Page 15 - Bird R.B. Transport phenomena

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§A.3 Tensor Operations in Terms of §C2 Expansions of Functions in Taylor
Components 815 Series 853
§A.4 Vector and Tensor Differential Operations 819 §C3 Differentiation of Integrals (the Leibniz
Ex. A.4-1 Proof of a Tensor Identity 822 Formula) 854
§A.5 Vector and Tensor Integral Theorems 824 §C4 The Gamma Function 855
§A.6 Vector and Tensor Algebra in Curvilinear §C5 The Hyperbolic Functions 856
Coordinates 825 §C6 The Error Function 857
§A.7 Differential Operations in Curvilinear
Coordinates 829 Appendix D The Kinetic Theory of Gases 858
Ex. Л.7-1 Differential Operations in Cylindrical
Coordinates 831 §D.l The Boltzmann Equation 858
Ex. A.7-2 Differential Operations in Spherical §D.2 The Equations of Change 859
Coordinates 838 §D.3 The Molecular Expressions for the
§A.8 Integral Operations in Curvilinear Fluxes 859
Coordinates 839 §D.4 The Solution to the Boltzmann Equation 860
§A.9 Further Comments on Vector-Tensor §D.5 The Fluxes in Terms of the Transport
Notation 841 Properties 860
§D.6 The Transport Properties in Terms of the
Appendix В Fluxes and the Equations of Intermolecular Forces 861
Change 843 §D.7 Concluding Comments 861
§B.l Newton's Law of Viscosity 843 Appendix E Tables for Prediction of
§B.2 Fourier's Law of Heat Conduction 845
§B.3 Fick's (First) Law of Binary Diffusion 846 Transport Properties 863
§B.4 The Equation of Continuity 846 §E.l Intermolecular Force Parameters and Critical
§B.5 The Equation of Motion in Terms of т 847 Properties 864
§B.6 The Equation of Motion for a Newtonian Fluid §E.2 Functions for Prediction of Transport Properties
with Constant p and fi 848 of Gases at Low Densities 866
§B.7 The Dissipation Function Ф. for Newtonian
о
Fluids 849
§B.8 The Equation of Energy in Terms of q 849 Appendix F Constants and Conversion
§B.9 The Equation of Energy for Pure Newtonian Factors 867
Fluids with Constant p and к 850 §F.l Mathematical Constants 867
§B.1O The Equation of Continuity for Species a in Terms §F.2 Physical Constants 867
of ) a 850 §F.3 Conversion Factors 868
§B.l 1 The Equation of Continuity for Species A in
Terms of o) for Constant p%b AB 851 Notation 872
A
Appendix С Mathematical Topics 852
Author Index 877
§C.l Some Ordinary Differential Equations and Their
Solutions 852 Subject Index 885