Modeling with Differential Equations in Chemical Engineering'Modelling with Differential Equations in Chemical Engineering' covers the modelling of rate processes of engineering in terms of differential equations. While it includes the purely mathematical aspects of the solution of differential equations, the main emphasis is on the derivation and solution of major equations of engineering and applied science. Methods of solving differential equations by analytical and numerical means are presented in detail with many solved examples, and problems for solution by the reader. Emphasis is placed on numerical and computer methods of solution. A key chapter in the book is devoted to the principles of mathematical modelling. These principles are applied to the equations in important engineering areas. The major disciplines covered are thermodynamics, diffusion and mass transfer, heat transfer, fluid dynamics, chemical reactions, and automatic control. These topics are of particular value to chemical engineers, but also are of interest to mechanical, civil, and environmental engineers, as well as applied scientists. The material is also suitable for undergraduate and beginning graduate students, as well as for review by practising engineers. |
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Page 102
... phase plane . Analysis of some such systems have been made ( Kocak , 1989 ) . Phase plane analysis employs a plot of y against x from a solution of either Eq . ( 5.5 ) or Eq . ( 5.7 ) . The plot of the set of solutions ( for different ...
... phase plane . Analysis of some such systems have been made ( Kocak , 1989 ) . Phase plane analysis employs a plot of y against x from a solution of either Eq . ( 5.5 ) or Eq . ( 5.7 ) . The plot of the set of solutions ( for different ...
Page 103
... Phase Portrait The van der Pol equation , d2x dt2 μ ( 1 dx x2 ) dt + x = 0 ( 1 ) will be taken with μ = 1 and with x = O and dx / dt = 1 when t = 0. The equivalent pair of first - order equations is dx dt У = μ ... PHASE PLANE ANALYSIS 103.
... Phase Portrait The van der Pol equation , d2x dt2 μ ( 1 dx x2 ) dt + x = 0 ( 1 ) will be taken with μ = 1 and with x = O and dx / dt = 1 when t = 0. The equivalent pair of first - order equations is dx dt У = μ ... PHASE PLANE ANALYSIS 103.
Page 104
... phase plane trajectory is a spiral that converges on the origin as increases . A neutral process is represented in Figure 5.2 ; 1.0 k = 0.1 the variable never comes to rest but its amplitude remains bounded , and the phase plane ...
... phase plane trajectory is a spiral that converges on the origin as increases . A neutral process is represented in Figure 5.2 ; 1.0 k = 0.1 the variable never comes to rest but its amplitude remains bounded , and the phase plane ...
Common terms and phrases
a₁ a²u applied arctan auxiliary conditions ax² ay² b₁ becomes Bessel equation Bessel functions boundary conditions C₁ C₂ chemical coefficients convergence coordinates curve d²y derivative diffusion diskette dx dy dx/dt dx² dy/dx eigenvalues equa Example Figure finite first-order flow fluid formulas Gaussian elimination heat equation heat transfer homogeneous independent variables initial conditions input integral equation inverse k₁ Laplace equation Laplace transform linear differential equations linear equations mathematical method nodes nonhomogeneous nonlinear numerical ODEs orthogonal parameters Partial Differential Equations phase plane plane polynomials problem reaction reactor region result roots second-order separation of variables sinh solution solved substitution T₁ Table temperature tion u₁ V₁ values vector velocity x₁ x²y y₁ zero ди др ду дх