Metal Foams: A Design Guide

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230 Metal Foams: A Design Guide where h is the average heat transfer coefficient from the electronics into the coolant, and Tf is the average temperature of the fluid. The design used to approach this maximum entails the use of heat spreaders and planar microheat-pipes. Based on equations (17.1) and (17.2), for the heat sink to be reduced to 3 cm, a heat transfer coefficient exceeding about 3 kW/m 2 Kis needed. Such levels can be readily realized using liquids, but are well in excess of those now achievable with air cooling (Figure 17.12). The challenge is to determine whether cellular metals can attain such high h with air. Cellular metal performance For the airflows needed to realize these h, a fan/blower configuration with requisite operating characteristics must be designed. These characteristics typically exhibit a nearly linear interdependence between back pressure 1p and volume flow rate, PV (Table 17.1), with 1p Ł and PV Ł as the respective perfor- Table 17.1 Formulae for calculating achievable heat dissipation (1) Heat extracted over sink area (4b 2 ) q D v[Tj T0] fcp⊲Hs/2bhs⊳[1 exp⊲ 2bhs/ℓ⊳] (2) Transfer length ℓ D 4.1v ⊲1 � fcpHsd 1 C ⊳kmBi ⊲1 2 ⊳ p Bi tanh � p Hs Bi 1.24d (3) Biot number Bi D 1.04 � fcp kf �0.4 � vd �0.4 � � kf 1 ˛ (where ˛ D 0.37 p C 0.055 ) (4) Pressure drop in sink 1p D 0.75 p � 0.4 f v1.6 d 1.4 ⊲1 ˛⊳ 1.6 (5) Operating characteristics of pump 1p D 1pŁ [1 vhsbhs/ PV Ł ] (6) Fluid flow rate � km 1pŁ [1 2vbhs/ PV Ł 0.4 p fvf ] D 0.75 d 1.4 v 1.6 ⊲1 ˛⊳ 1.6 �� 1
q *(MW/m 2) 15 10 Power density fixed ∆p*(8 kPa) 0.4 0.5 ∆p* 5 0.3 ρ/ρs 0.2 0 100 200 300 400 ∆p q max d (mm) Air Pump ⋅ V Case studies 231 Heat sink Pump Figure 17.15 Maximum on-chip thermal performance using mesocell metal heat sinks mance coefficients (Figure 17.15). These characteristics overlay with the pressure drop in the heat sink, also given in Table 17.1. Equating the pressure drop with the operating characteristics results in an explicit flow rate for each heat sink (Figure 17.15): that is, for given cell size, relative density and thickness. With this defined flow rate, a specific heat flux, q, can be accommodated by the design. Accordingly, for a prescribed fan, the heat sink exhibits a heat flux domain wherein the relative density and cell size are the variables. One such domain is indicated in Figure 17.15, calculated for bhs D 3cm and bsi D 0.5 cm. Note that there is a ridge of high heat flux coincident with an optimum cell size. At a cell size smaller than this optimum, the pressure drop is excessive: conversely, at a larger cell size, the diminished heat transfer limits the performance. Along the ridge, there is a weak dependence of heat flux on relative density in the practical range ( / s D 0.2–0.5). By selecting cellular materials that reside along the heat flux ridge, the requirements for the fan can be specified, resulting in a relationship between ⋅ V *
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Metal Foams: A Design Guide
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Copyright © 2000 by Butterworth-He
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vi Contents 4.3 Foam property chart
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viii Contents 17 Case studies 217 1
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List of contributors M.F. Ashby Cam
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Table of physical constants and con
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Chapter 1 Introduction Metal foams
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Activity Research Industrial take-u
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Application Comment Introduction Bi
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Cell size (cm) Making metal foams 7
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Making metal foams solidify. The th
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Making metal foams 11 2.4 Gas-relea
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a) Preform Polymer ligaments d) Rem
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a) Vapor deposition of Nickel b) Bu
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Process Steps a) Powder / Can prepa
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Making metal foams 19 flight in a t
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a) Metal - Hydrogen binary phase di
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Entrapped gas expansion Making meta
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(a) (b) (c) 100µm Characterization
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E/E bulk σ peak /σ bulk 1.2 1.0 0
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Stress (MPa) Characterization metho
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Characterization methods 31 foam sp
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Characterization methods 33 ž Prop
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F/2 F/2 F/2 F/2 τ Core Characteriz
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Characterization methods 37 40 40 4
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Characterization methods 39 Gioux,
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(a) (b) (c) Properties of metal foa
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Table 4.1 (a) Ranges a for mechanic
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Stress, σ Schematic Young's modulu
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Properties of metal foams 47 foams.
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Properties of metal foams 49 show t
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Modulus 0.5 /Density (GPa 0.5 /(Mg/
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elations take the form P Ł � Ł
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Chapter 5 Design analysis for mater
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Table 5.1 Design requirements Desig
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Design analysis for material select
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5.4 Where might metal foams excel?
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Table 6.1 Constitutive equations fo
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h SECTION h o h i d d o a b ;;; QQQ
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6.3 Elastic deflection of beams and
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6.4 Failure of beams and panels (a)
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;; ;;; ;; M ;; ;;; ;; ;;; ;; ;; ;;
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Torsion of shafts T T,q T T,q Yield
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R a 2 Flow field R F R 2a 2 F F s c
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;; ; QQ Q ¢¢ ¢ ;; ;; QQ QQ ¢¢
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; ;; Creep p e p e • Area A u F 2
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and its deviatoric (i.e. shear) com
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Normalized effective stress 1.4 1.2
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A constitutive model for metal foam
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A constitutive model for metal foam
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Stress amplitude, ∆σ + Stress,
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Axial strain (%) 5 4 3 2 1 0 0 σma
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Nominal compressive strain Nominal
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σ max σ pl τ max τ pl σ max σ
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Design for fatigue with metal foams
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the net section stress criterion re
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E σ pl (m) 10 1 0.1 0.01 0.1 Relat
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Chapter 9 Design for creep with met
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Design for creep with metal foams 1
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instead to: � Pε 3 D Pε0 2 s Ł
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Time to failure (hours) 10 2 10 1 1
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Design for creep with metal foams 1
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Chapter 10 Sandwich structures Sand
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Sandwich structures 115 The elastic
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Indentation Sandwich structures 117
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H H Core shear Core shear Collapse
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0.5 10−1 t c t c 10 −2 0.5 10
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Sandwich structures 123 the contact
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Sandwich structures 125 four sectio
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c t p p Figure 10.9 Sandwich panel
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Sandwich structures 129 with k ¾ D
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c/ Face sheet yielding 0.14 0.12 0.
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Weight index, ψ 10 −1 10 −2 10
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Sandwich structures 135 To construc
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Sandwich structures 137 The associa
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Sandwich structures 139 Note that,
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where D � 2⊲1 Eft 2 f ⊳GcR Sa
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Weight index ψ = W/2πR 2 ρ s W c
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Sandwich structures 145 plastic yie
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Sandwich structures 147 within the
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Sandwich structures 149 Shuaeib, F.
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Energy management: packaging and bl
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Energy/Unit cost (kJ/£) 10 1 0.1 0
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ys crushes axially at the load Ener
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peak pressure MPa Impulse/(mass of
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Chapter 12 Sound absorption and vib
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Sound absorption and vibration supp
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Sound absorption and vibration supp
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0 Sound absorption and vibration su
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Page 193 and 194: Chapter 13 Thermal management and h
Page 195 and 196: Thermal management and heat transfe
Page 197 and 198: Thermal management and heat transfe
Page 199 and 200: ~ P ~ Re 2.6 1000 800 600 400 200 0
Page 201 and 202: Chapter 14 Electrical properties of
Page 203 and 204: Electrical properties of metal foam
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Page 207 and 208: 15.3 Joining of metal foams Cutting
Page 209 and 210: Pull-out load, F p (N) 10 5 10 4 10
Page 211 and 212: Cyclic loading of fasteners Cutting
Page 213 and 214: Time, material, energy, capital, in
Page 215 and 216: Cost estimation and viability 203 A
Page 217 and 218: $/Unit Melting Schematic of the liq
Page 219 and 220: Performance metric, P2 B Non-domina
Page 221 and 222: Cost estimation and viability 209 t
Page 223 and 224: Cost estimation and viability 211 i
Page 225 and 226: P 2 = 1/Loss coefficient (−) 1000
Page 227 and 228: Cost estimation and viability 215 C
Page 229 and 230: Chapter 17 Case studies Metal foams
Page 231 and 232: Case studies 219 Figure 17.2 A pres
Page 233 and 234: Case studies 221 Figure 17.4 Highwa
Page 235 and 236: Case studies 223 Figure 17.6 DUOCEL
Page 237 and 238: Case studies 225 density and high t
Page 239 and 240: Case studies 227 required for compa
Page 241: Maximum power density at electronic
Page 245 and 246: Case studies 233 which optimized sk
Page 247 and 248: e-mail: cymat@ican.net Web: www.cym
Page 249 and 250: Tel: C0043 7722 801-2125 Fax: C0043
Page 251 and 252: Chapter 19 Web sites An increasing
Page 253 and 254: http://www.seac.nl/english/recemat/
Page 255 and 256: (b) (continued) Appendix: Catalogue
Page 257 and 258: (f) Vibration-limited design Append
Page 259 and 260: Index (Company and trade names are
Page 261 and 262: Heat transfer 4, 182 Heat transfer
Page 263: Surface strain mapping 36 Syntactic
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Metal Foams: A Design Guide

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