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 191
... values on this row are unknown Node values on this row are krown The second derivative at E is taken as the average of the values at A and D , or a2T ax2 E 1 / a2 T a2T = - + ax2 D 2 TAXI m - 1 M m + 1 O Specified Initial Conditions ...
... values on this row are unknown Node values on this row are krown The second derivative at E is taken as the average of the values at A and D , or a2T ax2 E 1 / a2 T a2T = - + ax2 D 2 TAXI m - 1 M m + 1 O Specified Initial Conditions ...
Page 193
... value of the function is the aver- age of the values at the four neighboring nodes when Ax = Ay , Eq . ( 7.118 ) . 1 , j + " For the values at the nodes of the column next to the right boundary , Tb - 1 , n + 1 = ( 1 - 2M ) Tb - 1 , n + ...
... value of the function is the aver- age of the values at the four neighboring nodes when Ax = Ay , Eq . ( 7.118 ) . 1 , j + " For the values at the nodes of the column next to the right boundary , Tb - 1 , n + 1 = ( 1 - 2M ) Tb - 1 , n + ...
Page 196
... values of T at five neighboring nodes by Eq . ( 7.118 ) . When Ax = = Ay , that relation is -4Tm , n + Tm , n − 1 + ... values are the following . 1. Values at all interior nodes are made the same , the averages of boundary values . T1 ...
... values of T at five neighboring nodes by Eq . ( 7.118 ) . When Ax = = Ay , that relation is -4Tm , n + Tm , n − 1 + ... values are the following . 1. Values at all interior nodes are made the same , the averages of boundary values . T1 ...
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