Learn · Introduction to Scaling Analysis and Perturbation Methods for Chemical Engineers
Lecture 58 of 60Week 12:
Lecture 58 : Applying O(1) scaling: Flow Reactor for Hydrogen production from Methane (Contd…)
Prof. Sourav Sengupta · IIT-ISM Dhanbad
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- Introduction to Scaling Analysis and Perturbation Methods for Chemical Engineers, IIT-ISM Dhanbad (at NPTEL)
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All the lectures
- 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
- 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
- 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)
- 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
- 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
- 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
- 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
- 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
- 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)
- 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
- 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
- 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