Lecture 1Chapter 0

Introduction

27th January 2014

Total Marks 100Contact hrs: 3 per week

Text Book “Transport Phenomena”

by R. Byron Bird, Warren E. Stewart, Edwin N.

Lightfoot Second Edition

Course ContentsCh.E-407 TRANSPORT PHENOMENAViscosity and the mechanism of momentum transport;

Velocity distributions in laminar flow; The equations of change for isothermal systems; Velocity distribution with more than one independent variable

Thermal conductivity and mechanism of energy transport; Temperature distribution in solids and in laminar flow; The equations of change for non-isothermal systems

Diffusivity and the mechanisms of mass transport; Concentration distribution in solids and in laminar flow; The equations of change for multi-component systems.

What are Transport Phenomena?

Fluid Dynamics (transport of momentum)Heat Transfer (transport of energy)Mass Transfer (transport of mass)

Why Study Transport Phenomena?The 3 processes occur simultaneously in

industrial, biological and agricultural problems.

The basic equations are closely related.Mathematical tools used are similar.The molecular mechanisms in these are

nearly similar.

How to study Transport Phenomena?Study the transportation of momentum, heat,

mass through media as governed by various laws of nature.

Basic parameters representing the phenomena and nomenclature

Entity Being Transported/

Type of Transport

MOMENTUM ENERGY MASS

TRANSPORT BY MOLECULAR MOTION

VISCOSITY µ

Newton’s law of viscosity.Temperature, Pressure & Composition dependence on µKinetic theory of µ

THERMAL CONDUCTIVITY kFourier’s law of heat conduction Temperature, Pressure, and compositiondependence on k

Kinetic theory of k

DIFFUSIVITY DAB

Fick’s law of diffusionTemperature, Pressure, and composition dependence on DAB

Kinetic theory of DAB

TRANSPORT in LAMINAR FLOW or in SOLIDS, in ONE DIMENSION

SHELL MOMENTUM BALANCES

Velocity profilesAverage velocityMomentum flux at surfaces

SHELL ENERGY BALANCES

Temperature profilesAverage temperatureEnergy flux at surfaces

SHELL MASS BALANCES

Concentration profiles Average concentrationMass flux at surfaces

Continue…

Entity Being Transported

Type of Transport

MOMENTUM ENERGY MASS

TRANSPORT in an ARBITRARY CONTINUUM

EQUATION OF CHANGE (Isothermal)

Equation of continuityEquation of motion Equation of energy

EQUATION OF CHANGE (Non-isothermal)

Equation of continuity Equation of motion for forced and free convectionEquation of energy

EQUATION OF CHANGE (Multi-component)

Equation of continuity for each speciesEquation of motion for forced and free convectionEquation of energy

TRANSPORT IN LAMINAR FLOW or in SOLIDS, WITH TWO INDEPENDENT VARIABLES

MOMENTUM TRANSPORT

Unsteady viscous flowTwo-dimensional viscous flowBoundary-layer momentum transport

ENERGY TRANSPORT

Unsteady heat conductionHeat conduction in viscous flowTwo-dimensional heat conduction in solidsBoundary-layer energy transport

MASS TRANSPORT

Unsteady diffusionDiffusion in viscous flow Two-dimensional diffusion in solidsBoundary-layer mass transport

Continue…

Entity Being Transported

Type of Transport

MOMENTUM ENERGY MASS

TRANSPORT IN TURBULENT FLOW

TURBULENT MOMENTUM TRANSPORT

Time-smoothing of equation of changeEddy viscosity

Turbulent velocity profiles

TURBULENT ENERGY TRANSPORT

Time-smoothing of equation of changeEddy thermal conductivity

Turbulent temperature profiles

TURBULENT MASS TRANSPORT

Time-smoothing of equation of changeEddy diffusivity

Turbulent concentration profiles

TRANSPORT Between TWO PHASES

INTERPHASE MOMENTUM TRASNPORT

Friction factor f

Dimensionless correlations

INTERPHASE ENERGY TRASNPORT

Heat-transfer coefficient h

Dimensionless correlations (forced and free convection)

INTERPHASE MASS TRASNPORT

Heat-transfer coefficient kx

Dimensionless correlations (forced and free convection)

Continue…

Entity Being Transported

Type of Transport

MOMENTUM ENERGY MASS

TRANSPORT BY RADIATION

MOMENTUM TRANSPORT IN POLYMERIC LIQUIDS

Behavior of Polymeric LiquidsMolecular theories of polymeric liquidsRheometry

RADIENT ENERGY TRANSPORT

Planck’s radiation lawStefan-Boltzmann lawGeometrical problemsRadiation through absorbing media

MASS TRANSPORT IN MULTI-COMPONENT SYSTEMSConcentration diffusion and driving forceMass transfer across permeable membranesMass transfer in porous media

TRANSPORT IN LARGE FLOW SYSTEMS

MICROSOPIC BALANCES (Isothermal)

Mass balance Mechanical energy balance (Bernoulli equation)

MICROSOPIC BALANCES (Non-isothermal)

Mass balanceMomentum balance Mechanical and total energy balance

MICROSOPIC BALANCES (Multi-component)

Mass balance of each speciesMomentum balanceMechanical and total energy balance

THREE LEVELS OF STUDY OF TRANSPORT PHENOMENA1. Macroscopic Level2. Microscopic Level3. Molecular Level

Macroscopic Level

No attempt to understand the details of what is going on within the control volume

Mainly used for the global assessment of the problem

Integral Analysis

A Macroscopic Balance of1. Mass2. Momentum3. EnergyDue to various inputs & outputs from our control volume

Microscopic Level

An attempt to understand the details of what is going on within the control volume

Mainly used to get information of1. Velocity profiles2. Temperature profiles3. Concentration profiles

A Microscopic Balance of1. Mass2. Momentum3. EnergyDue to various inputs & outputs from our control volume

Differential Analysis

To understand the process and optimize it

Molecular Level

To seek the fundamental understanding of the process of1. Mass transfer2. Momentum transfer3. Energy transferIn terms of molecular structure & intermolecular forces

A job primarily for 1. Theoretical Physicists2. Physical ChemistSome times Engineers/applied scientists do get involved in cases of1. Complex molecules2. Extreme temperatures/pressures3. Chemical Reacting Flows

Each of these levels involve typical length scales

Molecular Level 1 to 1000 nanometers

Macroscopic Level Order of cm or m

Microscopic Level Micron to cm range

Requirements For Good Understanding Of This Subject

Physical Interpretation of key mathematical resultsGet into the habit of relating physical ideas to equations

Comparison of intuition and results obtained

MATHEMATICS, Differential Equations, Vectors, Calculus

Understanding of dimensional analysis

Division of BookChapters 1-8: Flow of pure fluids at constant

temperature (momentum transport)Chapters 9-16: Flow of pure fluids with

varying temperature (energy transport)Chapters 17-24: Flow of fluid mixtures with

varying composition (convective mass transport)