Theory ofthe Ultimate Heat Transfer ofCylindrical Heat Pipes, Int.. Liquid Mass Transport in Annular Two-Phase Flow, Two-Phase Momen-tum, Heat and Mass Transfer in Chemical, Process, an
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dry dryout
evaporator section eff effective
fin
g gravitational
inertial interface
surface
wick wetting
axial hydrostatic pressure + normal hydrostatic pressure
REFERENCES
Akachi, H., and Polasek, F (1995) Pulsating Heat Pipe Review ofthe Present State ofthe Art,
Technical Report ITRI-ERL, Chutung, Taiwan, May.
Ambrose, J H., Chow, L C., and Beam, J E (1987) Transient Heat Pipe Response and
Rewetting Behavior, J Thermophys Heat Transfer, 1(3), 222–227.
Babin, B R., Peterson, G P., and Wu, D (1990) Experimental Investigation ofa Flexible
Bellows Heat Pipe for Cooling Discrete Heat Sources, J Heat Transfer, 112(3), 602–607.
Bankston, C A., and Smith, J H (1971) Incompressible Laminar Vapor Flow in Cylindrical
Heat Pipes, ASME-71-WA/HT-15, ASME, New York.
Bowman, W J (1991) Numerical Modeling ofHeat-Pipe Transients, J Thermophys Heat
Transfer, 5(3), 374–379.
Trang 21 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
[1228],(48)
Lines: 1250 to 1298
———
9.0pt PgVar
———
Custom Page (-4.0pt) PgEnds: TEX [1228],(48)
Brennan, P J., and Kroliczek, E J (1979) Heat Pipe Design Handbook, NASA Contract
Report NAS5-23406
Busse, C A (1973) Theory ofthe Ultimate Heat Transfer ofCylindrical Heat Pipes, Int J.
Heat Mass Transfer, 16, 169–186.
Busse, C A., and Kemme, J E (1980) Dry-out Phenomena in Gravity-Assist Heat Pipes with
Capillary Flow, Int J Heat Mass Transfer, 23, 643–654.
Carey, V P (1992) Liquid–Vapor Phase-Change Phenomena, Taylor & Francis,
Washing-ton, DC
Chang, W S., and Colwell, G T (1985) Mathematical Modeling ofthe Transient Operating
Characteristics ofa Low-Temperature Heat Pipe, Numer Heat Transfer, 8, 169–186.
Chi, S W (1976) Heat Pipe Theory and Practice, Hemisphere Publishing, Washington, DC.
Colwell, G T., and Modlin, J M (1992) Mathematical Heat Pipe Models, Proc 8th
Interna-tional Heat Pipe Conference, Vol 1, pp 162–166.
Cotter, T P (1967) Heat Pipe Startup Dynamics, Proc SAE Thermionic Conversion Specialist
Conference, Palo Alto, CA.
Delhaye, J M (1981) Basic Equations for Two-Phase Flow Modeling, in Two-Phase Flow
and Heat Transfer in the Power and Process Industries, A E Bergles, J G Collier, and
J M Delhaye, eds., Hemisphere Publishing, Washington, DC
Deverall, J E., Kemme, J E., and Florschuetz, L W (1970) Sonic Limitations and Startup
Problems ofHeat Pipes, Report LA-4578, Los Alamos Scientific Laboratory, Los
Ala-mos, NM
Dunbar, N., and Cadell, P (1998) Working Fluids and Figures ofMerit for CPL/LHP
Appli-cations, CPL-98 Workshop Proc., Aerospace Corporation, El Segundo, CA, Mar 2–3.
Dunbar, N., and Supper, W (1997) Spacecraft Capillary Pumped Loop Technology towards a
Qualified Thermal Control Tool, Proc 10th International Heat Pipe Conference, Stuttgart,
Germany
Dunn, P D., and Reay, D A (1982) Heat Pipes, 3rd ed., Pergamon Press, New York.
Faghri, A (1995) Heat Pipe Science and Technology, Taylor & Francis, Washington, DC.
Gaugler, R S (1944) Heat Transfer Devices, U.S patent 2,350,348
Grover, G M., Cotter, T P., and Erikson, G F (1964) Structures ofVery High Thermal
Conductivity, J Appl Phys., 218, 1190–1191.
Hewitt, G F (1979) Liquid Mass Transport in Annular Two-Phase Flow, Two-Phase
Momen-tum, Heat and Mass Transfer in Chemical, Process, and Energy Engineering Systems, Vol.
1, Hemisphere Publishing, New York, pp 273–302
Incropera, F P., and DeWitt, D P (1996) Fundamentals ofHeat and Mass Transfer, 4th ed., Wiley, New York
Ivanovskii, M N., Sorokin, V P., and Yagodkin, I V (1982) The Physical Properties of Heat
Pipes, Clarendon Press, Oxford.
Kemme, J E (1969) Ultimate Heat Pipe Performance, IEEE Trans Electron Devices, 16,
717–723
Kemme, J E (1976) Vapor Flow Consideration in Conventional and Gravity-Assist Heat
Pipes, Proc 2nd International Heat Pipe Conference, pp 11–21.
Ku, J (1997) Recent Advances in Capillary Pumped Loop Technology, AIAA-97-3870, AIAA,
New York
Trang 31 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
[1229],(49)
Lines: 1298 to 1339
———
13.0pt PgVar
———
Custom Page (-4.0pt) PgEnds: TEX [1229],(49)
Langer, H., and Mayinger, F (1979) Entrainment in Annular Two-Phase Flow under Steady
and Transient Flow Conditions, Two-Phase Momentum, Heat and Mass Transfer in
Chem-ical, Process, and Energy Engineering Systems, Vol 2, Hemisphere Publishing, New York,
pp 695–706
Levy, E K (1968) Theoretical Investigation ofHeat Pipes Operating at Low Vapor Pressure,
J Eng Ind., 90, 547–552.
Levy, E K., and Chou, S F (1973) The Sonic Limit in Sodium Heat Pipes, J Heat Transfer,
95, 218–223
Maidanik, Y F., and Fershtater, Y G (1997) Theoretical Basis and Classification ofLoop
Heat Pipes and Capillary Pumped Loops, Proc 10th International Heat Pipe Conference,
Stuttgart, Germany, Sept
Marcus, B D (1965) On the Operation ofHeat Pipes, Report 9895-6001-TU-000, TRW,
Redondo Beach, CA
Moody, L F (1944) Friction Factors for Pipe Flow, Trans ASME, 66, 671–684.
Nguyen-Chi, H., and Groll, M (1981) Entrainment or Flooding Limit in a Closed Two-Phase
Thermosyphon, Proc 4th International Heat Pipe Conference, pp 147–162.
Ochterbeck, J M (1997) Modeling ofRoom-Temperature Heat Pipe Startup from the Frozen
State, J Thermophys Heat Transfer, 11(2), 165–172.
Ochterbeck, J M., Peterson, G P., and Ungar, E (1995) Depriming/Rewetting ofExternal
Artery Heat Pipes: Comparison with SHARE-II Flight Experiment, J Thermophys Heat
Transfer, 9(1), 101–108.
Peterson, G P (1994) An Introduction to Heat Pipe, Wiley, New York.
Peterson, G P., and Bage, B (1991) Entrainment Limitations in Thermosyphons and Heat
Pipes, J Energy Resour Technol., 113(3), 147–154.
Prenger, F C (1984) Performance Limits of Gravity-Assist Heat Pipes, Proc 5th International
Heat Pipe Conference, pp 1–5.
Prenger, F C., and Kemme, J E (1981) Performance Limits of Gravity-Assist Heat Pipes with
Simple Wick Structures, Proc 4th International Heat Pipe Conference, pp 137–146.
Rice, G., and Fulford, D (1987) Influence of a Fine Mesh Screen on Entrainment in Heat
Pipes, Proc 6th International Heat Pipe Conference, pp 168–172.
Rohani, A R., and Tien, C L (1974) Analysis ofthe Effects ofVapor Pressure Drop on Heat
Pipe Performance, Int J Heat Mass Transfer, 17, 61–67.
Stenger, F J (1966) Experimental Feasibility Study ofWater-Filled Capillary Pumped Heat
Transfer Loops, NASA X-1310, NASA LeRC Report.
Tien, C L., and Chung, K S (1979) Entrainment Limits in Heat Pipes, AIAA J., 17(6), 643–
646
Trefethen, L (1962) On the Surface Tension Pumping ofLiquids or a Possible Role ofthe Candlewick in Space Exploration, GE Tech Int Ser No G15-D114, General Electric Co., Schenectady, NY
Vinz, P., and Busse, C A (1973) Axial Heat Transfer Limits of Cylindrical Sodium Heat Pipes between 25 W-cm−2and 15.5 kW-cm−2, Proc 1st International Heat Pipe Conference,
Stuttgart, Germany, Paper 2-1
Wayner, P C., Jr (1999) Long Range Intermolecular Forces in Change-of-Phase Heat Transfer,
Proc 33rd National Heat Transfer Conference, Albuquerque, NM, Aug 15–17.
Trang 41 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]
[1230],(50)
Lines: 1339 to 1347
———
443.04701pt PgVar
———
Normal Page PgEnds: TEX [1230],(50)
Wu, D., Peterson, G P., and Chang, W S (1991) Transient Experimental Investigation of
Micro Heat Pipes, J Thermophys Heat Transfer, 5(4), 539–545.
Wulz, H., and Embacher, E (1990) Capillary Pumped Loops for Space Applications: Ex-perimental and Theoretical Studies on the Performance of Capillary Evaporator Designs,
AIAA-90-1739, AIAA, New York.
Yan, Y., and Ochterbeck, J M (1999) Analysis ofthe Supercritical Startup Behavior for
Cryogenic Heat Pipes, J Thermophys Heat Transfer, 13(1), 140–145.
Zucrow, M J., and Hoffman, J D (1976) Gas Dynamics, Wiley, New York.
Trang 52 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
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CHAPTER 17
Heat Transfer in Manufacturing and Materials Processing
RICHARD N SMITH
Department of Mechanical Engineering, Aeronautical Engineering and Mechanics Rensselaer Polytechnic Institute
Troy, New York
C HARIS DOUMANIDIS
Department of Mechanical Engineering Tufts University
Medford, Massachusetts
RANGA PITCHUMANI
Department of Mechanical Engineering Universityof Connecticut
Storrs, Connecticut
17.1 Introduction 17.2 Heat transfer to moving materials undergoing thermal processing 17.2.1 Uniform thermal environment
Thin solid model Two-dimensional workpieces 17.2.2 Interaction between a discrete heat source and a continuously moving work-piece
Thin plate or rod with a moving planar heat source Thin plate with a moving line heat source Semi-infinite solid with a moving point source Semi-infinite plane with finite size moving heat source 17.3 Thermal issues in heat treatment ofsolids
17.4 Machining processes: metal cutting 17.4.1 Background
17.4.2 Thermal analysis Tool–chip interface temperature rise Energy generation at the shear plane Assessment ofsteady-state metal cutting temperature models 17.5 Machining processes: grinding
17.5.1 Background 17.5.2 Workpiece temperatures during grinding 17.6 Thermal–fluid effects in continuous metal forming processes 17.6.1 Background
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17.6.2 Considerations for thermal–fluid modeling in extrusion and drawing Deformation heating considerations
Frictional heating considerations 17.7 Processing ofpolymer-matrix composite materials 17.7.1 Introduction
17.7.2 Processing ofthermosetting-matrix composites Thermal model
Kinetics model Laminate consolidation model 17.7.3 Processing ofthermoplastic-matrix composites Heat transfer
Void dynamics Interlaminar bonding Polymer degradation Solidification (crystallization) 17.8 Thermal process control for manufacturing 17.8.1 Control ofSISO thermal systems Thermostatic (on–off) control Proportional–integral–derivative (PID) control Software implementation of SISO controllers 17.8.2 Control ofMIMO thermal systems
State controllers by pole placement State observers by pole placement 17.8.3 Optimal formulation: linear quadratic Gaussian Optimal control: linear quadratic regulator (LQR) Optimal observation: Kalman–Bucy filter 17.8.4 Smith prediction
17.8.5 Sliding mode control 17.8.6 Adaptive control Model reference adaptive control (MRAC) Self-tuning regulation
17.8.7 Parameter identification Orthogonal projection Least squares Nomenclature
References
17.1 INTRODUCTION
The last two decades ofthe twentieth century have witnessed a significant move
in the thermal-fluid sciences toward studying fundamental problems motivated by applications in manufacturing and materials processing Establishment of a number ofindustrially supported research centers within universities had the express purpose ofdeveloping advances that could directly affect U.S industrial competitiveness in manufacturing and that could train a new generation of technical specialists
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Recognition that many processes, such as casting, welding, spray deposition, quenching, crystal growth, extrusion and drawing, rolling, and metal cutting, are enabled and/or controlled by heat transfer and fluid mechanics phenomena has led heat transfer researchers to turn their attention to these types of problems The report ofthe National Science Foundation (NSF)-sponsored workshop on critical technolo-gies in the thermal systems (Jacobs and Hartnett, 1992) emphasized the importance ofwork in this area The proceedings ofseveral recent international symposia (Shah
et al., 1992; Tanasawa and Lior, 1992; Guceri, 1993) have provided significant col-lections ofreview articles and ofrecent research results which can be ofgreat utility
to engineers and researchers In 1988, the Heat Transfer Division of the American Society ofMechanical Engineers (ASME) initiated a new technical committee
(K-15, Heat and Mass Transfer in Manufacturing and Materials Processing, referred to subsequently as MMP) to coordinate the orderly presentation ofresearch results at division-sponsored meetings These activities were recently celebrated with a more focused NSF-sponsored workshop (Prasad et al., 1998) Kitto et al (1995) highlighted critical technologies associated with thermal phenomena, with particular emphasis on MMP A new journal devoted to this subject was also initiated (Guceri, 1992), and two other handbook chapters have appeared (Radford and Tong, 2000; Viskanta and Bergman, 2000)
Necessarily, the scope ofthis presentation must be limited First, MMP is an ex-tremely broad subject, and it is difficult to identify common technological founda-tions among such disparate topics as, for example, machining and injection molding and chemical vapor deposition, even with a focus strictly on thermal-fluid aspects
Furthermore, the thermal-fluid elements ofeven a single process cannot be separated fully from other fundamental engineering elements, such as material behavior, me-chanics, and control Indeed, entire books have been devoted even to a single type ofmanufacturing process (e.g., DeVries, 1992; Steen, 1991) Nonetheless, the goal ofthe present chapter is to characterize the important transport phenomena, particu-larly heat transfer, that are associated with a number of manufacturing and materials processing operations The general approach will be to introduce and review the es-sential features of a particular manufacturing process, to identify appropriate physical models of the process that are useful for describing the thermal and transport fields,
to show how the physical model leads to a mathematical model ofthe process, and
to interpret these models in light ofexperimental results and in terms ofthe expected performance and operation of the actual process
The particular subjects have been chosen largely from segments of three graduate courses taught by the authors, developed independently between 1995 and 2000 The focus is more on manufacturing operations than on materials processes (as much as those two can be distinguished), and there is limited overlap with similar monographs (Radford and Tong, 2000; Viskanta and Bergman, 2000), so that no specific reference will be made to them Examples oftopics that have reluctantly been omitted are most phases ofsolidification processing, chemical and vapor deposition processes, poly-mer processes (except for composites processing), and others that the reader will note Some texts that may serve as appropriate background in some ofthese areas are Poirier and Poirier (1992), Guthrie (1989), Gaskell (1992), Flemings (1974), Poirier
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and Geiger (1994), Yang et al (1994), and Kou (1996) For background on general manufacturing and materials processes, the reader is referred to classical texts (Schey, 2000; Kalpakjian, 1996; DeGarmo et al., 1997) The authors have chosen not to at-tempt a complete literature review ofthe particular subjects Rather, important refer-ences that comprise the essential focus will be cited, in addition to broad background references
Most ofthe necessary background in conduction, convection, and radiation phe-nomena has been discussed in earlier chapters ofthis book Unique features ofMMP that must be considered carefully in developing appropriate physical models are un-usual boundary conditions, conjugate heat transfer problems, in which two adjoining media are thermally coupled; moving heat sources or sinks; multimode heat transfer (convection and radiation); and phase change Some background material on con-duction heat transfer to objects in motion and on the thermal response of a solid to
a moving, local, or distributed heat source is offered first These elements are com-mon to several ofthe process descriptions that follow Section 17.3 contains a very briefreview ofsome ofthe issues in heat treatment In Sections 17.4 to 17.6 some material removal and metal forming processes are discussed In Section 17.7 some thermal characteristics ofcomposite materials manufacturing are introduced Finally,
in Section 17.8 we present an introduction to analysis for thermal control, which has common application in almost any manufacturing operation involving an applied heat source In all cases, the heat transfer elements are emphasized over considerations of mechanical behavior and material property response
17.2 HEAT TRANSFER TO MOVING MATERIALS UNDERGOING THERMAL PROCESSING
A large variety ofprocesses involve the continuous movement ofa workpiece or man-ufactured part through a thermal environment These can include rolling, extrusion and drawing, continuous casting, crystal growth, welding, and heat treatment The thermal environment can be localized, such as the forming zone of a rolling process,
or continuous, such as quenching ofa wire following a drawing process When a heat source is localized, it may be that the source itselfis moving and the workpiece stationary, although it is often convenient to consider the thermal field from the point ofview ofa stationary source Processing speeds can vary from a few centimeters per hour (Czochralski crystal growth) to several meters per second (wire drawing)
17.2.1 Uniform Thermal Environment
Consider first the case ofa continuously moving workpiece exposed to a uniform thermal environment Jaluria (1993) has discussed three basic approaches in the math-ematical modeling ofsuch processes In the first approach, only conduction heat transfer in the solid material (workpiece), including the advection associated with the workpiece motion, is considered The external heating or cooling is accommo-dated by a known surface heat transfer coefficient and/or radiative environment or
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Figure 17.1 Conjugate temperature and velocity fields in a moving material undergoing convective cooling
by a specified distribution ofsurface heat flux The second approach focuses on the convective flow field in the surroundings, which is induced, at least partially, by the workpiece movement One attempts to obtain a distribution ofthe local surface heat
transfer coefficient from the thermal field calculated in the fluid The thermal
condi-tions in the solid workpiece are prescribed as boundary condicondi-tions (This would be considered a classical convection problem.) The third approach is a combination of
the first two, called a conjugate problem ofheat transfer, as illustrated schematically
in Fig 17.1 The thermal fields in the workpiece and in the surroundings are both determined, with a coupling ofthe thermal and fluid conditions at the solid–fluid interface The concentration here is only on the first approach, because attention is necessarily focused on the workpiece thermal response However, it should be rec-ognized that a determination ofsurface heat transfer coefficients, presumed as being known and uniform in most of what follows, is seldom a straightforward task
the cross section ofthe workpiece is negligible compared to that along its length
For a workpiece moving at a uniform velocity (implying that the cross section of the workpiece is uniform in the direction of motion), an energy balance on a differential control volume ofsizedA c × dx yields the following equation for the temperature
distribution as a function of time and distancex along the workpiece (Fig 17.2):
1 α
∂T
∂t =
∂2T
∂x2 −Vα ∂T ∂x −kA hP
c (T − T∞) (17.1a) with some very simple boundary conditions:
T = T o at x = 0
∂T
∂x = 0 at x = L (17.1b)
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Figure 17.2 Continuously moving material whose surface is exposed to a convective heat transfer environment
Under steady-state conditions, the following dimensionless parameters may conve-niently be introduced:
x∗= xγ θ = T T − T∞
o − T∞ Pe=
V γ
α
L∗= L
hγ k
(17.2)
whereγ ≡ A c /P (P is the perimeter) The dimensionless form of eq (17.1a) is
d2θ
dx∗2− Pedx dθ∗ − Bi · θ = 0 (17.3a) subject to
θ = θo at x∗ = 0
∂θ
The solution to eq (17.3) is straightforward:
θ(x)
θo =m1e m1L∗
e m2x∗
− m2 e m2L∗
e m1x∗
m1e m1L∗− m2 e m2L∗ (17.4) where
m1andm2= Pe±
Pe2+ 4 Bi