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September 23, 2023

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Description

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)

Course Curriculum

  • Lecture 01 – Introduction and Overview of the Course: Multiphase Flows Unlimited
  • Lecture 02 – Stratified Flow in a Microchannel: Velocity Profile Unlimited
  • Lecture 03A – Stratified Flow in a Microchannel: Effects of Physical Parameters Unlimited
  • Lecture 03B – Flow Regimes in Microchannels: Modeling and Experiments Unlimited
  • Lecture 04 – Scaling Analysis: Introduction Unlimited
  • Lecture 05 – Scaling Analysis: Worked Examples Unlimited
  • Lecture 06 – Interfacial Tension and its Role in Multiphase Flows Unlimited
  • Lecture 07 – Eulerian and Lagrangian Approaches Unlimited
  • Lecture 08 – Reynolds Transport Theorem and the Equation of Continuity Unlimited
  • Lecture 09 – Derivation of Navier-Stokes Equation Unlimited
  • Lecture 10 – Vector Operations in General Orthogonal Coordinates: Gradient, Divergence, Laplacian Unlimited
  • Lecture 11 – Normal and Shear Stresses on Arbitrary Surfaces: Force Balance Unlimited
  • Lecture 12 – Normal and Shear Stresses on Arbitrary Surfaces: Stress Tensor Formulation Unlimited
  • Lecture 13 – Stresses on Deforming Surfaces: Introduction to Perturbation Theory Unlimited
  • Lecture 14 – Pulsatile Flow: Analytical Solution Unlimited
  • Lecture 15 – Pulsatile Flow: Analytical Solution and Perturbation Solution for Rw≪1 Unlimited
  • Lecture 16 – Pulsatile Flow: Perturbation Solution for Rw≫1 Unlimited
  • Lecture 17 – Viscous Heating: Apparent Viscosity in a Viscometer Unlimited
  • Lecture 18 – Domain Perturbation Methods: Flow between Wavy Walls Unlimited
  • Lecture 19 – Flow between Wavy Walls: Velocity Profile Unlimited
  • Lecture 20 – Introduction to Stability of Dynamical Systems: ODEs Unlimited
  • Lecture 21 – Stability of Distributed Systems (PDEs): Reaction Diffusion Example Unlimited
  • Lecture 22 – Stability of a Reaction-Diffusion System (cont.) Unlimited
  • Lecture 23 – Rayleigh-Benard Convection: Physics and Governing Equations Unlimited
  • Lecture 24A – Rayleigh-Benard Convection: Linear Stability Analysis 1 Unlimited
  • Lecture 24B – Rayleigh-Benard Convection: Linear Stability Analysis 2 Unlimited
  • Lecture 24C – Rayleigh-Benard Convection: Linear Stability Analysis 3 Unlimited
  • Lecture 25 – Rayleigh-Benard Convection: Discussion of Results Unlimited
  • Lecture 26 – Rayleigh-Taylor Heavy over Light Instability Unlimited
  • Lecture 27 – Rayleigh-Taylor Instability (cont.) Unlimited
  • Lecture 28 – Capillary Jet Instability: Problem Formulation Unlimited
  • Lecture 29 – Capillary Jet Instability: Linear Stability Analysis Unlimited
  • Lecture 30 – Capillary Jet Instability: Rayleigh’s Work Principle Unlimited
  • Lecture 31 – Tutorial Session: Solution of Assignment 4 on Linear Stability Unlimited
  • Lecture 32 – Turing Patterns: Instability in Reaction-Diffusion Systems Unlimited
  • Lecture 33 – Turing Patterns: Results Unlimited
  • Lecture 34 – Marangoni Convection: Generalised Tangential and Normal Stress Boundary Conditions Unlimited
  • Lecture 35 – Marangoni Convection: Stability Analysis Unlimited
  • Lecture 36 – Flow in a Circular Curved Channel: Governing Equations and Scaling Unlimited
  • Lecture 37 – Flow in a Circular Curved Channel: Solution by Regular Perturbation Unlimited
  • Lecture 38 – Stability of Flow through Curved Channels: Problem Formulation Unlimited
  • Lecture 39 – Stability of Flow through Curved Channels: Numerical Calculation Unlimited
  • Lecture 40 – Viscous Fingering: Darcy’s Law Unlimited
  • Lecture 41 – Viscous Fingering: Stability Analysis Unlimited
  • Lecture 42 – Shallow Cavity Flows Unlimited

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