Course10310500260 lectures
Introduction to Scaling Analysis and Perturbation Methods for Chemical Engineers
Prof. Sourav Sengupta · IIT-ISM Dhanbad
About
The course “Introduction to scaling analysis and perturbation methods for chemical engineers” is intended to equip the learners with a host of tools from applied mathematics, that are critical towards modelling and simulating a range of scenarios in chemical engineering (science and engineering in general), especially towards scale-up and optimization, by suitable simplification and subsequent approximate solution of complex multiphysics governing equations. Being a graduate-level elective course, the focus is on understanding and employing approximate methods such as scaling and asymptotics. Specifically, the students will
learn the building blocks of modelling a process, i.e., formulating physicochemical processes.
learn about the importance and utility of scaling analysis.
get introduced to perturbation and asymptotic methods.
learn how to use aforementioned methods for solving engineering problems of interest (mainly from transport and reaction processes).
Intended audience: Senior undergraduates, postgraduates, PhD and postdoctoral candidates, and faculty members from Chemical Engineering, Mechanical Engineering, Biochemical Engineering, Biomedical Engineering, Physics/Applied Mathematics, etc., as well as industry professionals employed in process industries in consulting/design/simulation/R&D roles.
Prerequisites: Basic Engineering MathematicsFluid MechanicsTransport PhenomenaChemical Reaction Engineering
Lectures
Week 1:
- Lecture 01 : What is Mathematical Modelling? Definition, Philosophy and Procedure
- Lecture 02 : Motivation for modelling in Chemical Engineering: Case study from Nature and Industry
- Lecture 03 : Classification of Mathematical Models
- Lecture 04 : Types of Mathematical Models: Finite, Fuzzy, Statistical, Difference and differential equations, stochastic
- Lecture 05 : Building Blocks of Mathematical Model - Postulates, assumptions, equations, closure conditions
Week 2:
- Lecture 06 : What is Scaling Analysis?
- Lecture 07 : Motivation I : Simplification and Design of Experiments
- Lecture 08 : Motivation II : Perturbation Methods and Numerics
- Lecture 09 : Mathematical Basis of Scaling Analysis : Lie Group Theory
- Lecture 10 : Worked Example : Putting it all together
Week 3 :
- Lecture 11: The Eight-Step o(1) Procedure: Steps 1-3 & Interpretation
- Lecture 12 : The Eight-Step o(1) Procedure: Steps 4-8 & Interpretation
- Lecture 13 : Scaling as an alternative to Dimensional Analysis (Motivation & Brief introduction to the 11 -step Procedure)
- Lecture 14 : Scaling as an alternative to Dimensional Analysis: The 11 -step Procedure (Steps 1-8 & Interpretation)
- Lecture 15 : Scaling as an alternative to Dimensional Analysis: The 11 -step Procedure (Steps 9-11 & Interpretation)
Week 4 :
- Lecture 16 : Motivation & Advantages/Limitations, Non-dimensionalisation, and Example Problems
- Lecture 17 : Expansions (Binomial & Taylor), Gauge Functions
- Lecture 18 : Order Symbols (O,o), Asymptotic Sequence and Expressions
- Lecture 19 : Uniform vs. Nonuniform Expansions, Parameter Perturbation, Coordinate Perturbation
- Lecture 20 : Regular vs. Singular Perturbation, Week 4 Review
Week 5:
- Lecture 21 : Method of matched asymptotic expansions: Historical Introduction, and building the Outer Expansion
- Lecture 22 : Method of matched asymptotic expansions: The Inner Expansion, Matching, and the Composite Solution
- Lecture 23 : Overlap region, higher order composite solution, and Van Dyke’s matching principle
- Lecture 24 : Solving Coupled Equations I: Fast/Slow Systems in Theory
- Lecture 25 : Solving Coupled Equations II: A Complete Reactor Example, Week 5 Review
Week 6:
- Lecture 26 : Method of Strained Coordinates: The idea, and the principle
- Lecture 27 : The Method of strained parameters (Lindstedt - Poincare)
- Lecture 28 : The Method of strained coordinates(Lighthill's technique)
- Lecture 29 : Comparison between strained co-ordinates and matched asymptotic expansions
- Lecture 30 : Limitation of the Method of Strained Coordinates, Week 6 Review
Week 7:
- Lecture 31 : Why Method of Multiple Scales? The Derivative-Expansion Method
- Lecture 32 : The Two-Variable Expansion Procedure
- Lecture 33 : The Generalised Method of Nonlinear Scales
- Lecture 34 : The WKB Method-General Theory and Example
- Lecture 35 : Limitations of the three variants of Multiple-Scale Methods; Week 7 Summary
Week 8:
- Lecture 36 : Applying o(1) scaling: Fully Developed Laminar Flow between parallel plates
- Lecture 37 : Flow in a Wavy-Wall Channel: The Domain Perturbation Method (Flow Parallel to the Corrugation Grooves)
- Lecture 38 : Flow in a Wavy-Wall Channel - The Domain Perturbation Method (Flow Perpendicular to the Corrugation Grooves)
- Lecture 39 : Cross-Flow Filtration: Exact solution and regular perturbation solution
- Lecture 40 : Cross-Flow Filtration: Singular perturbation solution, and Summary of Week 8
Week 9:
- Lecture 41 : Applying o(1) scaling: Unsteady-state, one-dimensional heat conduction
- Lecture 42 : A Heated Wire with Temperature-Dependent Properties: Regular Perturbation Solution
- Lecture 43 : A Thin Fin with Uniform Base Temperature Losing Heat to the Surrounding Air
- Lecture 44 : Fin with Non-Uniform Base Temperature: Singular Perturbation Solution (Outer Solution)
- Lecture 45 : Fin with Non-Uniform Base Temperature: Singular Perturbation (Inner Solution, Matching, and Composite Solution)
Week 10:
- Lecture 46 : Applying o(1) scaling : Large Pe Approximation for Mass Transfer in Falling Film Flow
- Lecture 47 : Applying o(1) scaling : Large Pe Approximation for Mass Transfer in Falling Film Flow(Contd.)
- Lecture 48 : Large Pe Approximation for Mass Transfer in Falling Film Flow: Matched Asymptotic Expansions Part 1 - The Outer Solution and the Failing of a Regular Expansion
- Lecture 49 : Large Pe Approximation for Mass Transfer in Falling Film Flow: Matched Asymptotic Expansions Part 2 - The Inner Region Leading Order Solution
- Lecture 50 : Large Pe Approximation for Mass Transfer in Falling Film Flow: Matched Asymptotic Expansions Part 3 - Assembling the Composite Solution and Summary of Week 10
Week 11:
- Lecture 51 : Applying O(1) scaling: Microscale modelling of Chemisorption process
- Lecture 52 : Applying O(1) scaling: Microscale modelling of Chemisorption process (Contd…)
- Lecture 53 : Reaction with an Immobile Substrate: Regular Perturbation Analysis
- Lecture 54 : The Quasi-Steady-State Approximation (QSSA) Part I: Singular Perturbation and the Need for Matched Asymptotics
- Lecture 55 : Beyond Quasi-Steady-State Approximation Part II: Inner Solution and Composite Solution
Week 12:
- Lecture 56 : Applying o(1) scaling : Flow Reactor for Hydrogen production from Methane
- Lecture 57 : Applying o(1) scaling : Flow Reactor for Hydrogen production from Methane(Contd.)
- Lecture 58 : Applying O(1) scaling: Flow Reactor for Hydrogen production from Methane (Contd…)
- Lecture 59 : Catalyst Slab Part 1 - Small Thiele Modulus
- Lecture 60 : Catalyst Slab Part II – Large Thiele Modulus, Summary of Week 12 & this Course
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT-ISM Dhanbad
- Department
- Chemical Engineering
- Teacher
- Prof. Sourav Sengupta
- Level
- Undergraduate
- Language
- English
- Subjects
- Chemistry, Engineering
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Kharagpur.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
More like this
NPTEL103105782
Course
Introduction to Python and Petroleum Data Analytics
60 lectures · Video
NPTEL103105001
Course
Applied Reservoir Engineering
40 lectures · Source's player
NPTEL103105223
Course
Petroleum Formation Evaluation
59 lectures · Source's player
NPTEL103105460
Course
Enhanced Oil Recovery Techniques
60 lectures · Source's player
NPTEL103105680
Course
Engineering Aspects of Biofuels and Biomass Conversion Technologies
60 lectures · Source's player
NPTEL103105837
Course
Fundamental of Carbon Capture, Utilization and Storage
60 lectures · Video
NPTEL105105002
Course
Meshfree Methods and Peridynamics for Fracture Mechanics
60 lectures · Source's player
NPTEL105105004
Course
Seismological Data Analysis
51 lectures · Source's player
NPTEL105105005
Course
Rock Slope Engineering
61 lectures · Source's player
NPTEL105105225
Course
Earthquake Seismology
57 lectures · Source's player
NPTEL105105226
Course
Engineering Geology
60 lectures · Source's player
NPTEL105105464
Course
Geoengineering
60 lectures · Source's player