List of Tables
3.1 Roots of the Bessel functions Jν and Yν 40
4.1 Important series 52
4.2 Useful Taylor series 61
4.3 The first 16 Bernouilli numbers 62
5.1 Important Fourier transform pairs 83
5.2 Important Laplace transform pairs 88
6.1 Specific gas constants of commonly used gases 101
6.2 Gas molecule diameters of some commonly used gases 102
6.3 Standard formation enthalpy of some compounds 112
6.4 Standard entropy of some compounds 113
6.5 Standard enthalpy of vaporization of some compounds 115
6.6 Free standard enthalpy of formation of important compounds 119
6.7 Boiling points of some gases 124
6.8 Thermal conductivity of selected substances 126
6.9 A selection of diffusion constants 134
8.1 Common approaches for partial fraction expansion 201
8.2 Solutions to differential equations with characteristic polynomials 220
9.1 Some values for calculating the Lennard-Jones potential 246
9.2 Important dimensionless numbers 258
9.3 Some examples for Prandtl values 260
9.4 A selection of Schmidt and Lewis values 260
17.1 Hydraulic resistance of most important geometries 359
17.2 Compactness and correction factor values for elliptical cross-sections 364
17.3 Compactness and correction factor values for planar infinitesimally extended cross-sections 366
17.4 Compactness and correction factor values for rectangular cross-sections 366
20.1 Free surface energy values of the elements 422
20.2 Surface tension of commonly used liquids 423
22.1 Liquids used for determining free surface energies 461
22.2 Critical surface tension values for polymers 464
22.3 Critical surface tension values for modified surfaces 464
26.1 Values obtained from the solver implementing Newton’s method 546
26.2 Second set of values obtained from the solver implementing Newton’s method (instable) 547
27.1 Computational output of the Euler method 551
27.2 Computational results of the Euler method 554
27.3 Family of the Adams-Moulton formulae 565
27.4 Comparison of computational results of forward Euler method, second-order Adams-Moulton, second-order Adams-Bashforth, and fourth-order Runge-Kutta methods 567
27.5 Family of the Adams-Moulton formulae 570
27.6 Family of the Runge-Kutta formulae 573
32.1 Index matrix used in FEM 656