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Multiphase Flows: Analytical Solutions and Stability Analysis

Multiphase Flows: Analytical Solutions and Stability Analysis. Instructor: Prof. S. Pushpavanam, Department of Chemical Engineering, IIT Madras. This course concentrates on obtaining analytical and semi-analytical solutions to multiphase flow problems. The emphasis is on using a very fundamental approach: equations of conservation of mass, momentum and energy without any empiricism. The focus is on getting approximate solutions using perturbation theory, and analysing stability of systems using linear stability analysis. This will help prepare students for doing research in these areas. (from nptel.ac.in)

Lecture 20 - Introduction to Stability of Dynamical Systems: ODEs

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Lecture 01 - Introduction and Overview of the Course: Multiphase Flows

Lecture 02 - Stratified Flow in a Microchannel: Velocity Profile

Lecture 03A - Stratified Flow in a Microchannel: Effects of Physical Parameters

Lecture 03B - Flow Regimes in Microchannels: Modeling and Experiments

Lecture 04 - Scaling Analysis: Introduction

Lecture 05 - Scaling Analysis: Worked Examples

Lecture 06 - Interfacial Tension and its Role in Multiphase Flows

Lecture 07 - Eulerian and Lagrangian Approaches

Lecture 08 - Reynolds Transport Theorem and the Equation of Continuity

Lecture 09 - Derivation of Navier-Stokes Equation

Lecture 10 - Vector Operations in General Orthogonal Coordinates: Gradient, Divergence, Laplacian

Lecture 11 - Normal and Shear Stresses on Arbitrary Surfaces: Force Balance

Lecture 12 - Normal and Shear Stresses on Arbitrary Surfaces: Stress Tensor Formulation

Lecture 13 - Stresses on Deforming Surfaces: Introduction to Perturbation Theory

Lecture 14 - Pulsatile Flow: Analytical Solution

Lecture 15 - Pulsatile Flow: Analytical Solution and Perturbation Solution for Rw≪1

Lecture 16 - Pulsatile Flow: Perturbation Solution for Rw≫1

Lecture 17 - Viscous Heating: Apparent Viscosity in a Viscometer

Lecture 18 - Domain Perturbation Methods: Flow between Wavy Walls

Lecture 19 - Flow between Wavy Walls: Velocity Profile

Lecture 20 - Introduction to Stability of Dynamical Systems: ODEs

Lecture 21 - Stability of Distributed Systems (PDEs): Reaction Diffusion Example

Lecture 22 - Stability of a Reaction-Diffusion System (cont.)

Lecture 23 - Rayleigh-Benard Convection: Physics and Governing Equations

Lecture 24A - Rayleigh-Benard Convection: Linear Stability Analysis 1

Lecture 24B - Rayleigh-Benard Convection: Linear Stability Analysis 2

Lecture 24C - Rayleigh-Benard Convection: Linear Stability Analysis 3

Lecture 25 - Rayleigh-Benard Convection: Discussion of Results

Lecture 26 - Rayleigh-Taylor Heavy over Light Instability

Lecture 27 - Rayleigh-Taylor Instability (cont.)

Lecture 28 - Capillary Jet Instability: Problem Formulation

Lecture 29 - Capillary Jet Instability: Linear Stability Analysis

Lecture 30 - Capillary Jet Instability: Rayleigh's Work Principle

Lecture 31 - Tutorial Session: Solution of Assignment 4 on Linear Stability

Lecture 32 - Turing Patterns: Instability in Reaction-Diffusion Systems

Lecture 33 - Turing Patterns: Results

Lecture 34 - Marangoni Convection: Generalised Tangential and Normal Stress Boundary Conditions

Lecture 35 - Marangoni Convection: Stability Analysis

Lecture 36 - Flow in a Circular Curved Channel: Governing Equations and Scaling

Lecture 37 - Flow in a Circular Curved Channel: Solution by Regular Perturbation

Lecture 38 - Stability of Flow through Curved Channels: Problem Formulation

Lecture 39 - Stability of Flow through Curved Channels: Numerical Calculation

Lecture 40 - Viscous Fingering: Darcy's Law

Lecture 41 - Viscous Fingering: Stability Analysis

Lecture 42 - Shallow Cavity Flows