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 34
... called a negative exponential ramp . The response includes an exponential term whose effect vanishes at larger values of t and that is consequently called a transient . Clearly the ultimate steady pattern still depends on the parameter ...
... called a negative exponential ramp . The response includes an exponential term whose effect vanishes at larger values of t and that is consequently called a transient . Clearly the ultimate steady pattern still depends on the parameter ...
Page 66
... called being analytic . This concept leads to a classification of points or values of the independent variable x . An ordinary point x = x1 of a linear differential equation is one for which all of the coefficients have all finite ...
... called being analytic . This concept leads to a classification of points or values of the independent variable x . An ordinary point x = x1 of a linear differential equation is one for which all of the coefficients have all finite ...
Page 120
... called a complete solution , for instance , = au + Bv ( 6.58 ) dz P ax az + Q ду = R where P , Q , and R are functions of ( x , y , z ) . A function z = p ( x , y ) or ( x , y , z ) = 0 ( 6.51 ) ( 6.52 ) that satisfies the PDE is called ...
... called a complete solution , for instance , = au + Bv ( 6.58 ) dz P ax az + Q ду = R where P , Q , and R are functions of ( x , y , z ) . A function z = p ( x , y ) or ( x , y , z ) = 0 ( 6.51 ) ( 6.52 ) that satisfies the PDE is called ...
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