BOOKCOMP, Inc. — John Wiley & Sons / Page 1177 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 1177 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1177], (47) Lines: 1629 to 1672 ——— 3.0pt PgVar ——— Short Page PgEnds: T E X [1177], (47) Bejan, A., and Morega, A. M. (1993). Optimal Arrays of Pin Fins and Plate Fins in Laminar and Forced Convection, J. Heat Transfer, 115, 75–81. Bejan, A., and Poulikakos, D. (1984). The Non-Darcy Regime for Vertical Boundary Layer Natural Convection in a Porous Medium, Int. J. Heat Mass Transfer, 27, 717–722. Bejan, A., and Sciubba, E. (1992). The Optimal Spacing of Parallel Plates Cooled by Forced Convection, Int. J. Heat Mass Transfer, 35, 3259–3264. Bejan, A., and Tien, C. L. (1978). Natural Convection in a Horizontal Porous Medium Sub- jected to End-to-End Temperature Difference, J. Heat Transfer, 100, 191–198; errata (1983), 105, 683–684. Bejan, A., and Tien, C. L. (1979). Natural Convection in Horizontal Space Bounded by Two Concentric Cylinders with Different End Temperatures, Int. J. Heat Mass Transfer, 22, 919– 927. Bejan, A., Dincer, I., Lorent, S., Miguel, A. F., and Reis, A. H. (2004). Porous and Complex Flow Structures, in Modern Technologies, Springer, New York. Bhattacharjee, S., and Grosshandler, W. L. (1988). The Formation of a Wall Jet near a High Temperature Wall under Microgravity Environment, ASME-HTD-96, ASME, New York, pp. 711–716. Blake, K. R., Bejan, A., and Poulikakos, D. (1984). Natural Convection near 4°C in a Water Saturated Porous Layer Heated from Below, Int. J. Heat Mass Transfer, 27, 2355–2364. Brinkman, H. C. (1947). A Calculation of the Viscous Force Extended by a Flowing Fluid on a Dense Swarm of Particles, Appl. Sci. Res., A1, 26–34. Buretta, R. J.,and Berman, A. S. (1976). Convective Heat Transfer in a Liquid Saturated Porous Layer, J. Appl. Mech., 43, 249–253. Burns, P. J., and Tien, C. L. (1979). Natural Convection in Porous Media Bounded by Concen- tric Spheres and Horizontal Cylinders, Int. J. Heat Mass Transfer, 22, 929–939. Caltagirone, J. P. (1976). Thermoconvective Instabilities in a Porous Medium Bounded by Two Concentric Horizontal Cylinders, J. Fluid Mech., 76, 337–362. Carslaw, J. S., and Jaeger, J. C. (1959). Conduction of Heat in Solids, 2nd ed., Oxford Univer- sity Press, Oxford. Cheng, P. (1978). Heat Transfer in Geothermal Systems, Adv. Heat Transfer, 14, 1–105. Cheng, P. (1982). Mixed Convection about a Horizontal Cylinder and a Sphere in a Fluid Saturated Porous Medium, Int. J. Heat Mass Transfer, 25, 1245–1247. Cheng, P., and Chang, I. D. (1976). Buoyancy Induced Flows in a Saturated Porous Medium Adjacent to Impermeable Horizontal Surfaces, Int. J. Heat Mass Transfer, 19, 1267–1272. Cheng, P., and Minkowycz, W. J. (1977). Free Convection about a Vertical Plate Embedded in a Saturated Porous Medium with Application to Heat Transfer from a Dike, J. Geophys. Res., 82, 2040–2044. Combarnous, M. A., and Bories, S. A. (1975). Hydrothermal Convection in Saturated Porous Media, Adv. Hydrosci., 10, 231–307. Ergun, S. (1952). Fluid Flow through Packed Columns, Chem. Eng. Prog., 48(2), 89–94. Gebhart, B., and Mollendorf, J. C. (1977). A New Density Relation for Pure and Saline Water, Deep Sea Res., 24, 831–841. Haajizadeh, M., and Tien, C. L. (1983). Natural Convection in a Rectangular Porous Cavity with One Permeable End wall, J. Heat Transfer, 105, 803–808. BOOKCOMP, Inc. — John Wiley & Sons / Page 1178 / 2nd Proofs / Heat Transfer Handbook / Bejan 1178 POROUS MEDIA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1178], (48) Lines: 1672 to 1712 ——— 6.0pt PgVar ——— Normal Page PgEnds: T E X [1178], (48) Havstad, M. A., and Burns, P. J. (1982). Convective Heat Transfer in Vertical Cylindrical Annuli Filled with a Porous Medium, Int. J. Heat Mass Transfer, 25, 1755–1766. Hickox, C. E. (1981). Thermal Convection at Low Rayleigh Number from Concentrated Sources in Porous Media, J. Heat Transfer, 103, 232–236. Hickox, C. E., and Gartling, D. K. (1981). A Numerical Study of Natural Convection in a Horizontal Porous Layer Subjected to an End-to-End Temperature Difference, J. Heat Transfer, 103, 797–802. Hickox, C. E., and Watts, H. A. (1980). Steady Thermal Convection from a Concentrated Source in a Porous Medium, J. Heat Transfer, 102, 248–253. Horton, C. W., and Rogers, F. T. (1945). Convection Currents in a Porous Medium, J. Appl. Phys., 16, 367–370. Ingham, D. B., and Pop, I., eds. (1998). Transport Phenomena in Porous Media, Pergamon Press, Oxford. Ingham, D. B., and Pop, I., eds. (2002). Transport Phenomena, in Porous Media II, Pergamon Press, Amsterdam. Ingham, D. B., Merkin, H., and Pop, I. (1983). The Collision of Free-Convective Boundary Layers on a Horizontal Cylinder Embedded in a Porous Medium, Q. J. Mech. Appl. Math., 36, 313–335. Kaviany, M. (1995). Principles of Heat Transfer in Porous Media, 2nd ed., Springer-Verlag, New York. Kimura, S., Bejan, A., and Pop, I. (1985). Natural Convection near a Cold Plate Facing Upward in a Porous Medium, J. Heat Transfer, 107, 819–825. Kimura, S., Schubert, G., and Straus, J. M. (1986). Route to Chaos in Porous-Medium Thermal Convection, J. Fluid Mech., 166, 305–324. Kulacki, F. A., and Freeman, R. G. (1979). A Note on Thermal Convection in a Saturated Heat-Generating Porous Layer, J. Heat Transfer, 101, 169–171. Lai, F. C., Kulacki, F. A., and Prasad, V. (1991). Mixed Convection in Saturated Porous Media, in Convective Heat and Mass Transfer in Porous Media, S. Kakac¸, B. Kilkis, F. A. Kulacki, and F. Arinc, eds., Kluwer Academic, Dordrecht, The Netherlands, pp. 225–287. Lapwood, E. R. (1948). Convection of a Fluid in a Porous Medium, Proc. Cambridge Philos. Soc., 44, 508–521. Ledezma, G. A., Morega, A. M., and Bejan, A. (1996). Optimal Spacing between Fins with Impinging Flow, J. Heat Transfer, 118, 570–577. Lorente, S. (2002). Heat Losses through Building Walls with Closed, Open and Deformable Cavities, Int. J. Energy Res., 26, 611–632. Lorente, S., and Bejan, A. (2002). Combined ‘Flow and Strength’ Geometric Optimization: Internal Structure in a Vertical Insulating Wall with Air Cavities and Prescribed Strength, Int. J. Heat Mass Transfer, 45, 3313–3320. Lorente, S., Petit, M., and Javelas, R. (1996). Simplified Analytical Model for Thermal Transfer in a Vertical Hollow Brick, Energy and Buildings, 24, 95–103. Lorente, S., Petit, M., and Javelas, R. (1998). The Effects of Temperature Conditions on the Thermal Resistance of Walls Made with Different Shapes Vertical Hollow Brick, Energy and Buildings, 28, 237–240. Morega, A. M., and Bejan, A. (1994). Heatline Visualization of Convection in Porous Media, Int. J. Heat Fluid Flow, 15, 42–47. BOOKCOMP, Inc. — John Wiley & Sons / Page 1179 / 2nd Proofs / Heat Transfer Handbook / Bejan REFERENCES 1179 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1179], (49) Lines: 1712 to 1753 ——— 6.0pt PgVar ——— Normal Page PgEnds: T E X [1179], (49) Nakayama, A., and Pop, I. (1991). A Unified Similarity Transformation for Free, Forced and Mixed Convection in Darcy and Non-Darcy Porous Media, Int. J. Heat Mass Transfer, 34, 357–367. Nelson, R. A., Jr., and Bejan, A. (1998). Constructal Optimization of Internal Flow Geometry in Convection, J. Heat Transfer, 120, 357–364. Nield, D. A. (1968). Onset of Thermohaline Convection in a Porous Medium, Water Resour. Res., 4, 553–560. Nield, D. A. (1991). Estimation of the Stagnant Thermal Conductivity of Saturated Porous Media, Int. J. Heat Mass Transfer, 34, 1575–1576. Nield, D. A., and Bejan, A. (1999). Convection in Porous Media, 2nd ed., Springer-Verlag, New York. Nield, D. A., and Joseph, D. D. (1985). Effects of Quadratic Drag on Convection in a Saturated Porous Medium, Phys. Fluids, 28, 995–997. Petrescu, S. (1994). Comments on the Optimal Spacing of Parallel Plates Cooled by Forced Convection, Int. J. Heat Mass Transfer, 37, 1283. Plumb, O. A., and Huenefeld, J. S. (1981). Non-Darcy Natural Convection from Heated Sur- faces in Saturated Porous Media, Int. J. Heat Mass Transfer, 24, 765–768. Pop, I., and Ingham, D. B. (2001). Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media, Pergamon Press, Oxford. Pop, I., and Cheng, P. (1983). The Growth of a Thermal Layer in a Porous Medium Adjacent to a Suddenly Heated Semi-infinite Horizontal Surface, Int. J. Heat Mass Transfer, 26, 1574– 1576. Poulikakos, D. (1984). Maximum Density Effects on Natural Convection in a Porous Layer Differentially Heated in the Horizontal Direction, Int. J. Heat Mass Transfer, 27, 2067– 2075. Poulikakos, D., and Bejan, A. (1983a). Natural Convection in Vertically and Horizontally Layered Porous Media Heated from the Side, Int. J. Heat Mass Transfer, 26, 1805–1814. Poulikakos, D., and Bejan, A. (1983b). Numerical Study of Transient High Rayleigh Number Convection in an Attic-Shaped Porous Layer, J. Heat Transfer, 105, 476–484. Poulikakos, D., and Bejan, A. (1984a). Penetrative Convection in Porous Medium Bounded by a Horizontal Wall with Hot and Cold Spots, Int. J. Heat Mass Transfer, 27, 1749–1758. Poulikakos, D., and Bejan, A. (1984b). Convection in a Porous Layer Heated and Cooled along One Vertical Side, Int. J. Heat Mass Transfer, 27, 1879–1891. Prasad, V., Kulacki, F. A., and Keyhani, M. (1985). Natural Convection in Porous Media, J. Fluid Mech., 150, 89–119. Prasad, V., Kladias, N., Bandyopadhaya, A., and Tian, Q. (1989). Evaluation of Correlations for Stagnant Thermal Conductivity of Liquid-Saturated Porous Beds of Spheres, Int. J. Heat Mass Transfer, 32, 1793–1796. Ramilison, J. M., and Gebhart, B. (1980). Buoyancy Induced Transport in Porous Media Saturated with Pure or Saline Water at Low Temperatures, Int. J. Heat Mass Transfer, 23, 1521–1530. Rohsenow, W. M., and Choi, H. Y. (1961). Heat, Mass and Momentum Transfer, Prentice-Hall, Englewood Cliffs, NJ. Rohsenow, W. M., and Hartnett, J. P. (1973). Handbook of Heat Transfer, McGraw-Hill, New York. BOOKCOMP, Inc. — John Wiley & Sons / Page 1180 / 2nd Proofs / Heat Transfer Handbook / Bejan 1180 POROUS MEDIA 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [Last Page] [1180], (50) Lines: 1753 to 1781 ——— 225.04701pt PgVar ——— Normal Page PgEnds: T E X [1180], (50) Scheiddeger, A. E. (1957). The Physics of Flow through Porous Media, Macmillan, New York. Simpkins, P. G., and Blythe, P. A. (1980). Convection in a Porous Layer, Int. J. Heat Mass Transfer, 23, 881–887. Stanescu, G., Fowler, A. J., and Bejan, A. (1996). The Optimal Spacing of Cylinders in Free- Stream Cross-Flow Forced Convection, Int. J. Heat Mass Transfer, 39, 311–317. Sun, Z. S., Tien, C., and Yen, Y. C. (1970). Onset of Convection in a Porous Medium Containing Liquid with a Density Maximum, Heat Transfer 1970, Vol. IV, Paper NC 2.11. Trevisan, O. V., and Bejan, A. (1985). Natural Convection with Combined Heat and Mass Transfer Buoyancy Effects in a Porous Medium, Int. J. Heat Mass Transfer, 28, 1597–1611. Trevisan, O. V., and Bejan, A. (1986). Mass and Heat Transfer by Natural Convection in a Vertical Slot Filled with Porous Medium, Int. J. Mass Transfer, 29, 403–415. Vafai, K., ed. (2000). Handbook of Porous Media, Marcel Dekker, New York. Vafai, K., and Tien, C L. (1981). Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media, Int. J. Heat Mass Transfer, 24, 195–203. Vargas, J. V. C., Laursen, T. A., and Bejan, A. (1995). Nonsimilar Solutions for Mixed Con- vection on a Wedge Embedded in a Porous Medium, Int. J. Heat Fluid Flow, 16, 211–216. Vasile, C., Lorente, S., and Perrin, B. (1998). Study of Convective Phenomena inside Cavities Coupled with Heat and Mass Transfers through Porous Media—Application to Vertical Hollow Bricks—A First Approach, Energy and Buildings, 28, 229–235. Ward, J. C. (1964). Turbulent Flow in Porous Media, J. Hydraul. Div. ASCE, 90(HY5), 1–12. Weber, J. E. (1975). The Boundary Layer Regime for Convection in a Vertical Porous Layer, Int. J. Heat Mass Transfer, 18, 569–573. Wooding, R. A. (1963). Convection in a Saturated Porous Medium at Large Rayleigh or P ´ eclet Number, J. Fluid Mech., 15, 527–544. Zhukauskas, A. (1987). Convective Heat Transfer in Cross Flow, in Handbook of Single-Phase Convective Heat Transfer, S. Kakac¸, R. K. Shah, and W. Aung, eds., Wiley, New York. BOOKCOMP, Inc. — John Wiley & Sons / Page 1181 / 2nd Proofs / Heat Transfer Handbook / Bejan 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [First Page] [1181], (1) Lines: 0 to 78 ——— * 27.22607pt PgVar ——— Normal Page * PgEnds: PageBreak [1181], (1) CHAPTER 16 Heat Pipes JAY M. OCHTERBECK Department of Mechanical Engineering Clemson University Clemson, South Carolina 16.1 Introduction 16.1.1 Heat pipe basics 16.1.2 Wick structures 16.1.3 Classification by type of control 16.1.4 Capillary action 16.2 Transport limitations 16.2.1 Introduction 16.2.2 Capillary limit 16.2.3 Boiling limit 16.2.4 Entrainment limit 16.2.5 Viscous limit 16.2.6 Sonic limit 16.2.7 Condenser limit 16.3 Heat pipe thermal resistance 16.4 Figures of merit 16.5 Transient operation 16.5.1 Continuum vapor and liquid-saturated wick 16.5.2 Wick depriming and rewetting 16.5.3 Freeze–thaw issues 16.5.4 Supercritical startup 16.6 Special types of heat pipes 16.6.1 Variable conductance heat pipes 16.6.2 Micro and miniature heat pipes 16.6.3 Pulsating heat pipes 16.6.4 Loop heat pipes and capillary pumped loops Nomenclature References 1181 BOOKCOMP, Inc. — John Wiley & Sons / Page 1182 / 2nd Proofs / Heat Transfer Handbook / Bejan 1182 HEAT PIPES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1182], (2) Lines: 78 to 99 ——— 5.7pt PgVar ——— Normal Page PgEnds: T E X [1182], (2) 16.1 INTRODUCTION 16.1.1 Heat Pipe Basics Capillary-driven two-phase systems offer significant advantages over traditional single-phase systems. With the typically increased thermal capacity associated with the phase change of a working fluid, considerably smaller mass flow rates are re- quired to transport equivalent amounts than in single-phase liquid or gas systems for a given temperature range. Moreover, heat transfer coefficients of two-phase sys- tems are much greater than in single-phase flows and result in enhanced heat transfer. Lower mass flow rates and enhanced thermal characteristics provide the benefits of smaller system size (and weight) while providing increased performance. The thermal capacity of a single-phase system depends on the temperature change of the work- ing fluid; thus, a large temperature gradient or a high mass flow rate is required to transfer a large amount of heat. However, a two-phase system can provide essentially isothermal operation regardless of variations in the heat load. Additionally, single- phase systems require the use of mechanical pumps and fans to circulate the working fluid, while capillary-driven two-phase systems have no external power requirements, which make such systems more reliable and free of vibration. The best known capillary-driven two-phase system is the heat pipe, where a sche- matic of a conventional heat pipe is shown in Fig. 16.1. The concept of the heat pipe was first presented by Gaugler (1944) and Trefethen (1962), but was not widely pub- licized until an independent development by Grover et al. (1964) at the Los Alamos Scientific Laboratories. Heat pipes are passive devices that transport heat from a heat source (evaporator) to a heat sink (condenser) over relatively long distances via the latent heat of vaporization of a working fluid. As shown, a heat pipe generally has three sections: an evaporator section, an adiabatic (or transport) section, and a con- denser section. The major components of a heat pipe are a sealed container, a wick structure, and a working fluid. The wick structure is placed on the inner surface of the heat pipe wall and is saturated with the liquid working fluid and provides the structure to develop the capillary action for liquid returning from the condenser to the evapoator section. With evaporator heat addition, the working fluid is evaporated as it absorbs an amount of heat equivalent to the latent heat of vaporization, while in the condenser section, the working fluid vapor is condensed. The mass addition in the vapor core of the evaporator section and mass rejection in the condenser end results in a pressure gradient along the vapor channel which drives the corresponding vapor flow. Return of the liquid to the evaporator from the condenser is provided by the wick structure. As vaporization occurs in the evaporator, the liquid meniscus recedes correspondingly into the wick structure, as shown in Fig. 16.1. Similarly, as vapor condenses in the condenser region, the mass addition results in an advanced meniscus. The difference between the capillary radii in the evaporator and condenser ends of the wick structure results in a net pressure difference in the liquid-saturated wick. This pressure differ- ence drives the liquid from the condenser through the wick structure to the evaporator region, thus allowing the overall process to be continuous. BOOKCOMP, Inc. — John Wiley & Sons / Page 1183 / 2nd Proofs / Heat Transfer Handbook / Bejan INTRODUCTION 1183 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1183], (3) Lines: 99 to 128 ——— 1.097pt PgVar ——— Normal Page PgEnds: T E X [1183], (3) Figure 16.1 (a) Typical heat pipe construction and operation; (b) radii of curvature of the liquid–vapor interface in the evaporator and condenser. Due to the two-phase characteristics, the heat pipe is ideal for transferring heat over long distances with a very small temperature drop and for creating a nearly isothermal surface for temperature stabilization. As the working fluid operates in a thermody- namic saturated state, heat is transported using the latent heat of vaporization instead of sensible heat or conduction where the heat pipe then operates in a nearly isother- mal condition. This nearly isothermal condition offers benefits of transporting large amounts of heat efficiently, decreasing the overal heat transfer area and saving system weight. The amount of heat that can be transported through the use of latent heat is typically several orders of magnitude greater than transported by sensible heat for a geometrically equivalent system. Additionally, no mechanical pumping systems are required due to the capillary-driven working fluid. Given the wide range of operat- ing temperatures for working fluids, the high efficiencies, the low relative weights, and the absence of external pumps in heat pipes, these systems are seen as attractive options in a wide range of heat transfer applications. BOOKCOMP, Inc. — John Wiley & Sons / Page 1184 / 2nd Proofs / Heat Transfer Handbook / Bejan 1184 HEAT PIPES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1184], (4) Lines: 128 to 144 ——— -0.11395pt PgVar ——— Long Page PgEnds: T E X [1184], (4) TABLE 16.1 Typical Heat Pipe Working Fluids Working Triple Point Critical Point Useful Range Fluid (K) (K) (K) Oxygen 54.3 154.8 55–154 Nitrogen 63.1 126.2 65–125 Ethane 89.9 305.5 100–305 Butane 134.8 425.0 260–350 Methanol 175.2 513.2 273–503 Toluene 178.1 593.9 275–473 Acetone 180.0 508.2 250–475 Ammonia 195.5 405.6 200–405 Mercury 234.3 1763 280–1070 Water 273.2 647.3 273–643 Potassium 336.4 2250 400–1800 Sodium 371.0 2500 400–1500 Lithium 453.7 3800 500–2100 Silver 1234 7500 1600–2400 Theoretically, heat pipe operation is possible at any temperature between the triple state and the critical point of the working fluid utilized, albeit at significantly reduced transport capabilities near the two extremes due to the fluid property characteristics of surface tension and viscosity. Several typical heat pipe working fluids are given in Table 16.1, along with the corresponding triple point, critical point, and most widely utilized temperature range for each individual fluid. Classification of heat pipes may be in terms of geometry, intended applications, or the type of working fluid utilized. Each heat pipe application has a temperature range in which the heat pipe is in- tended to operate. Therefore, the working fluid must be chosen to take into account this operating temperature (along with the pressure condition), but also its chemical compatibility with the container and wick materials. Depending on operating temper- ature, four different types of heat pipes are usually described with regard to commonly used working fluids: 1. Cryogenic heat pipes designed to operate from 1 to 200 K, with working fluids such as helium, argon, neon, nitrogen, and oxygen. These typically have relatively low heat transfer capabilities, due to very low values of the latent heat of vaporization, h fg , and low surface tensions of the working fluids. In addition, startup of the heat pipe involves transitioning from a supercritical state to an operating liquid–vapor condition. 2. Room (low)-temperature heat pipes with operating temperatures ranging be- tween 200 and 550 K. Working fluids typically used in this range include methanol, ethanol, ammonia, acetone, and water. 3. Medium-temperature heat pipes with operating temperatures ranging from 550 to 700 K. Mercury and sulfur are typical fluids in this range, along with some organic fluids (e.g., naphthalene and biphenyl). BOOKCOMP, Inc. — John Wiley & Sons / Page 1185 / 2nd Proofs / Heat Transfer Handbook / Bejan INTRODUCTION 1185 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1185], (5) Lines: 144 to 158 ——— 0.0pt PgVar ——— Long Page * PgEnds: Eject [1185], (5) 4. High (liquid-metal)-temperature heat pipes operating above 700 K. Very high heat fluxes can be obtained using liquid metals due to the characteristics of the fluid: namely, very large surface tensions and high latent heats of vaporization. Examples of liquid metals commonly used include potassium, sodium, and silver. In the case of liquid metal heat pipes, startup typically involves starting from an initially frozen working fluid. Because the amount of heat transferred by a heat pipe depends on the latent heat of vaporization, the transfer of appreciable quantities of heat is possible, even for long distances. Axial heat flows of 10 8 W/m 2 are easily reachable with sodium heat pipes. By calculating an effective thermal conductivity k eff , values may reach 10 8 W/m ·K (sodium heat pipe) (Ivanovskii et al., 1982), which is several orders of magnitude greater than the conductivity of the best conductors. One of the most common applications of a heat pipe is that of a heat flux trans- former. Using a heat pipe, high heat fluxes from a heat source can be injected over a small surface area, which is then rejected over a larger condenser surface area. Thermal flux transformation ratios greater than 10 : 1 can allow systems to employ final heat rejection with low cooling capability methods, such as natural convection or single-phase cooling. 16.1.2 Wick Structures The wick provides a means for the flow of liquid from the condenser to the evaporator section of the heat pipe. It also provides surface pores that are required at the liquid– vapor interface for development of the required capillary pressure. The wick structure also has an impact on the radial temperature drop at the evaporator end between the inner heat pipe surface and the liquid–vapor surface. Thus, an effective wick requires large internal pores in a direction normal to the heat flow path. This will minimize liquid flow resistance. In addition, small surface pores are required for the development of high capillary pressure and a highly conductive heat flow path for minimization of the radial surface to liquid–vapor surface temperature drop. To satisfy these requirements, two types of wick structure have been developed. These are the homogeneous wicks made of a single material, examples of which are shown in Fig. 16.2, and the composite wicks containing two or more materials, with some typical examples displayed in Fig. 16.3. One common wick structure is the wrapped screen wick shown in Fig. 16.2a. This type of wick structure is designated by its mesh number, which is an indication of the number of pores per unit length or unit surface area. The surface pore size is inversely proportional to the mesh number and the liquid flow resistance can be controlled by the tightness of the wrapping. This is attractive, but because of the interruptions in the wick metal by a liquid of low thermal conductivity in the moderate-range heat pipe, the radial temperature drop from the inner pipe surface to the liquid–vapor surface at the evaporator end can be quite high. This problem can be alleviated through use of the sintered metal wick structure shown in Fig. 16.2b. Notice here that the pore size is small but the small pores will make it more difficult for the liquid to flow from the condenser to the evaporator. BOOKCOMP, Inc. — John Wiley & Sons / Page 1186 / 2nd Proofs / Heat Transfer Handbook / Bejan 1186 HEAT PIPES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1186], (6) Lines: 158 to 173 ——— 0.178pt PgVar ——— Long Page * PgEnds: Eject [1186], (6) Figure 16.2 Cross sections of homogeneous wick structures. (From Chi, 1976, with per- mission.) Figure 16.3 Cross sections of composite wick structures. (From Chi, 1976, with permission.) . in heat pipes, these systems are seen as attractive options in a wide range of heat transfer applications. BOOKCOMP, Inc. — John Wiley & Sons / Page 1184 / 2nd Proofs / Heat Transfer Handbook. heat pipes, startup typically involves starting from an initially frozen working fluid. Because the amount of heat transferred by a heat pipe depends on the latent heat of vaporization, the transfer. Saturated Heat- Generating Porous Layer, J. Heat Transfer, 101, 169–171. Lai, F. C., Kulacki, F. A., and Prasad, V. (1991). Mixed Convection in Saturated Porous Media, in Convective Heat and Mass Transfer