Borgmeyer, B., Cheng, P., and Zhang, Y., Heat transport capability in an oscillating heat pipe, J. Heat Transfer, vol. 130, , Rohsenow, W. M., Hartnett, J. P. and Ganic, E. N., Handbook of Heat Transfer Fundamentals, 2nd ed., Chap. 7, New York: McGraw-Hill, Sahin, A. Z. and Ben-Mansour, R., Entropy generation in laminar fluid flow through a circular pipe, Entropy, vol. 5, no. 5, pp , Shao, W. and Zhang, Y., Thermally induced oscillatory flow and heat transfer in a U-shaped minichannel, J. Enhanced Heat Transfer, vol. 18, no. 3, pp , Tong, B., Wong, T., and Ooi, K., Closed-loop pulsating heat pipe, Appl. Thermal Eng., vol. 21, no. 18, pp , Trefethen, L., On the surface tension pumping of liquids or a possible role of the candlewick in space exploration, G. E. Tech. Info., Serial No. 615 D114, Zhang, X., Xu, J. L., and Zhou, Z. Q., Experimental study of a pulsating heat pipe using FC-72, ethanol, and water as working fluids, Exp. Heat Transfer, vol. 17, no. 1, pp , Zhang, Y. and Faghri, A., Heat transfer in a pulsating heat pipe with open end, Int. J. Heat Mass Transfer, vol. 45, no. 4, pp , Zhang, Y., Faghri, A., and Shafii, M. B., Analysis of liquid-vapor pulsating flow in a U-shaped miniature tube, Int. J. Heat Mass Transfer, vol. 45, no. 12, pp , Heat Transfer Research