Muutke küpsiste eelistusi

E-raamat: Vector Fields with Applications to Thermodynamics and Irreversibility [Taylor & Francis e-raamat]

, (University of Lisbon, Portugal)
Teised raamatud teemal:
  • Taylor & Francis e-raamat
  • Hind: 124,64 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Tavahind: 178,05 €
  • Säästad 30%
Vector Fields with Applications to Thermodynamics and IrreversibilitySuurem pilt
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003186595
Vector Fields with Applications to Thermodynamics and Irreversibility is part of the series "Mathematics and Physics for Science and Technology", which combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. Volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to: acoustic, elastic, water, electromagnetic and other waves; the diffusion of heat, mass and electricity; and their interactions. This is the first book of the volume.

The second book of volume V continues this book on thermodynamics, focusing on the equation of state and energy transfer processes including adiabatic, isothermal, isobaric and isochoric. These are applied to thermodynamic cycles, like the Carnot, Atkinson, Stirling and Barber-Brayton cycles, that are used in thermal devices, including refrigerators, heat pumps, and piston, jet and rocket engines. In connection with jet propulsion, adiabatic flows and normal and oblique shock waves in free space and nozzles with variable cross-section are considered. The equations of fluid mechanics are derived for compressible two-phase flow in the presence of shear and bulk viscosity, thermal conduction and mass diffusion. The thermodynamic cycles are illustrated by detailed calculations modelling the operation of piston, turbojet and rocket engines in various ambient conditions, ranging from sea level, the atmosphere of the earth at altitude and vacuum of space, for the propulsion of land, sea, air and space vehicles.

The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics.

This book:





Simultaneously covers rigorous mathematics, general physical principles and engineering applications with practical interest Provides interpretation of results with the help of illustrations Includes detailed proofs of all results

L.M.B.C. Campos was chair professor and the Coordinator of the Scientific Area of Applied and Aerospace Mechanics in the Department of Mechanical Engineering and also the director (and founder) of the Center for Aeronautical and Space Science and Technology until retirement in 2020.

L.A.R.Vilela is currently completing an Integrated Master's degree in Aerospace Engineering at Institute Superior Tecnico (1ST) of Lisbon University.
List of Notes, Tables, and Diagrams
xv
Series Preface xvii
Preface to Volume V xix
About the Authors xxiii
Acknowledgments xxv
List of Mathematical Symbols
xxvii
List of Physical Quantities
xxxv
Chapter 1 Classes of Equations and Similarity Solutions
1(94)
1.1 Hierarchy of Partial Differential Equations
1(5)
1.1.1 Single Equations and Simultaneous Systems
1(1)
1.1.2 Partial Differential Equation in N Variables
2(2)
1.1.3 One Dependent and Two Independent Variables
4(2)
1.2 General Integral and Arbitrary Functions
6(1)
1.2.1 First-Order P.D.E. and One Arbitrary Function
6(1)
1.2.2 P.D.E. of Order N and N Arbitrary Functions
7(1)
1.3 Unforced P.D.E. with First-Order Derivatives
7(6)
1.3.1 Classification of P.D.E.S of First Order
8(1)
1.3.2 Family of Hypersurfaces Tangent to a Vector Field
9(1)
1.3.3 Characteristic Curve Tangent to a Vector Field
10(1)
1.3.4 Characteristic Variables as Solutions of the Characteristic Equations
10(1)
1.3.5 Plane Curve Tangent to a Vector Field
11(1)
1.3.6 Example of the Family of Surfaces Tangent to the Position Vector
12(1)
1.4 Quasi-Linear and Forced First-Order P.D.E.s
13(3)
1.4.1 Quasi-Linear P.D.E. of the First-Order
13(1)
1.4.2 Solution as Implicit Function of N Variables
14(1)
1.4.3 Linear Forced P.D.E. with First-Order Derivatives
15(1)
1.4.4 Plane Curves with Unit Projection on the Position Vector
15(1)
1.5 Differentials of First-Degree in Three Variables
16(32)
1.5.1 Exact, Inexact and Non-Integrable Differentials
17(1)
1.5.2 Linear and Angular Velocities and Helicity
18(2)
1.5.3 Exact Differential and Immediate Integrability
20(1)
1.5.4 Inexact Differential with an Integrating Factor
21(1)
1.5.5 Inexact Differential without Integrating Factor
21(1)
1.5.6 Irrotational/Rotational and Non-Helical/Helical Vector Fields
22(1)
1.5.7 Irrotational or Conservative Vector Field as the Gradient of a Scalar Potential
23(1)
1.5.8 Rotational Non-Helicoidal Vector Field and Two Scalar Potentials
24(1)
1.5.9 Helical Vector Field and Three Scalar Potentials
25(2)
1.5.10 Existence and Determination of the Three Scalar Potentials
27(1)
1.5.11 Scalar Poisson Equation Forced by the Divergence of a Vector Field
28(1)
1.5.12 Vector Poisson Equation Forced by the Curl of a Vector Field
29(1)
1.5.13 Potential Vector Field and Laplace Equation
29(1)
1.5.14 Scalar and Vector Potentials for a General Vector Field
30(1)
1.5.15 Three Alternative Scalar Euler or Clebsch Potentials
31(1)
1.5.16 Eight Cases of Three-Dimensional Vector Fields
32(1)
1.5.17 Potential Vector Field with Scalar or Vector Potentials
32(4)
1.5.18 Irrotational Vector Field and One Scalar Potential
36(1)
1.5.19 Solenoidal Vector Field and Vector Potential
37(2)
1.5.20 Non-Solenoidal, Rotational Vector Field and Scalar and Vector Potentials
39(1)
1.5.21 Rotational, Non-Helical Vector Field and Two Euler Scalar Potentials
40(1)
1.5.22 Helical Vector Field and Three Scalar Euler Potentials
41(1)
1.5.23 Rotational, Non-Solenoidal Vector Field and Three Scalar Clebsch Potentials
42(2)
1.5.24 Partial Differential Equations and Characteristic Systems
44(2)
1.5.25 Unicity of Scalar and Vector Potentials
46(1)
1.5.26 Characteristic Systems for Euler and Clebsch Potentials
47(1)
1.6 P.D.E.s with Constant Coefficients and All Derivatives of Same Order
48(6)
1.6.1 P.D.E. of Constant Order and Characteristic Polynomial
48(1)
1.6.2 Similarity Solutions for a Linear Combination of Variables
49(1)
1.6.3 General Integral for Distinct Roots
49(1)
1.6.4 Single or Multiple Roots of the Characteristic Polynomial
50(1)
1.6.5 Method of Variation of Parameters
51(1)
1.6.6 Method of Parametric Differentiation
51(1)
1.6.7 General Integral for Multiple Roots
52(1)
1.6.8 Linear P.D.E. with Constant Coefficients and Second-Order Derivatives
53(1)
1.7 Harmonic and Biharmonic Functions on the Plane
54(6)
1.7.1 Laplace Equation in Cartesian Coordinates
55(1)
1.7.2 Real/Complex Harmonic Functions and Boundary Conditions
56(1)
1.7.3 Biharmonic Equation in the Cartesian Plane
57(1)
1.7.4 Real/Complex Biharmonic Functions and Forcing
58(2)
1.8 Forced Linear P.D.E. with of Derivatives Constant Order
60(8)
1.8.1 Forcing of P.D.E. by a Similarity Function
60(1)
1.8.2 Similarity Forcing in the Non-Resonant Case
61(1)
1.8.3 Parametric Differentiation for Multiple Resonance
62(1)
1.8.4 Multiple Resonance via L'Hospital Rule
62(1)
1.8.5 Comparison of Resonant and Non-Resonant Cases
63(1)
1.8.6 Forcing by an Exponential Similarity Function
63(2)
1.8.7 Forcing by a Sinusoidal Similarity Function
65(1)
1.8.8 General, Particular and Complete Integrals
66(1)
1.8.9 Complete Integrals with Simple/Double Resonances
67(1)
1.9 Forced Harmonic and Biharmonic Equations
68(25)
1.9.1 General Forcing of the Laplace Equation
69(1)
1.9.2 Complete Integral of the Harmonic Equation
69(1)
1.9.3 General Forcing of the Double Laplace Equation
70(1)
1.9.4 Complete Integral of the Biharmonic Equation
70(1)
1.9.5 Method of Similarity Variables for Arbitrary Forcing
71(1)
1.9.6 Fourth-Order Equation with Two Independent and Three Similarity Variables
72(2)
1.9.7 Two Methods for Exponential Forcing
74(19)
1.10 Conclusion
93(2)
Chapter 2 Thermodynamics and Irreversibility
95(132)
2.1 Work, Heat, Entropy and Temperature
96(28)
2.1.1 Work of Conservative and Non-Conservative Forces
97(1)
2.1.2 Internal Energy and First Principle of Thermodynamics
98(1)
2.1.3 Inertia Force and Kinetic Energy
99(1)
2.1.4 Mass and Gravity Field, Potential, Force and Energy
100(1)
2.1.5 Electric Charge, Field, Scalar Potential and Force
101(1)
2.1.6 Electric Displacement, Work and Energy
102(1)
2.1.7 Dielectric Permittivity Tensor and Scalar
103(1)
2.1.8 Work in Terms of the Electric Field and Displacement
104(1)
2.1.9 Electric Current and Magnetic Vector Potential
105(2)
2.1.10 Magnetic Field, Induction and Energy
107(1)
2.1.11 Magnetic Permeability Tensor and Scalar
108(1)
2.1.12 Permutation Symbol, Curl and Outer Vector Product
109(1)
2.1.13 Anisotropic Inhomogeneous Poisson Equation
110(1)
2.1.14 Work in Terms of the Magnetic Field and Induction
111(1)
2.1.15 Work of the Pressure in a Volume Change
112(1)
2.1.16 Volume Forces Associated with Surface Pressure or Stresses
112(2)
2.1.17 Work of the Surface Stresses in a Displacement
114(1)
2.1.18 Balance of Moment of Forces and Symmetric Stress Tensor
114(1)
2.1.19 Displacement and Strain Tensors and Rotation Vector
115(1)
2.1.20 Mole and Avogadro Numbers and Chemical Work, Potential and Affinity
116(2)
2.1.21 Matter with Two Phases and a Combustion Reaction
118(2)
2.1.22 Total Work and Augmented Internal Energy: The Total Work (2.96)
120(1)
2.1.23 Energy Balance and Modified Internal Energy
120(1)
2.1.24 Extensive and Intensive Thermodynamic Parameters
121(1)
2.1.25 Thermal, Electrical, Magnetic, Mechanical and Chemical Equilibrium
122(1)
2.1.26 Temperature, Entropy, Heat and Internal Energy
123(1)
2.2 Functions of State and Constitutive Properties
124(32)
2.2.1 Duality Transformation of First-Order Differentials (Legendre)
125(1)
2.2.2 Free Energy (Helmholtz) and Enthalpy (Gibbs)
126(1)
2.2.3 Free Enthalpy as a Fourth Function of State
126(1)
2.2.4 First-Order Derivatives and Conjugate Thermodynamic Variables
127(2)
2.2.5 Second-Order Derivatives and Constitutive Properties
129(1)
2.2.6 Specific Heat, Dielectric Permittivity, Magnetic Permeability and Elastic Stiffness
130(2)
2.2.7 Pyroelectric/Magnetic Vectors, Electromagnetic Coupling, Thermoelastic, and Piezoelectric/Magnetic Tensors
132(4)
2.2.8 Maximum Number of Constitutive Coefficients for Anisotropic Matter
136(1)
2.2.9 Constitutive Properties of Anisotropic and Isotropic Matter
136(1)
2.2.10 Absence of Electromagnetic Coupling in Isotropic Matter
137(1)
2.2.11 Absence of Electro/Magnetoelastic Interaction in Isotropic Matter
137(1)
2.2.12 Lame Moduli, Young Modulus and Poisson Ratio
138(1)
2.2.13 Constitutive Relations for Isotropic Matter
139(1)
2.2.14 Basic Thermodynamic System with Thermomechanical Coupling
140(1)
2.2.15 Non-Linear, Anisotropic, Inhomogeneous and Unsteady Matter
140(1)
2.2.16 Twenty-Four Cases of Constitutive Relations
141(1)
2.2.17 Analogies among Mechanics, Electricity, Magnetism and Elasticity
142(3)
2.2.18 Inequalities for the Isotropic Constitutive Coefficients
145(1)
2.2.19 Vector and Tensor Quadratic Forms for Energies
145(1)
2.2.20 Definite, Semi-Definite and Indefinite Quadratic Forms
146(1)
2.2.21 Eigenvalues, Eigenvectors, Diagonalization and Sum of Squares (Sylvester)
147(1)
2.2.22 Classification of Quadratic Forms by the Eigenvalues of the Matrix
148(1)
2.2.23 Conditions for Positive Electric, Magnetic and Elastic Energies
149(1)
2.2.24 Biaxial, Uniaxial and Isotropic Materials
149(1)
2.2.25 Principal Submatrices and Subdeterminants of a Square Matrix
150(1)
2.2.26 Subdeterminants and Positive/Negative Definiteness
151(2)
2.2.27 Necessary and Sufficient Conditions for Positive/Negative Definiteness
153(1)
2.2.28 Inequalities for Constitutive Tensors Ensuring Positive Energies
154(1)
2.2.29 Indefinite Second-Order Differential of the Free Energy
155(1)
2.3 Three Principles and Four Processes of Thermodynamics
156(42)
2.3.1 Complete and Basic Thermodynamic System
157(1)
2.3.2 Five Functions of State
157(1)
2.3.3 Cases When Work and Heat Are Functions of State
158(1)
2.3.4 Adiabatic Process and Pressure Equilibrium
159(1)
2.3.5 Isochoric Process and Thermal Equilibrium
159(2)
2.3.6 Work and Heat in an Isobaric Process
161(1)
2.3.7 Heat and Work in an Isothermal Process
161(1)
2.3.8 Four Thermodynamic Variables and Four Relations between Derivatives (Maxwell 1867)
162(1)
2.3.9 Skew-Symmetry, Inversion and Product Properties of Jacobians
163(2)
2.3.10 Specific Heats at Constant Volume and Pressure
165(1)
2.3.11 Coefficients of Thermal Expansion and Isothermal Compression
166(1)
2.3.12 Adiabatic and Isothermal Sound Speeds
167(1)
2.3.13 Non-Adiabatic Pressure and Volume Coefficients
168(1)
2.3.14 Twelve Non-Inverse Thermodynamic Derivatives
169(5)
2.3.15 Three Independent Thermodynamic Derivatives
174(1)
2.3.16 The Second Principle of Thermodynamics and Entropy Growth
175(1)
2.3.17 Paths on the Convex Thermodynamic Surface
176(3)
2.3.18 Stable Equilibrium and Minimum Internal Energy
179(2)
2.3.19 Inequalities for Thermodynamic Derivatives
181(1)
2.3.20 First and Second-Order Derivatives of Entropy
182(1)
2.3.21 Thermodynamic Derivatives at Constant Internal Energy
183(1)
2.3.22 Thermodynamic Stability and Maximum Entropy
184(2)
2.3.23 Inexistence of Extremals for Enthalpy and Free Energy and Maximum for Free Enthalpy
186(2)
2.3.24 Fluid Transfer Between Full and Empty Reservoirs
188(1)
2.3.25 Transfer at Constant Pressure Through a Porous Wall (Joule-Thomson 1882)
189(1)
2.3.26 Body Reducing Environmental Disturbances (Le Chatelier 1898)
190(2)
2.3.27 Body in Pressure/Thermal Equilibrium with Environment
192(1)
2.3.28 Thermodynamic Properties at Zero Absolute Temperature
192(1)
2.3.29 Third Principle of Thermodynamics (Nerst 1907)
193(3)
2.3.30 System with a Variable Number of Particles
196(1)
2.3.31 Differentials of Chemical Potentials (Gibbs 1876--1878, Duhem 1886)
197(1)
2.4 Entropy Production and Diffusive Properties
198(29)
2.4.1 Heat Conduction and Flux in a Domain
199(1)
2.4.2 Thermal Conductivity (Fourier 1818) Scalar and Tensor
200(1)
2.4.3 Electromagnetic Energy Density, Flux and Dissipation
200(1)
2.4.4 Joule (1847) Effect, Ohm (1827) Law and Electrical Conductivity/Resistivity
201(1)
2.4.5 Coupling of Heat Flux and Electric Current
202(1)
2.4.6 Gradients, Fluxes and Reciprocity (Onsager 1931)
203(1)
2.4.7 Isotropic Thermoelectric Diffusion Scalars
203(1)
2.4.8 Anisotropic Thermoelectric Diffusion Tensors
204(1)
2.4.9 Stresses and Rates-of-Strain for a Viscous Fluid
205(1)
2.4.10 Shear and Bulk Viscosities for a Newtonian Fluid
206(1)
2.4.11 Positive Viscosities in the Navier (1822) - Stokes (1845) Equation
207(1)
2.4.12 Decoupling of Viscosity from Thermal and Electrical Conduction
208(1)
2.4.13 Decoupling of Thermoelectric Conduction from the Pressure Gradient
209(1)
2.4.14 Electric Current in Linear and Non-Linear Media
210(1)
2.4.15 Ohm (1827) and Hall (1879) Effects and Ionic Propulsion
211(1)
2.4.16 Thomson (1851) Thermoelectric Effect Including Convection
211(2)
2.4.17 Volta (1821) -- Seeback (1822) -- Peltier (1834) Effect and Thermoelectromotive Force
213(1)
2.4.18 Mass Diffusion (Fick 1855) in a Two-Phase Medium
214(1)
2.4.19 Entropy Production by Mass Diffusion
215(1)
2.4.20 Coupled Thermoelectric Diffusion Equations
216(3)
2.4.21 Anisothermal Dissipative Piezoelectromagnetism (Campos, Silva & Moleiro 2020)
219(1)
2.4.22 Isotropic Media and Steady Fields
220(2)
2.4.23 Thermoelastic Electromagnetism in a Slab
222(5)
References 227(2)
Bibliography 229
Index 1
Luis Manuel Braga da Costa Campos was Chair Professor and the Coordinator of the Scientific Area of Applied and Aerospace Mechanics in the Department of Mechanical Engineering and also the director (and founder) of the Center for Aeronautical and Space Science and Technology until retirement in 2020.

L.A. R. Vilela is currently completing an Integrated Master's degree in Aerospace Engineering at Institute Superior Tecnico (1ST) of Lisbon University.
Püsilink: https://www.kriso.ee/db/9781003186595_pe.html
Märksõnad: