Roger Prud'homme,
Prud′homme
John Wiley & Sons
e druk, 2012
9781848214255
Flows and Chemical Reactions
Specificaties
Gebonden, 352 blz.
|
Engels
John Wiley & Sons |
e druk, 2012
ISBN13: 9781848214255
Rubricering
Onderdeel van serie
ISTE
Verwachte levertijd ongeveer 16 werkdagen
Samenvatting
The aim of this book is to relate fluid flows to chemical reactions. It focuses on the establishment of consistent systems of equations with their boundary conditions and interfaces, which allow us to model and deal with complex situations.
Chapter 1 is devoted to simple fluids, i.e. to a single chemical constituent. The basic principles of incompressible and compressible fluid mechanics, are presented in the most concise and educational manner possible, for perfect or dissipative fluids. Chapter 2 relates to the flows of fluid mixtures in the presence of chemical reactions. Chapter 3 is concerned with interfaces and lines. Interfaces have been the subject of numerous publications and books for nearly half a century. Lines and curvilinear media are less known Several appendices on mathematical notation, thermodynamics and mechanics methods are grouped together in Chapter 4.
This summary presentation of the basic equations of simple fluids, with exercises and their solutions, as well as those of chemically reacting flows, and interfaces and lines will be very useful for graduate students, engineers, teachers and scientific researchers in many domains of science and industry who wish to investigate problems of reactive flows. Portions of the text may be used in courses or seminars on fluid mechanics.
Specificaties
ISBN13:9781848214255
Taal:Engels
Bindwijze:gebonden
Aantal pagina's:352
Uitgever:John Wiley & Sons
Serie:ISTE
Inhoudsopgave
<p>Preface xiii</p>
<p>List of the Main Symbols xv</p>
<p>Chapter 1. Simple Fluids 1</p>
<p>1.1. Introduction 1</p>
<p>1.2. Key elements in deformation theory Lagrangian coordinates and Eulerian coordinates 2</p>
<p>1.2.1. Strain rates 2</p>
<p>1.2.2. Lagrangian coordinates and Eulerian coordinates 7</p>
<p>1.2.3. Trajectories, stream lines, emission lines 8</p>
<p>1.3. Key elements in thermodynamics Reversibility, irreversible processes: viscosity, heat conduction 9</p>
<p>1.3.1. Thermodynamic variables, definition of a system, exchanges, differential manifold of equilibrium states, transformation 9</p>
<p>1.3.2. Laws of thermodynamics 11</p>
<p>1.3.3. Properties of simple fluids at equilibrium. 14</p>
<p>1.4. Balance equations in fluid mechanics. Application to incompressible and compressible perfect fluids and viscous fluids 18</p>
<p>1.4.1. Mass balance 18</p>
<p>1.4.2. Concept of a particle in a continuous medium: local state 19</p>
<p>1.4.3. Balance for the property F 20</p>
<p>1.4.4. Application to volume, to momentum and to energy 22</p>
<p>1.4.5. Entropy balance and the expression of the rate of production of entropy 23</p>
<p>1.4.6. Balance laws for discontinuity 25</p>
<p>1.4.7. Application to incompressible perfect fluids 26</p>
<p>1.4.8. Application to dissipative fluids 31</p>
<p>1.5. Examples of problems with 2D and 3D incompressible perfect fluids 32</p>
<p>1.5.1. Planar 2D irrotational flows: description in the complex plane of steady flows 32</p>
<p>1.5.2. 3D irrotational flows of incompressible perfect fluids: source, sink, doublet 36</p>
<p>1.5.3. Rotational flows of incompressible perfect fluids 41</p>
<p>1.6. Examples of problems with a compressible perfect fluid: shockwave, flow in a nozzle, and characteristics theory 44</p>
<p>1.6.1. General theorems 44</p>
<p>1.6.2. Propagation of sound in an ideal gas 44</p>
<p>1.6.3. Discontinuities 46</p>
<p>1.6.4. Unsteady characteristics 47</p>
<p>1.6.5. Steady normal shockwave: Hugoniot and Prandtl relations 48</p>
<p>1.6.6. Flow in a de Laval nozzle 49</p>
<p>1.6.7. Simple wave 53</p>
<p>1.7. Examples of problems with viscous fluids 56</p>
<p>1.7.1. General equations 56</p>
<p>1.7.2. Incompressible viscous fluid 57</p>
<p>1.7.3. Flow of a compressible dissipative fluid: structure of a shockwave 61</p>
<p>1.8. Exercises 64</p>
<p>1.8.1. Exercises in kinematics (section 1.2) 64</p>
<p>1.8.2. Exercises in thermodynamics (section 1.3). 67</p>
<p>1.8.3. Exercises for the balance equations in fluid mechanics (section 1.4) 68</p>
<p>1.8.4. Examples of problems with 2D and 3D incompressible perfect fluids (section 1.5) 70</p>
<p>1.8.5. Examples of problems with a compressible perfect fluid (section 1.6) 74</p>
<p>1.8.6. Examples of problems with viscous fluids (section 1.7) 77</p>
<p>1.9. Solutions to the exercises 79</p>
<p>1.9.1. Solutions to the exercises in kinematics. 79</p>
<p>1.9.2. Solutions to the Exercises in thermodynamics 83</p>
<p>1.9.3. Solutions to the exercises for the balance of equations in fluid mechanics 88</p>
<p>1.9.4. Solutions to the examples of problems with 2D and 3D incompressible perfect fluids 89</p>
<p>1.9.5. Solutions to the examples of problems with a compressible perfect fluid 93</p>
<p>1.9.6. Solutions to the examples of problems with viscous fluids 95</p>
<p>Chapter 2. Reactive Mixtures 101</p>
<p>2.1. Introduction 101</p>
<p>2.2. Equations of state 103</p>
<p>2.2.1. Definition of the variables of state of a mixture 103</p>
<p>2.2.2. Thermodynamic properties of mixtures 108</p>
<p>2.2.3. Reactive mixture 118</p>
<p>2.2.4. Other issues relating to the thermodynamics of mixtures 123</p>
<p>2.3. Balance equations of flows of reactive mixtures 124</p>
<p>2.3.1. Balance of mass of the species j and overall balance of mass 124</p>
<p>2.3.2. General balance equation of a property F. 127</p>
<p>2.3.3. Momentum balance 129</p>
<p>2.3.4. Energy balance 129</p>
<p>2.3.5. Balance relations in a discrete system. 132</p>
<p>2.3.6. Entropy balance in a continuum 137</p>
<p>2.3.7. Balance equations at discontinuities in continuous media 140</p>
<p>2.4. Phenomena of transfer and chemical kinetics 142</p>
<p>2.4.1. Introduction 142</p>
<p>2.4.2. Presentation of the transfer coefficients by linear TIP 143</p>
<p>2.4.3. Other presentations of the transfer coefficients 147</p>
<p>2.4.4. Elements of chemical kinetics 152</p>
<p>2.5. Couplings 155</p>
<p>2.5.1. Heat transfer and diffusion 155</p>
<p>2.5.2. Shvab–Zeldovich approximation 158</p>
<p>Chapter 3. Interfaces and Lines 163</p>
<p>3.1. Introduction 163</p>
<p>3.1.1. Interfaces 163</p>
<p>3.1.2. Lines 165</p>
<p>3.2. Interfacial phenomena 166</p>
<p>3.2.1. General aspects 166</p>
<p>3.2.2. General form of an interfacial balance law 168</p>
<p>3.2.3. Constitutive laws for interfaces whose variables directly satisfy the classical equations in thermostatics and in 2D–TIP 173</p>
<p>3.2.4. Constitutive laws for interfaces deduced from classical thermostatics and 3D–TIP. Stretched flame example 177</p>
<p>3.2.5. Interfaces manifesting resistance to folding 179</p>
<p>3.2.6. Numerical modeling 179</p>
<p>3.2.7. Interfaces and the second gradient theory. 182</p>
<p>3.2.8. Boundary conditions of the interfaces 185</p>
<p>3.2.9. Conclusion 185</p>
<p>3.3. Solid and fluid curvilinear media: pipes, fluid lines and filaments 186</p>
<p>3.3.1. General aspects 186</p>
<p>3.3.2. Establishing the balance equations in a curvilinear medium. 188</p>
<p>3.3.3. Simplified theories 209</p>
<p>3.3.4. Triple line and second gradient theory 216</p>
<p>3.3.5. Conclusion 220</p>
<p>3.4. Exercises 222</p>
<p>3.4.1. Exercises regarding solid curvilinear media 222</p>
<p>3.4.2. Exercises regarding fluid curvilinear media 222</p>
<p>3.5. Solutions to the exercises 223</p>
<p>3.5.1. Solutions to exercises regarding solid curvilinear media. 223</p>
<p>3.5.2. Solutions to the exercises regarding fluid curvilinear media 225</p>
<p>APPENDICES 229</p>
<p>Appendix 1. Tensors, Curvilinear Coordinates, Geometry and Kinematics of Interfaces and Lines 231</p>
<p>A1.1. Tensor notations 231</p>
<p>A1.1.1. Tensors and operations on tensors 231</p>
<p>A1.2. Orthogonal curvilinear coordinates. 234</p>
<p>A1.2.1. General aspects 234</p>
<p>A1.2.2. Curl of a vector field 236</p>
<p>A1.2.3. Divergence of a vector field 237</p>
<p>A1.2.4. Gradient of a scalar 238</p>
<p>A1.2.5. Laplacian of a scalar 238</p>
<p>A1.2.6. Differentiation in a curvilinear basis 238</p>
<p>A1.2.7. Divergence of a second order tensor 239</p>
<p>A1.2.8. Gradient of a vector 239</p>
<p>A1.2.9. Cylindrical coordinates and spherical coordinates 240</p>
<p>A1.3. Interfacial layers 242</p>
<p>A1.3.1. Prevailing directions of an interfacial medium 242</p>
<p>A1.3.2. Operators of projection for interfaces 244</p>
<p>A1.3.3. Surface gradients of a scalar field 245</p>
<p>A1.3.4. Curvature vector of a curve 245</p>
<p>A1.3.5. Normal and tangential divergences of a vector field 246</p>
<p>A1.3.6. Extension of surface per unit length 246</p>
<p>A1.3.7. Average normal curvature of a surface 247</p>
<p>A1.3.8. Breakdown of the divergence of a vector field 248</p>
<p>A1.3.9. Breakdown of the Laplacian of a scalar field 249</p>
<p>A1.3.10. Breakdown of the divergence of a second order tensor 249</p>
<p>A1.3.11. Projection operators with the intrinsic definition of a surface 252</p>
<p>A1.3.12. Comparison between the two descriptions 253</p>
<p>A1.4. Curvilinear zones 254</p>
<p>A1.4.1. Presentation 254</p>
<p>A1.4.2. Geometry of the orthogonal curvilinear coordinates 256</p>
<p>A1.4.3. Projection operators and their consequences 257</p>
<p>A1.5. Kinematics in orthogonal curvilinear coordinates 260</p>
<p>A1.5.1. Kinematics of interfacial layers 260</p>
<p>A1.5.2. Kinematics of curvilinear zones 266</p>
<p>A1.5.3. Description of the center line 269</p>
<p>Appendix 2. Additional Aspects of Thermostatics 277</p>
<p>A2.1. Laws of state for real fluids with a single constituent 277</p>
<p>A2.1.1. Diagram of state for a pure fluid 277</p>
<p>A2.1.2. Approximate method to determine the thermodynamic functions 278</p>
<p>A2.1.3. Van der Waals fluid 279</p>
<p>A2.1.4. Other laws for dense gases and liquids 279</p>
<p>A2.2. Mixtures of real fluids 280</p>
<p>A2.2.1. Mixture laws for a real mixture 280</p>
<p>A2.2.2. Expression of the free energy of a real mixture 281</p>
<p>Appendix 3. Tables for Calculating Flows of Ideal Gas × ­1.4 283</p>
<p>A3.1. Calculating the parameters in continuous steady flow (section 1.6.6.2) 286</p>
<p>A3.2. Formulae for steady normal shockwaves 288</p>
<p>Appendix 4. Extended Irreversible Thermodynamics. 289</p>
<p>A4.1. Heat balance equations in a non–deformable medium in EIT 290</p>
<p>A4.2. Application to a 1D case of heat transfer 293</p>
<p>A4.3. Application to heat transfer with the evaporation of a droplet 296</p>
<p>A4.3.1. Reminders about evaporating droplets 296</p>
<p>A4.3.2. Evaporating droplet with EIT. 300</p>
<p>A4.4. Application to thermal shock 302</p>
<p>A4.4.1. Presentation of the problem and solution using CIT 302</p>
<p>A4.4.2. Thermal shock and EIT 303</p>
<p>A4.4.3. Application of the second order approximation into two examples of thermal shock 305</p>
<p>A4.5. Outline of EIT 307</p>
<p>A4.6. Applications and perspectives of EIT 310</p>
<p>Appendix 5. Rational Thermodynamics 313</p>
<p>A5.1. Introduction 313</p>
<p>A5.2. Fundamental hypotheses and axioms 314</p>
<p>A5.2.1. Basic hypotheses 314</p>
<p>A5.2.2. Basic axioms 316</p>
<p>A5.3. Constitutive laws 318</p>
<p>A5.4. Case of the reactive mixture 320</p>
<p>A5.4.1. Principle of material frame indifference 320</p>
<p>A5.4.2. Constitutive laws for a reactive mixture 321</p>
<p>A5.5. Critical remarks 324</p>
<p>Appendix 6. Torsors and Distributors in Solid Mechanics 325</p>
<p>A6.1. Introduction 325</p>
<p>A6.1.1. Torsor 325</p>
<p>A6.1.2. Distributor 325</p>
<p>A6.1.3. Power 326</p>
<p>A6.2. Derivatives of torsors and distributors which depend on a single position parameter 326</p>
<p>A6.2.1. Derivative of the velocity distributor 327</p>
<p>A6.2.2. Derivative of the tensor of forces 328</p>
<p>A6.3. Derivatives of torsors and distributors dependent on two positional parameters 328</p>
<p>A6.3.1. Expression of the velocity distributor 329</p>
<p>A6.3.2. Derivative of the velocity distributor 329</p>
<p>Appendix 7. Virtual Powers in a Medium with a Single Constituent 331</p>
<p>A7.1. Introduction 331</p>
<p>A7.2. Virtual powers of a system of n material points 332</p>
<p>A7.3. Virtual power law 333</p>
<p>A7.4. The rigid body and systems of rigid bodies 333</p>
<p>A7.4.1. The rigid body 333</p>
<p>A7.4.2. System of rigid bodies, concept of a link 334</p>
<p>A7.5. 3D deformable continuous medium 335</p>
<p>A7.5.1. First gradient theory 335</p>
<p>A7.5.2. A 3D case of perfect internal linkage: the incompressible perfect fluid 337</p>
<p>A7.5.3. Second gradient theory 337</p>
<p>A7.6. 1D continuous deformable medium 338</p>
<p>A7.6.1. First gradient theory 338</p>
<p>A7.6.2. A 1D case of perfect internal linkage: perfectly flexible and inextensible wires 340</p>
<p>A7.7. 2D deformable continuous medium 340</p>
<p>Bibliography 343</p>
<p>Index 355</p>
<p>List of the Main Symbols xv</p>
<p>Chapter 1. Simple Fluids 1</p>
<p>1.1. Introduction 1</p>
<p>1.2. Key elements in deformation theory Lagrangian coordinates and Eulerian coordinates 2</p>
<p>1.2.1. Strain rates 2</p>
<p>1.2.2. Lagrangian coordinates and Eulerian coordinates 7</p>
<p>1.2.3. Trajectories, stream lines, emission lines 8</p>
<p>1.3. Key elements in thermodynamics Reversibility, irreversible processes: viscosity, heat conduction 9</p>
<p>1.3.1. Thermodynamic variables, definition of a system, exchanges, differential manifold of equilibrium states, transformation 9</p>
<p>1.3.2. Laws of thermodynamics 11</p>
<p>1.3.3. Properties of simple fluids at equilibrium. 14</p>
<p>1.4. Balance equations in fluid mechanics. Application to incompressible and compressible perfect fluids and viscous fluids 18</p>
<p>1.4.1. Mass balance 18</p>
<p>1.4.2. Concept of a particle in a continuous medium: local state 19</p>
<p>1.4.3. Balance for the property F 20</p>
<p>1.4.4. Application to volume, to momentum and to energy 22</p>
<p>1.4.5. Entropy balance and the expression of the rate of production of entropy 23</p>
<p>1.4.6. Balance laws for discontinuity 25</p>
<p>1.4.7. Application to incompressible perfect fluids 26</p>
<p>1.4.8. Application to dissipative fluids 31</p>
<p>1.5. Examples of problems with 2D and 3D incompressible perfect fluids 32</p>
<p>1.5.1. Planar 2D irrotational flows: description in the complex plane of steady flows 32</p>
<p>1.5.2. 3D irrotational flows of incompressible perfect fluids: source, sink, doublet 36</p>
<p>1.5.3. Rotational flows of incompressible perfect fluids 41</p>
<p>1.6. Examples of problems with a compressible perfect fluid: shockwave, flow in a nozzle, and characteristics theory 44</p>
<p>1.6.1. General theorems 44</p>
<p>1.6.2. Propagation of sound in an ideal gas 44</p>
<p>1.6.3. Discontinuities 46</p>
<p>1.6.4. Unsteady characteristics 47</p>
<p>1.6.5. Steady normal shockwave: Hugoniot and Prandtl relations 48</p>
<p>1.6.6. Flow in a de Laval nozzle 49</p>
<p>1.6.7. Simple wave 53</p>
<p>1.7. Examples of problems with viscous fluids 56</p>
<p>1.7.1. General equations 56</p>
<p>1.7.2. Incompressible viscous fluid 57</p>
<p>1.7.3. Flow of a compressible dissipative fluid: structure of a shockwave 61</p>
<p>1.8. Exercises 64</p>
<p>1.8.1. Exercises in kinematics (section 1.2) 64</p>
<p>1.8.2. Exercises in thermodynamics (section 1.3). 67</p>
<p>1.8.3. Exercises for the balance equations in fluid mechanics (section 1.4) 68</p>
<p>1.8.4. Examples of problems with 2D and 3D incompressible perfect fluids (section 1.5) 70</p>
<p>1.8.5. Examples of problems with a compressible perfect fluid (section 1.6) 74</p>
<p>1.8.6. Examples of problems with viscous fluids (section 1.7) 77</p>
<p>1.9. Solutions to the exercises 79</p>
<p>1.9.1. Solutions to the exercises in kinematics. 79</p>
<p>1.9.2. Solutions to the Exercises in thermodynamics 83</p>
<p>1.9.3. Solutions to the exercises for the balance of equations in fluid mechanics 88</p>
<p>1.9.4. Solutions to the examples of problems with 2D and 3D incompressible perfect fluids 89</p>
<p>1.9.5. Solutions to the examples of problems with a compressible perfect fluid 93</p>
<p>1.9.6. Solutions to the examples of problems with viscous fluids 95</p>
<p>Chapter 2. Reactive Mixtures 101</p>
<p>2.1. Introduction 101</p>
<p>2.2. Equations of state 103</p>
<p>2.2.1. Definition of the variables of state of a mixture 103</p>
<p>2.2.2. Thermodynamic properties of mixtures 108</p>
<p>2.2.3. Reactive mixture 118</p>
<p>2.2.4. Other issues relating to the thermodynamics of mixtures 123</p>
<p>2.3. Balance equations of flows of reactive mixtures 124</p>
<p>2.3.1. Balance of mass of the species j and overall balance of mass 124</p>
<p>2.3.2. General balance equation of a property F. 127</p>
<p>2.3.3. Momentum balance 129</p>
<p>2.3.4. Energy balance 129</p>
<p>2.3.5. Balance relations in a discrete system. 132</p>
<p>2.3.6. Entropy balance in a continuum 137</p>
<p>2.3.7. Balance equations at discontinuities in continuous media 140</p>
<p>2.4. Phenomena of transfer and chemical kinetics 142</p>
<p>2.4.1. Introduction 142</p>
<p>2.4.2. Presentation of the transfer coefficients by linear TIP 143</p>
<p>2.4.3. Other presentations of the transfer coefficients 147</p>
<p>2.4.4. Elements of chemical kinetics 152</p>
<p>2.5. Couplings 155</p>
<p>2.5.1. Heat transfer and diffusion 155</p>
<p>2.5.2. Shvab–Zeldovich approximation 158</p>
<p>Chapter 3. Interfaces and Lines 163</p>
<p>3.1. Introduction 163</p>
<p>3.1.1. Interfaces 163</p>
<p>3.1.2. Lines 165</p>
<p>3.2. Interfacial phenomena 166</p>
<p>3.2.1. General aspects 166</p>
<p>3.2.2. General form of an interfacial balance law 168</p>
<p>3.2.3. Constitutive laws for interfaces whose variables directly satisfy the classical equations in thermostatics and in 2D–TIP 173</p>
<p>3.2.4. Constitutive laws for interfaces deduced from classical thermostatics and 3D–TIP. Stretched flame example 177</p>
<p>3.2.5. Interfaces manifesting resistance to folding 179</p>
<p>3.2.6. Numerical modeling 179</p>
<p>3.2.7. Interfaces and the second gradient theory. 182</p>
<p>3.2.8. Boundary conditions of the interfaces 185</p>
<p>3.2.9. Conclusion 185</p>
<p>3.3. Solid and fluid curvilinear media: pipes, fluid lines and filaments 186</p>
<p>3.3.1. General aspects 186</p>
<p>3.3.2. Establishing the balance equations in a curvilinear medium. 188</p>
<p>3.3.3. Simplified theories 209</p>
<p>3.3.4. Triple line and second gradient theory 216</p>
<p>3.3.5. Conclusion 220</p>
<p>3.4. Exercises 222</p>
<p>3.4.1. Exercises regarding solid curvilinear media 222</p>
<p>3.4.2. Exercises regarding fluid curvilinear media 222</p>
<p>3.5. Solutions to the exercises 223</p>
<p>3.5.1. Solutions to exercises regarding solid curvilinear media. 223</p>
<p>3.5.2. Solutions to the exercises regarding fluid curvilinear media 225</p>
<p>APPENDICES 229</p>
<p>Appendix 1. Tensors, Curvilinear Coordinates, Geometry and Kinematics of Interfaces and Lines 231</p>
<p>A1.1. Tensor notations 231</p>
<p>A1.1.1. Tensors and operations on tensors 231</p>
<p>A1.2. Orthogonal curvilinear coordinates. 234</p>
<p>A1.2.1. General aspects 234</p>
<p>A1.2.2. Curl of a vector field 236</p>
<p>A1.2.3. Divergence of a vector field 237</p>
<p>A1.2.4. Gradient of a scalar 238</p>
<p>A1.2.5. Laplacian of a scalar 238</p>
<p>A1.2.6. Differentiation in a curvilinear basis 238</p>
<p>A1.2.7. Divergence of a second order tensor 239</p>
<p>A1.2.8. Gradient of a vector 239</p>
<p>A1.2.9. Cylindrical coordinates and spherical coordinates 240</p>
<p>A1.3. Interfacial layers 242</p>
<p>A1.3.1. Prevailing directions of an interfacial medium 242</p>
<p>A1.3.2. Operators of projection for interfaces 244</p>
<p>A1.3.3. Surface gradients of a scalar field 245</p>
<p>A1.3.4. Curvature vector of a curve 245</p>
<p>A1.3.5. Normal and tangential divergences of a vector field 246</p>
<p>A1.3.6. Extension of surface per unit length 246</p>
<p>A1.3.7. Average normal curvature of a surface 247</p>
<p>A1.3.8. Breakdown of the divergence of a vector field 248</p>
<p>A1.3.9. Breakdown of the Laplacian of a scalar field 249</p>
<p>A1.3.10. Breakdown of the divergence of a second order tensor 249</p>
<p>A1.3.11. Projection operators with the intrinsic definition of a surface 252</p>
<p>A1.3.12. Comparison between the two descriptions 253</p>
<p>A1.4. Curvilinear zones 254</p>
<p>A1.4.1. Presentation 254</p>
<p>A1.4.2. Geometry of the orthogonal curvilinear coordinates 256</p>
<p>A1.4.3. Projection operators and their consequences 257</p>
<p>A1.5. Kinematics in orthogonal curvilinear coordinates 260</p>
<p>A1.5.1. Kinematics of interfacial layers 260</p>
<p>A1.5.2. Kinematics of curvilinear zones 266</p>
<p>A1.5.3. Description of the center line 269</p>
<p>Appendix 2. Additional Aspects of Thermostatics 277</p>
<p>A2.1. Laws of state for real fluids with a single constituent 277</p>
<p>A2.1.1. Diagram of state for a pure fluid 277</p>
<p>A2.1.2. Approximate method to determine the thermodynamic functions 278</p>
<p>A2.1.3. Van der Waals fluid 279</p>
<p>A2.1.4. Other laws for dense gases and liquids 279</p>
<p>A2.2. Mixtures of real fluids 280</p>
<p>A2.2.1. Mixture laws for a real mixture 280</p>
<p>A2.2.2. Expression of the free energy of a real mixture 281</p>
<p>Appendix 3. Tables for Calculating Flows of Ideal Gas × ­1.4 283</p>
<p>A3.1. Calculating the parameters in continuous steady flow (section 1.6.6.2) 286</p>
<p>A3.2. Formulae for steady normal shockwaves 288</p>
<p>Appendix 4. Extended Irreversible Thermodynamics. 289</p>
<p>A4.1. Heat balance equations in a non–deformable medium in EIT 290</p>
<p>A4.2. Application to a 1D case of heat transfer 293</p>
<p>A4.3. Application to heat transfer with the evaporation of a droplet 296</p>
<p>A4.3.1. Reminders about evaporating droplets 296</p>
<p>A4.3.2. Evaporating droplet with EIT. 300</p>
<p>A4.4. Application to thermal shock 302</p>
<p>A4.4.1. Presentation of the problem and solution using CIT 302</p>
<p>A4.4.2. Thermal shock and EIT 303</p>
<p>A4.4.3. Application of the second order approximation into two examples of thermal shock 305</p>
<p>A4.5. Outline of EIT 307</p>
<p>A4.6. Applications and perspectives of EIT 310</p>
<p>Appendix 5. Rational Thermodynamics 313</p>
<p>A5.1. Introduction 313</p>
<p>A5.2. Fundamental hypotheses and axioms 314</p>
<p>A5.2.1. Basic hypotheses 314</p>
<p>A5.2.2. Basic axioms 316</p>
<p>A5.3. Constitutive laws 318</p>
<p>A5.4. Case of the reactive mixture 320</p>
<p>A5.4.1. Principle of material frame indifference 320</p>
<p>A5.4.2. Constitutive laws for a reactive mixture 321</p>
<p>A5.5. Critical remarks 324</p>
<p>Appendix 6. Torsors and Distributors in Solid Mechanics 325</p>
<p>A6.1. Introduction 325</p>
<p>A6.1.1. Torsor 325</p>
<p>A6.1.2. Distributor 325</p>
<p>A6.1.3. Power 326</p>
<p>A6.2. Derivatives of torsors and distributors which depend on a single position parameter 326</p>
<p>A6.2.1. Derivative of the velocity distributor 327</p>
<p>A6.2.2. Derivative of the tensor of forces 328</p>
<p>A6.3. Derivatives of torsors and distributors dependent on two positional parameters 328</p>
<p>A6.3.1. Expression of the velocity distributor 329</p>
<p>A6.3.2. Derivative of the velocity distributor 329</p>
<p>Appendix 7. Virtual Powers in a Medium with a Single Constituent 331</p>
<p>A7.1. Introduction 331</p>
<p>A7.2. Virtual powers of a system of n material points 332</p>
<p>A7.3. Virtual power law 333</p>
<p>A7.4. The rigid body and systems of rigid bodies 333</p>
<p>A7.4.1. The rigid body 333</p>
<p>A7.4.2. System of rigid bodies, concept of a link 334</p>
<p>A7.5. 3D deformable continuous medium 335</p>
<p>A7.5.1. First gradient theory 335</p>
<p>A7.5.2. A 3D case of perfect internal linkage: the incompressible perfect fluid 337</p>
<p>A7.5.3. Second gradient theory 337</p>
<p>A7.6. 1D continuous deformable medium 338</p>
<p>A7.6.1. First gradient theory 338</p>
<p>A7.6.2. A 1D case of perfect internal linkage: perfectly flexible and inextensible wires 340</p>
<p>A7.7. 2D deformable continuous medium 340</p>
<p>Bibliography 343</p>
<p>Index 355</p>