Course Details
Subject {L-T-P / C} : CH6332 : Chemical Engineering Analysis: Application of Mathematical and Statistical Methods { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Basudeb Munshi
Syllabus
Modeling, Simulation, Types of Equation, Linear algebraic Equation ODE, IVP, Non Self adjoint systems, Gram-Schmidt Ortho-normalization. Matrices, Operators & Transformations (Matrices, Eigenvalues, Eigen vectors, Rayleigh’s Quotient) for solving process models in chemical Eng., Partial Differential Equation: Classification of PDE, boundary conditions, Developing PDE in Chemical Eng. Systems. Application of Sturm-Louiville Theory, Green’s function in solving ODES and PDES of chemical Engineering processes. Uniqueness condition for linear and non-linear systems: Maximum principles, Energy methods, Fredholm alternative, Steady State analysis of a Nonlinear dynamic System: application of method of continuation and homotopy continuation, Linear stability & limit cycles: Linear stability of a dynamic system, Bifurcation theory, Maps, e.g., application in stability analysis of reactive distillation system. Secondary bifurcations and Chaos: Landau-Hopf Scenario, Period -Doubling cascades, Ruelle- Takens Scenario, Characteristic of trajectories, application in nonlinear dynamic systems, bioprocess modeling. Probability concepts and distributions, random variables, error analysis, point estimation and confidence intervals, hypothesis testing, development of empirical chemical engineering models using regression techniques, design of experiments, process monitoring based on statistical quality control techniques. Case studies.
Course Objectives
- Develop knowledge on the solution of differential equations using Matrix method
- Understanding non-linear dynamics in chemical engineering by using bifurcation and chaos theories
- Develop knowledge on statistical modeling and data analysis of chemical engineering processes
Course Outcomes
Doing this course students will <br />(1) be able to take up any process design and development challenges. <br />(2) be able to do prototype design and feasibility study. <br />(3) be able to identify the behaviour of chemical engineering system. <br />(4) be able do stability analysis of the chemical engineering processes.
Essential Reading
- S. Pushpavanam, Mathematical Methods in Chemical Engineering, Prentice-Hall-India , 1998
- Madhusree Kundu, Palash Kumar Kundu, Seshu K. Damarla, Chemometric Monitoring: Product Quality Assessment, Process Fault Detection, and Applications, CRC Press , 2017
Supplementary Reading
- T. H. Owen and O. C. Sandall, Computational Methods in Chemical Engineering, Prentice-Hall-International, Inc , 1998
- Shardt, Yuri A.W., Statistics for Chemical and Process Engineers A Modern Approach, Springer , 2015