Chemical Engineering Hand Written_Notes_Part_62

# Chemical Engineering Hand Written_Notes_Part_62 - •...

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Chemical Engineering Hand Written_Notes_Part_62 - •...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online