Numerical Methods in Chemical Engineering
Paper Code: CHE 604
Module I:
Error Analysis: Taylor series expansion, Truncation error. Round-off error vs. Chopping-off error. Propagation of Error .
Solution of simultaneous linear equations: Gauss elimination Method, Gauss-Jordon Method -Pivoting and illconditioning.
Iterative method - Jacobi iteration, Gauss-Seidel Method. SOR method, Application in steady-state solution of isothermal CSTR in Series in which a first-order reaction is taking place and multiple reactions in CSTR. Tri-Diagonal Matrix Algorithm (TDMA).
Module II:
Solution of Non-linear equations:
Bisection method, Newton-Rapson method, Secant method, Modified Newton-Rapson methodfor multiple roots - Application in thermodynamic property calculation, buble point and dew point calculation. Finding of multiple roots of a polynomial. Solution of a set of non-linear equations - Newton’s method, Jacobian matrix, charactertics equations and
stability analysis of solution. Steady-state solution of a non-isothermal CSTR in which a first-order reaction is taking place.
Module III:
Curve-fitting : Linear least-square method for straight line and polynomial. Lagrange interpolation.
Numerical Solution of ODE: Initial and boundary value prolem- Euler’s Method, Runge-Kutta Method(2nd, 3rd and 4th order), Euler’s predictor-corrector method (Heun’ method)- finite difference method (forward, backward and central differences). Solution of a set of ODEs. Application in chemical and bio-chemical reaction.
Module IV:
Numerical Integration: Trapezoidal rule, Simpson’s 1/3rule.
Numerical Solution of PDE: Explicit, Implicit and Crank-Nicholson method for elliptical and parabolic equation.
Convergence and stability criteria of these methods. Application in unsteady-state heat transfer through a slab and unsteady-state tubular reaction problem.
Text Book and references
- Mathematical Methods in Chemical Engineering : V. G. Jenson and Jeffrey
- Applied Mathematics in Chemical Engineering: Mickley TMH
- Mathematical Methods in Chemical Engineering: S. Pushpavanam, PHI
- Numerical methods for Mathematics, Science and Engineering: John H. Mathews , PHI
- Applied Numerical Methods: Carnahan, H.A.Luther and J.O.Wilkes, Wiley
