Chemical Engineering Hand Written_Notes_Part_62

Chemical Engineering Hand Written_Notes_Part_62 - Dynamic...

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126 3. LINEAR ALGEBRAIC EQUATIONS AND RELATED NUMERICAL SCHEMES (35) Consider following set of nonlinear algebraic equations Perform 3 iter- ations using (a) Set 2 (Banana Function): 10( x 2 1 + x 2 )=0 x 1 1=0 x (0) = h 11 i T (36) The following coupled di f erential equations characterize a system d 2 u dz 2 +2 ue v = f 1 ( u, v, z ); u (0) = 0; u (1) = 5 d 2 v dz 2 +5 uv = f 2 ( u, v, z ); v (0) = 1; v (1) = 2 Obtain sets of nonlinear algebraic equations using (a) f nite di f er- ence method with 2 internal grid points and (b) orthogonal collocation with 2 collocation points. Also, arrange these equations as A x = G ( x ) so that method of successive substitution can be used for formulating iterative scheme.
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CHAPTER 4 ODE-IVPs and Related Numerical Schemes 1. Motivation In these lecture notes, we undertake the study of solution techniques for multivariable and coupled ODE-IVPs. The numerical techniques for solving ODE-IVPs form basis for a number of numerical schemes and are used for solving variety of problems such as
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Unformatted text preview: Dynamic simulation of lumped parameter systems Solution of ODE-BVP Solving Parabolic / Hyperbolic PDEs Solving simultaneous nonlinear algebraic equation and so on. In order to provide motivation for studying the numerical meth-ods for solving ODE-IVPs, we f rst formulate numerical schemes for the above problems in the following subsections. 1.1. Dynamic behavior of lumped parameter systems. Example 50 . Three isothermal CSTRs in series Consider three isothermal CSTRs in series in which a f rst order liquid phase reaction of the form (1.1) A B is carried out. It is assumed that volume and liquid density remains constant in each tank and (1.2) V 1 dC A 1 dt = F ( C A C A 1 ) kV 1 C A 1 (1.3) V 2 dC A 2 dt = F ( C A 1 C A 2 ) kV 2 C A 2 (1.4) V 3 dC A 3 dt = F ( C A 2 C A 3 ) kV 3 C A 3 127...
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Chemical Engineering Hand Written_Notes_Part_62 - Dynamic...

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