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 v
... Linear Differential Equations 14 2.1.4 . Total or Exact Equations 16 2.1.5 . F ( x , y , p ) = 0 Solvable Explicitly for One of the Variables 16 2.1.6 . Simultaneous Linear Differential Equations 17 2.1.7 . Simultaneous Autonomous Linear ...
... Linear Differential Equations 14 2.1.4 . Total or Exact Equations 16 2.1.5 . F ( x , y , p ) = 0 Solvable Explicitly for One of the Variables 16 2.1.6 . Simultaneous Linear Differential Equations 17 2.1.7 . Simultaneous Autonomous Linear ...
Page 14
... LINEAR DIFFERENTIAL EQUATIONS The first - order linear differential equation has the form dy + f ( x ) y = g ( x ) dx dCh dx == g ( x ) e ( 2.26 ) whence ( 2.21 ) Ch = = √ 8 ( x ) e dx + C ( 2.27 ) and finally ( 2.22 ) y = e ( 2.28 ) ...
... LINEAR DIFFERENTIAL EQUATIONS The first - order linear differential equation has the form dy + f ( x ) y = g ( x ) dx dCh dx == g ( x ) e ( 2.26 ) whence ( 2.21 ) Ch = = √ 8 ( x ) e dx + C ( 2.27 ) and finally ( 2.22 ) y = e ( 2.28 ) ...
Page 126
... LINEAR PDEs ( 6.86 ) For the representation of physical processes , the most prevalent and useful partial differential equations are linear ones of the second order . Some of them are listed in Table 6.1 . As in the case of linear ODEs ...
... LINEAR PDEs ( 6.86 ) For the representation of physical processes , the most prevalent and useful partial differential equations are linear ones of the second order . Some of them are listed in Table 6.1 . As in the case of linear ODEs ...
Common terms and phrases
a₁ a²T a²u applied arctan auxiliary conditions ax² ay² b₁ becomes Bessel Bessel equation Bessel functions boundary conditions C₁ C₂ chemical coefficients concentration convergence coordinates curve cylinder d²y derivative differential equation diffusion dr² dx dy dy/dx energy enthalpy equa Example Figure finite finite-difference first-order flow fluid formulas Gaussian elimination heat equation heat transfer homogeneous initial input inverse k₁ k₂ Laplace equation Laplace transform linear equation mathematical method nodes nonlinear numerical ODEs parameters partial differential equations phase plane plane polynomials problem rate equation reaction reactor region relation result second-order separation of variables sinh solution solved substitution surface T₁ T₂ Table temperature tion transfer function u₁ V₁ values vector velocity x₁ y₁ zero әс ди ду дх