Particle Dynamics: Brownian Diffusion

Size: px
Start display at page:

Download "Particle Dynamics: Brownian Diffusion"

Transcription

1 Particle Dynamics: Brownian Diffusion Prof. Sotiris E. Pratsinis Particle Technology Laboratory Department of Mechanical and Process Engineering, ETH Zürich, Switzerland 1 or or or or nucleation inception condensation surface growth v or v evaporation flocculation coalescence aggregation sintering chemical bonding Aerosol-based Technologies in Nanoscale Manufacturing: from Functional Materials to Devices through Core Chemical Engineering, AIChE J., 56, (2010) agglomeration attachement physical adhesion

2 Particle Dynamics Coagulation Fragmentation Convection in Shrinking by evaporation or dissolution Growth by condensation or chemical reaction Convection out Diffusion Settling 3 Theory: Population Balance Equation n t n u Dn dv n v dt c n convection diffusion growth external force 1 v 2 0 v~,v v~ n v~ n v v~ S v dv ~ coagulation v 0 fragmentation v,v ~ nv v,v ~ Snv~ nv nv~ dv ~ dv ~ u D c S u,u, u = gas velocity vector x y z = particle diffusivity = velocity of particles of size v (e.g. settling) = coagulation rate = fragmentation rate = fragment size distribution n u un n u 0 continuity 4

3 Mean Free Path: Continuum vs. Free-molecule regime The mean free path of a gas,, is the average distance traveled by gas molecules between their collisions. When particles are much larger than (e.g. d p > 10), they do not sense individual collisions with molecules feeling a continuum so particle motion takes place in the so-called continuum regime and described by the standard or classic Navier-Stokes equations, the gospel of engineering. When particles are much smaller than (e.g. d p < ), they are in the so-called free-molecule regime and their motion is described by the kinetic theory of gases. Inbetween, interpolations are devised specific to the process (e.g. for diffusion, coagulation or condensation) 5 1. DIFFUSION Particles suspended in a fluid medium exhibit a haphazard dancing motion Botanist Robert Brown discovered that this motion was a general property of matter regardless of its origin (dust vs. pollen) Hands-on experiment resembling the motion of oil droplets in water with ball bearings and metal rings on a vibrating table at the Museum of Fine Arts at the San Francisco Exploratorium organized by Dr. Frank Oppenheimer (brother of Robert the father of the Atomic Bomb) 6

4 Diffusion is the net migration of particles from regions of HIGH to LOW concentration Net rate of transport into that element: Friedlander, S.K., Smoke, Dust and Haze, Chapter 2, Oxford Press, 2nd Edition, New York, The rate of change of the number of particles per unit volume (& size), n, in the elemental volume δxδyδz is: From experimental observations: Fick s first law Substituting in the above gives second Fick s law: Coefficient of Diffusion or Diffusivity, D 8

5 D = f (particle size and gas properties) Consider particle transport in one dimension, x Release equally sized particles, N 0, at t=0 and observe the n distribution in space and time For the boundary conditions at x = 0, x = & t =0, the particle concentration distribution in x,t is 9 The mean square displacement of the particles from x=0 at time t is: We can measure chequered glass. by putting spheres in a liquid and follow their motion through a 10

6 The goal is to relate the mean square displacement of a particle with the energy required for this job. Force balance on a particle in Brownian motion: Now multiply both sides of eq. (5) by the displacement x and divide by m. For a single particle: x du f ux F() t x dt m m (6) 11 define as β = f/m and A = F(t)/m and remember that: Using these expressions eq. (6) becomes Integrate from t=0 to t and obtain: where t is a variable of integration representing time. 12

7 Average over all particles: Since there is no correlation between displacement x and kick, A, the second term of eq. (7) vanishes: You can also write: 13 Because the derivative of the mean over particles with respect to time is equal to the mean of the derivative: From eq. (8) & (9): Integrate over time from t = 0 to t for t >> 1/β (or β t >> 1): 14

8 Invoke the equipartition of energy, meaning that the kinetic energy of particles is equal to the kinetic energy of the surrounding gas molecules: This is the Stokes-Einstein expression for D. It relates D to the properties of the fluid and the particle through the friction coefficient. 15 Perrin s (1910) study allowed calculation of the Avogadro number N AV. By observing the motion of an emulsion he calculated the number of (attacking) molecules: where R is the gas constant He gave an experimental proof of the kinetic theory by measuring the net displacement Modern methods show that N AV = molecules/mol 16

9 Friction coefficient mean free path of gas medium with ρ : density of the medium (e.g. air) m 1 : molecular mass of the medium In the continuum regime (d P >> λ ): f = 3d P In the free molecular regime (d P << λ ): with a: accomodation coefficient 0.9 In the entire range: with C: Cunningham correction factor 17 Coefficients A1, A2, and A3 are empirical constants that have been obtained by measuring the settling velocities of particles in various gases. Table 1 gives these constants for various gases (Rader, D. J., Momentum slip correction factor for small particles in nine common gases, J. Aerosol Sci., 21 (1990), ) The ratio of the mean free path of the gas and the particle radius is the Knudsen number Kn = 2λ/dp. The Cunningham correction factor does not change very much with different gases for the same Kn (Table 2). 18

10 Diffusion and sedimentation dominate the particles motion at opposite size regimes (Table 3). 19 DIFFUSION during LAMINAR PIPE FLOW Entrance length: L = 0.04dRe (laminar flow) d : pipe diameter Re : Reynolds-number The momentum boundary layer develops rapidly while the concentration boundary layer follows: 20

11 Separation of variables: Result: So the average particle concentration is defined as: And in general it is given as: Where G k and λ k2 are given in Table 3.1 in the book by Friedlander (1977). The above ratio is called also the particle penetration, P, and it is defined as: 21 Penetration curves for particle diffusion to pipe walls Penetration versus deposition parameter for circular tubes and rectangular cross section channels: D: particle Diffusivity, L: tube or channel length, Q: gas flowrate, h: interplate distance, W: channel width (Hinds, 1982) 22

12 Rowell, J. M., Scientific American, October 1986,

13 MacChesney, J. B., O Connor, P. B. and Presby, H. M., 1974, A new technique for preparation of low-loss and graded index optical fibers. Proc. IEEE 62, J. Aerosol Sci., 20, (1989)

For one such collision, a new particle, "k", is formed of volume v k = v i + v j. The rate of formation of "k" particles is, N ij

For one such collision, a new particle, k, is formed of volume v k = v i + v j. The rate of formation of k particles is, N ij Coagulation Theory and The Smoluchowski Equation: Coagulation is defined as growth of particles by collisions among particles. It is usually associated with dense, 3-d growth, in contrast to aggregation

More information

EXPERIMENT 17. To Determine Avogadro s Number by Observations on Brownian Motion. Introduction

EXPERIMENT 17. To Determine Avogadro s Number by Observations on Brownian Motion. Introduction EXPERIMENT 17 To Determine Avogadro s Number by Observations on Brownian Motion Introduction In 1827 Robert Brown, using a microscope, observed that very small pollen grains suspended in water appeared

More information

Brownian Motion and The Atomic Theory

Brownian Motion and The Atomic Theory Brownian Motion and The Atomic Theory Albert Einstein Annus Mirabilis Centenary Lecture Simeon Hellerman Institute for Advanced Study, 5/20/2005 Founders Day 1 1. What phenomenon did Einstein explain?

More information

Evaluation of diffusion models for airborne nanoparticles transport and dispersion

Evaluation of diffusion models for airborne nanoparticles transport and dispersion Advances in Fluid Mechanics VII 111 Evaluation of diffusion models for airborne nanoparticles transport and dispersion F. Morency 1, S. Hallé 1, L. Dufresne 1 & C. Émond 2 1 École de technologie supérieure,

More information

C C C C 2 C 2 C 2 C + u + v + (w + w P ) = D t x y z X. (1a) y 2 + D Z. z 2

C C C C 2 C 2 C 2 C + u + v + (w + w P ) = D t x y z X. (1a) y 2 + D Z. z 2 This chapter provides an introduction to the transport of particles that are either more dense (e.g. mineral sediment) or less dense (e.g. bubbles) than the fluid. A method of estimating the settling velocity

More information

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds. Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,

More information

Fluid Mechanics Theory I

Fluid Mechanics Theory I Fluid Mechanics Theory I Last Class: 1. Introduction 2. MicroTAS or Lab on a Chip 3. Microfluidics Length Scale 4. Fundamentals 5. Different Aspects of Microfluidcs Today s Contents: 1. Introduction to

More information

Principles of Convection

Principles of Convection Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

More information

NUMERICAL PREDICTIONS OF DEPOSTION WITH A PARTICLE CLOUD TRACKING TECHNIQUE

NUMERICAL PREDICTIONS OF DEPOSTION WITH A PARTICLE CLOUD TRACKING TECHNIQUE Committed Individuals Solving Challenging Problems NUMERICAL PREDICTIONS OF DEPOSTION WITH A PARTICLE CLOUD TRACKING TECHNIQUE by James R. Valentine Reaction Engineering International Philip J. Smith Department

More information

INSTANTANEOUS AEROSOL DYNAMICS IN A TURBULENT FLOW

INSTANTANEOUS AEROSOL DYNAMICS IN A TURBULENT FLOW 1492 THERMAL SCIENCE, Year 2012, Vol. 16, No. 5, pp. 1492-1496 INSTANTANEOUS AEROSOL DYNAMICS IN A TURBULENT FLOW by Kun ZHOU * Clean Combustion Research Center, King Abdullah University of Science and

More information

Topics covered so far:

Topics covered so far: Topics covered so far: Chap 1: The kinetic theory of gases P, T, and the Ideal Gas Law Chap 2: The principles of statistical mechanics 2.1, The Boltzmann law (spatial distribution) 2.2, The distribution

More information

Diffusion and Adsorption in porous media. Ali Ahmadpour Chemical Eng. Dept. Ferdowsi University of Mashhad

Diffusion and Adsorption in porous media. Ali Ahmadpour Chemical Eng. Dept. Ferdowsi University of Mashhad Diffusion and Adsorption in porous media Ali Ahmadpour Chemical Eng. Dept. Ferdowsi University of Mashhad Contents Introduction Devices used to Measure Diffusion in Porous Solids Modes of transport in

More information

Population balance modeling -an application in particle technology

Population balance modeling -an application in particle technology Population balance modeling -an application in particle technology Sheryl Ehrman IITB and University of Maryland Link to Matlab: www.glue.umd.edu/~sehrman/popbal.htm Outline Aerosol reactors in industry

More information

Part I.

Part I. Part I bblee@unimp . Introduction to Mass Transfer and Diffusion 2. Molecular Diffusion in Gasses 3. Molecular Diffusion in Liquids Part I 4. Molecular Diffusion in Biological Solutions and Gels 5. Molecular

More information

Basic Fluid Mechanics

Basic Fluid Mechanics Basic Fluid Mechanics Chapter 6A: Internal Incompressible Viscous Flow 4/16/2018 C6A: Internal Incompressible Viscous Flow 1 6.1 Introduction For the present chapter we will limit our study to incompressible

More information

Chapter 10. Solids and Fluids

Chapter 10. Solids and Fluids Chapter 10 Solids and Fluids Surface Tension Net force on molecule A is zero Pulled equally in all directions Net force on B is not zero No molecules above to act on it Pulled toward the center of the

More information

2. Molecules in Motion

2. Molecules in Motion 2. Molecules in Motion Kinetic Theory of Gases (microscopic viewpoint) assumptions (1) particles of mass m and diameter d; ceaseless random motion (2) dilute gas: d λ, λ = mean free path = average distance

More information

Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems

Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems Biological Process Engineering An Analogical Approach to Fluid Flow, Heat Transfer, and Mass Transfer Applied to Biological Systems Arthur T. Johnson, PhD, PE Biological Resources Engineering Department

More information

Modeling Complex Flows! Direct Numerical Simulations! Computational Fluid Dynamics!

Modeling Complex Flows! Direct Numerical Simulations! Computational Fluid Dynamics! http://www.nd.edu/~gtryggva/cfd-course/! Modeling Complex Flows! Grétar Tryggvason! Spring 2011! Direct Numerical Simulations! In direct numerical simulations the full unsteady Navier-Stokes equations

More information

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER

FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES Liquid or gas flow through pipes

More information

Lecture 30 Review of Fluid Flow and Heat Transfer

Lecture 30 Review of Fluid Flow and Heat Transfer Objectives In this lecture you will learn the following We shall summarise the principles used in fluid mechanics and heat transfer. It is assumed that the student has already been exposed to courses in

More information

HEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1

HEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1 HEAT TRANSFER BY CONVECTION Dr. Şaziye Balku 1 CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in the

More information

The effect of Cartilaginous rings on Deposition by Convection, Brownian Diffusion and Electrostatics.

The effect of Cartilaginous rings on Deposition by Convection, Brownian Diffusion and Electrostatics. Excerpt from the Proceedings of the COMSOL Conference 21 Paris The effect of Cartilaginous rings on Deposition by Convection, Brownian Diffusion and Electrostatics. H.O. Åkerstedt Department of Applied

More information

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127 C ONTENTS Preface xviii Nomenclature xxvi CHAPTER ONE BASICS OF HEAT TRANSFER 1 1-1 Thermodynamics and Heat Transfer 2 Application Areas of Heat Transfer 3 Historical Background 3 1-2 Engineering Heat

More information

NUMERICAL MODELING OF THE GAS-PARTICLE FLUID FLOW AND HEAT TRANSFER IN THE SLIP REGIME

NUMERICAL MODELING OF THE GAS-PARTICLE FLUID FLOW AND HEAT TRANSFER IN THE SLIP REGIME Proceedings of the Asian Conference on Thermal Sciences 2017, 1st ACTS March 26-30, 2017, Jeju Island, Korea ACTS-P00394 NUMERICAL MODELING OF THE GAS-PARTICLE FLUID FLOW AND HEAT TRANSFER IN THE SLIP

More information

UNIT II CONVECTION HEAT TRANSFER

UNIT II CONVECTION HEAT TRANSFER UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid

More information

Aggregate Growth: R =αn 1/ d f

Aggregate Growth: R =αn 1/ d f Aggregate Growth: Mass-ractal aggregates are partly described by the mass-ractal dimension, d, that deines the relationship between size and mass, R =αn 1/ d where α is the lacunarity constant, R is the

More information

author's personal copy

author's personal copy Mechanics Research Communications 40 (2012) 46 51 Contents lists available at SciVerse ScienceDirect Mechanics Research Communications jo ur nal homep age : www.elsevier.com/locate/mechrescom Verifying

More information

FORMULA SHEET. General formulas:

FORMULA SHEET. General formulas: FORMULA SHEET You may use this formula sheet during the Advanced Transport Phenomena course and it should contain all formulas you need during this course. Note that the weeks are numbered from 1.1 to

More information

s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I

s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I Fundamentals of Engineering (FE) Exam General Section Steven Burian Civil & Environmental Engineering October 26, 2010 s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum

More information

THE VERIFICATION OF THE TAYLOR-EXPANSION MOMENT METHOD IN SOLVING AEROSOL BREAKAGE

THE VERIFICATION OF THE TAYLOR-EXPANSION MOMENT METHOD IN SOLVING AEROSOL BREAKAGE 144 THERMAL SCIENCE, Year 1, Vol. 16, No. 5, pp. 144-148 THE VERIFICATION OF THE TAYLOR-EXPANSION MOMENT METHOD IN SOLVING AEROSOL BREAKAGE by Ming-Zhou YU a,b * and Kai ZHANG a a College of Science, China

More information

Fluid-Particles Interaction Models Asymptotics, Theory and Numerics I

Fluid-Particles Interaction Models Asymptotics, Theory and Numerics I Fluid-Particles Interaction Models Asymptotics, Theory and Numerics I J. A. Carrillo collaborators: T. Goudon (Lille), P. Lafitte (Lille) and F. Vecil (UAB) (CPDE 2005), (JCP, 2008), (JSC, 2008) ICREA

More information

BROWNIAN MOVEMENTS. According to MATTER (Re-examined) Nainan K. Varghese,

BROWNIAN MOVEMENTS. According to MATTER (Re-examined) Nainan K. Varghese, BROWNIAN MOVEMENTS According to MATTER (Re-examined) Nainan K. Varghese, matterdoc@gmail.com http://www.matterdoc.info Abstract: Currently, analyses of Brownian motion are limited to its relevance to other

More information

KINETIC THEORY OF GASES

KINETIC THEORY OF GASES LECTURE 8 KINETIC THEORY OF GASES Text Sections 0.4, 0.5, 0.6, 0.7 Sample Problems 0.4 Suggested Questions Suggested Problems Summary None 45P, 55P Molecular model for pressure Root mean square (RMS) speed

More information

Contents. Microfluidics - Jens Ducrée Physics: Laminar and Turbulent Flow 1

Contents. Microfluidics - Jens Ducrée Physics: Laminar and Turbulent Flow 1 Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors

More information

CONVECTION HEAT TRANSFER

CONVECTION HEAT TRANSFER CONVECTION HEAT TRANSFER SECOND EDITION Adrian Bejan J. A. Jones Professor of Mechanical Engineering Duke University Durham, North Carolina A WILEY-INTERSCIENCE PUBUCATION JOHN WILEY & SONS, INC. New York

More information

ENMA490 Capstone: Design of Microfluidics Mixer

ENMA490 Capstone: Design of Microfluidics Mixer ENMA490 Capstone: Design of Microfluidics Mixer By: Elyse Canosa, Josh Davis, Colin Heikes, Gao Li, Pavel Kotlyarskiy, Christina Senagore, Maeling Tapp, Alvin Wilson Outline Motivation for Microfluidic

More information

convection coefficient, h c = 18.1 W m K and the surrounding temperature to be 20 C.) (20 marks) Question 3 [35 marks]

convection coefficient, h c = 18.1 W m K and the surrounding temperature to be 20 C.) (20 marks) Question 3 [35 marks] COP 311 June Examination 18 June 005 Duration: 3 hours Starting time: 08:30 Internal examiners: Prof. T. Majozi Mnr. D.J. de Kock Mnr. A.T. Tolmay External examiner: Mnr. B. du Plessis Metallurgists: Questions

More information

GAS LAWS. Boyle s Law: Investigating the dependence of Volume on Pressure (Temperature kept constant)

GAS LAWS. Boyle s Law: Investigating the dependence of Volume on Pressure (Temperature kept constant) 1 GAS LAWS Boyle s Law: Investigating the dependence of Volume on Pressure (Temperature kept constant) The diagram below shows the apparatus which gives a direct reading for both the volume and pressure

More information

Contents. I Introduction 1. Preface. xiii

Contents. I Introduction 1. Preface. xiii Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................

More information

Physical Properties of Fluids

Physical Properties of Fluids Physical Properties of Fluids Viscosity: Resistance to relative motion between adjacent layers of fluid. Dynamic Viscosity:generally represented as µ. A flat plate moved slowly with a velocity V parallel

More information

GAW - WCCAP recommendation for aerosol inlets and sampling tubes

GAW - WCCAP recommendation for aerosol inlets and sampling tubes GAW - WCCAP recommendation for aerosol inlets and sampling tubes Alfred Wiedensohler, Wolfram Birmili, Leibniz Institute for Tropospheric Research, Leipzig, Germany John Ogren, NOAA ESRL GMD, Boulder,

More information

CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel

CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel *1 Hüseyin Kaya, 2 Kamil Arslan 1 Bartın University, Mechanical Engineering Department, Bartın, Turkey

More information

Transport Properties: Momentum Transport, Viscosity

Transport Properties: Momentum Transport, Viscosity Transport Properties: Momentum Transport, Viscosity 13th February 2011 1 Introduction Much as mass(material) is transported within luids (gases and liquids), linear momentum is also associated with transport,

More information

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD) Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The

More information

Chapter 7.1. States of Matter

Chapter 7.1. States of Matter Chapter 7.1 States of Matter In this chapter... we will learn about matter and different states of matter, many of which we are already familiar with! Learning about Kinetic Molecular Theory will help

More information

4. The Green Kubo Relations

4. The Green Kubo Relations 4. The Green Kubo Relations 4.1 The Langevin Equation In 1828 the botanist Robert Brown observed the motion of pollen grains suspended in a fluid. Although the system was allowed to come to equilibrium,

More information

Convective Mass Transfer

Convective Mass Transfer Convective Mass Transfer Definition of convective mass transfer: The transport of material between a boundary surface and a moving fluid or between two immiscible moving fluids separated by a mobile interface

More information

Center of Mass & Linear Momentum

Center of Mass & Linear Momentum PHYS 101 Previous Exam Problems CHAPTER 9 Center of Mass & Linear Momentum Center of mass Momentum of a particle Momentum of a system Impulse Conservation of momentum Elastic collisions Inelastic collisions

More information

Forces. Prof. Yury Kolomensky Feb 9/12, 2007

Forces. Prof. Yury Kolomensky Feb 9/12, 2007 Forces Prof. Yury Kolomensky Feb 9/12, 2007 - Hooke s law - String tension - Gravity and Weight - Normal force - Friction - Drag -Review of Newton s laws Today s Plan Catalog common forces around us What

More information

BAE 820 Physical Principles of Environmental Systems

BAE 820 Physical Principles of Environmental Systems BAE 820 Physical Principles of Environmental Systems Estimation of diffusion Coefficient Dr. Zifei Liu Diffusion mass transfer Diffusion mass transfer refers to mass in transit due to a species concentration

More information

MYcsvtu Notes HEAT TRANSFER BY CONVECTION

MYcsvtu Notes HEAT TRANSFER BY CONVECTION www.mycsvtunotes.in HEAT TRANSFER BY CONVECTION CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in

More information

Origins of Modern Physics

Origins of Modern Physics PY1P0/PY1T0 Origins of Modern Physics S. Hutzler notes at: http://www.tcd.ie/physics/foams/lecture_notes/py1p0_origins_of_modern_physics 1. The existence of atoms. Fingerprints of Matter: Spectra 3. The

More information

SPRING 2011 Phys 450 Solution set 2

SPRING 2011 Phys 450 Solution set 2 SPRING 011 Phys 450 Solution set Problem 1 (a) Estimate the diameter of a ater molecule from its self-diffusion coefficient, and using the Stokes-Einstein relation, assuming that it is a spherical molecule.

More information

The structure of Atom I

The structure of Atom I The structure of Atom I Matter Matter Matter is anything that occupies space and has mass. The particle theory of matter The particle theory of matter states that matter is made up of a large number of

More information

FE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)

FE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering) Topic: Fluid Properties 1. If 6 m 3 of oil weighs 47 kn, calculate its specific weight, density, and specific gravity. 2. 10.0 L of an incompressible liquid exert a force of 20 N at the earth s surface.

More information

Chapter 7 Mixing and Granulation

Chapter 7 Mixing and Granulation Chapter 7 Mixing and Granulation 7.1 Mixing and Segregation (Chapter 9) Mixing vs. segregation (1) Types of Mixture * Perfect mixing Random mixing Segregating mixing Figure 9.1 (2) Segregation 1) Causes

More information

Phone: , For Educational Use. SOFTbank E-Book Center, Tehran. Fundamentals of Heat Transfer. René Reyes Mazzoco

Phone: , For Educational Use. SOFTbank E-Book Center, Tehran. Fundamentals of Heat Transfer. René Reyes Mazzoco 8 Fundamentals of Heat Transfer René Reyes Mazzoco Universidad de las Américas Puebla, Cholula, Mexico 1 HEAT TRANSFER MECHANISMS 1.1 Conduction Conduction heat transfer is explained through the molecular

More information

Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay

Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay Lecture No. 18 Forced Convection-1 Welcome. We now begin our study of forced convection

More information

K n. III. Gas flow. 1. The nature of the gas : Knudsen s number. 2. Relative flow : Reynold s number R = ( dimensionless )

K n. III. Gas flow. 1. The nature of the gas : Knudsen s number. 2. Relative flow : Reynold s number R = ( dimensionless ) III. Gas flow. The nature of the gas : Knudsen s number K n λ d 2. Relative flow : U ρ d η U : stream velocity ρ : mass density Reynold s number R ( dimensionless ) 3. Flow regions - turbulent : R > 2200

More information

PIPE FLOWS: LECTURE /04/2017. Yesterday, for the example problem Δp = f(v, ρ, μ, L, D) We came up with the non dimensional relation

PIPE FLOWS: LECTURE /04/2017. Yesterday, for the example problem Δp = f(v, ρ, μ, L, D) We came up with the non dimensional relation /04/07 ECTURE 4 PIPE FOWS: Yesterday, for the example problem Δp = f(v, ρ, μ,, ) We came up with the non dimensional relation f (, ) 3 V or, p f(, ) You can plot π versus π with π 3 as a parameter. Or,

More information

Brownian motion and the Central Limit Theorem

Brownian motion and the Central Limit Theorem Brownian motion and the Central Limit Theorem Amir Bar January 4, 3 Based on Shang-Keng Ma, Statistical Mechanics, sections.,.7 and the course s notes section 6. Introduction In this tutorial we shall

More information

CONVECTIVE HEAT TRANSFER

CONVECTIVE HEAT TRANSFER CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 3 LAMINAR BOUNDARY LAYER FLOW LAMINAR BOUNDARY LAYER FLOW Boundary

More information

Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows

Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows Published in Phys. Fluids 14, L73-L76 (22). Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows Koji Fukagata, Kaoru Iwamoto, and Nobuhide Kasagi Department of Mechanical

More information

SOLIDS AND LIQUIDS - Here's a brief review of the atomic picture or gases, liquids, and solids GASES

SOLIDS AND LIQUIDS - Here's a brief review of the atomic picture or gases, liquids, and solids GASES 30 SOLIDS AND LIQUIDS - Here's a brief review of the atomic picture or gases, liquids, and solids GASES * Gas molecules are small compared to the space between them. * Gas molecules move in straight lines

More information

8.6 Drag Forces in Fluids

8.6 Drag Forces in Fluids 86 Drag Forces in Fluids When a solid object moves through a fluid it will experience a resistive force, called the drag force, opposing its motion The fluid may be a liquid or a gas This force is a very

More information

PHYSICS PAPER 1. (THEORY) (Three hours)

PHYSICS PAPER 1. (THEORY) (Three hours) PHYSICS PAPER 1 (THEY) (Three hours) (Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.) All questions are compulsory. Question number

More information

The effective slip length and vortex formation in laminar flow over a rough surface

The effective slip length and vortex formation in laminar flow over a rough surface The effective slip length and vortex formation in laminar flow over a rough surface Anoosheh Niavarani and Nikolai V. Priezjev Movies and preprints @ http://www.egr.msu.edu/~niavaran A. Niavarani and N.V.

More information

CONVECTION HEAT TRANSFER

CONVECTION HEAT TRANSFER CONVECTION HEAT TRANSFER THIRD EDITION Adrian Bejan J. A. Jones Professor of Mechanical Engineering Duke University Durham, North Carolina WILEY JOHN WILEY & SONS, INC. CONTENTS Preface Preface to the

More information

SOLIDS AND LIQUIDS - Here's a brief review of the atomic picture or gases, liquids, and solids GASES

SOLIDS AND LIQUIDS - Here's a brief review of the atomic picture or gases, liquids, and solids GASES 30 SOLIDS AND LIQUIDS - Here's a brief review of the atomic picture or gases, liquids, and solids GASES * Gas molecules are small compared to the space between them. * Gas molecules move in straight lines

More information

Chapter 9 Generation of (Nano)Particles by Growth

Chapter 9 Generation of (Nano)Particles by Growth Chapter 9 Generation of (Nano)Particles by Growth 9.1 Nucleation (1) Supersaturation Thermodynamics assumes a phase change takes place when there reaches Saturation of vapor in a gas, Saturation of solute

More information

Table of Contents. Foreword... xiii. Preface... xv

Table of Contents. Foreword... xiii. Preface... xv Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers... 1 1.1. Fundamental equations... 1 1.1.1. Local equations... 1 1.1.2. Integral conservation equations...

More information

Applied Fluid Mechanics

Applied Fluid Mechanics Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

More information

Microfluidics 1 Basics, Laminar flow, shear and flow profiles

Microfluidics 1 Basics, Laminar flow, shear and flow profiles MT-0.6081 Microfluidics and BioMEMS Microfluidics 1 Basics, Laminar flow, shear and flow profiles 11.1.2017 Ville Jokinen Outline of the next 3 weeks: Today: Microfluidics 1: Laminar flow, flow profiles,

More information

Lecture-6 Motion of a Particle Through Fluid (One dimensional Flow)

Lecture-6 Motion of a Particle Through Fluid (One dimensional Flow) Lecture-6 Motion of a Particle Through Fluid (One dimensional Flow) 1 Equation of Motion of a spherical Particle (one dimensional Flow) On Board 2 Terminal Velocity Particle reaches a maximum velocity

More information

Brownian motion using video capture

Brownian motion using video capture INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 23 (2002) 1 5 EUROPEANJOURNAL OF PHYSICS PII: S0143-0807(02)33827-3 Brownian motion using video capture Reese Salmon, Candace Robbins and Kyle Forinash 1 School

More information

SEDIMENTATION INTRODUCTION

SEDIMENTATION INTRODUCTION SEDIMENTATION INTRODUCTION Sedimentation is removal of particulate materials suspended in water by quiescent settling due to gravity Commonly used unit operation in water and wastewater treatment plants

More information

High Vacuum Gas Pumping and Boundary Coupling

High Vacuum Gas Pumping and Boundary Coupling Presented at the COMSOL Conference 2008 Hannover Oral presentation at the COMSOL 2008 Conference, 4-6 th November 2008, Hanover High Vacuum Gas Pumping and Boundary Coupling Marco Cavenago Laboratori Nazionali

More information

Vacuum I. G. Franchetti CAS - Bilbao. 30/5/2011 G. Franchetti 1

Vacuum I. G. Franchetti CAS - Bilbao. 30/5/2011 G. Franchetti 1 Vacuum I G. Franchetti CAS - Bilbao 30/5/2011 G. Franchetti 1 Index Introduction to Vacuum Vacuum and the Beam Flow Regimes Creating Vacuum 30/5/2011 G. Franchetti 2 Vacuum in accelerators All beam dynamics

More information

Chapter 3 NATURAL CONVECTION

Chapter 3 NATURAL CONVECTION Fundamentals of Thermal-Fluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGraw-Hill, 2008 Chapter 3 NATURAL CONVECTION Mehmet Kanoglu Copyright The McGraw-Hill Companies,

More information

Heat Transfer Convection

Heat Transfer Convection Heat ransfer Convection Previous lectures conduction: heat transfer without fluid motion oday (textbook nearly 00 pages) Convection: heat transfer with fluid motion Research methods different Natural Convection

More information

PROPERTIES OF BULK MATTER

PROPERTIES OF BULK MATTER PROPERTIES OF BULK MATTER CONCEPTUAL PROBLEMS Q-01 What flows faster than honey. Why? Ans According to poiseuille s formula, the volume V of a liquid flowing per second through a horizontal narrow tube

More information

Modeling of Mature Soot Dynamics and Optical Properties

Modeling of Mature Soot Dynamics and Optical Properties Modeling of Mature Soot Dynamics and Optical Properties Georgios A. Kelesidis, Sotiris E. Pratsinis Particle Technology Laboratory, ETH Zurich, Zurich, Switzerland Aleksandar Duric, Martin Allemann Siemens

More information

Single Curved Fiber Sedimentation Under Gravity. Xiaoying Rong, Dewei Qi Western Michigan University

Single Curved Fiber Sedimentation Under Gravity. Xiaoying Rong, Dewei Qi Western Michigan University Single Curved Fiber Sedimentation Under Gravity Xiaoying Rong, Dewei Qi Western Michigan University JunYong Zhu, Tim Scott USDA Forest Products Laboratory ABSTRACT Dynamics of single curved fiber sedimentation

More information

Copyright 2008, University of Chicago, Department of Physics. Experiment I. RATIO OF SPECIFIC HEATS OF GASES; γ C p

Copyright 2008, University of Chicago, Department of Physics. Experiment I. RATIO OF SPECIFIC HEATS OF GASES; γ C p Experiment I RATIO OF SPECIFIC HEATS OF GASES; γ C p / C v 1. Recommended Reading M. W. Zemansky, Heat and Thermodynamics, Fifth Edition, McGraw Hill, 1968, p. 122-132, 161-2. 2. Introduction You have

More information

1 Brownian motion and the Langevin equation

1 Brownian motion and the Langevin equation Figure 1: The robust appearance of Robert Brown (1773 1858) 1 Brownian otion and the Langevin equation In 1827, while exaining pollen grains and the spores of osses suspended in water under a icroscope,

More information

Physics 3 Summer 1990 Lab 7 - Hydrodynamics

Physics 3 Summer 1990 Lab 7 - Hydrodynamics Physics 3 Summer 1990 Lab 7 - Hydrodynamics Theory Consider an ideal liquid, one which is incompressible and which has no internal friction, flowing through pipe of varying cross section as shown in figure

More information

1. Introduction, tensors, kinematics

1. Introduction, tensors, kinematics 1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and

More information

CONVECTIVE HEAT TRANSFER

CONVECTIVE HEAT TRANSFER CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 4 HEAT TRANSFER IN CHANNEL FLOW BASIC CONCEPTS BASIC CONCEPTS Laminar

More information

LIQUID/SOLID SEPARATIONS Filtration, Sedimentation, Centrifuges Ron Zevenhoven ÅA Thermal and Flow Engineering

LIQUID/SOLID SEPARATIONS Filtration, Sedimentation, Centrifuges Ron Zevenhoven ÅA Thermal and Flow Engineering 7 ÅA 44514 / 010 / 016 Fluid and Particulate systems 44514 /016 LIQUID/SOLID SEPARATIONS Filtration, Sedimentation, Centrifuges Ron Zevenhoven ÅA Thermal and Flow Engineering ron.zevenhoven@abo.fi 7.1

More information

2, where dp is the constant, R is the radius of

2, where dp is the constant, R is the radius of Dynamics of Viscous Flows (Lectures 8 to ) Q. Choose the correct answer (i) The average velocity of a one-dimensional incompressible fully developed viscous flow between two fixed parallel plates is m/s.

More information

Chapter -5(Section-1) Friction in Solids and Liquids

Chapter -5(Section-1) Friction in Solids and Liquids Chapter -5(Section-1) Friction in Solids and Liquids Que 1: Define friction. What are its causes? Ans : Friction:- When two bodies are in contact with each other and if one body is made to move then the

More information

A new differentially weighted operator splitting Monte Carlo method for aerosol dynamics

A new differentially weighted operator splitting Monte Carlo method for aerosol dynamics This paper is part of the Proceedings of the 24 International Conference th on Modelling, Monitoring and Management of Air Pollution (AIR 2016) www.witconferences.com A new differentially weighted operator

More information

CHAPTER 10. States of Matter

CHAPTER 10. States of Matter CHAPTER 10 States of Matter Kinetic Molecular Theory Kinetikos - Moving Based on the idea that particles of matter are always in motion The motion has consequences Explains the behavior of Gases, Liquids,

More information

CHAPTER 10. Kinetic Molecular Theory. Five Assumptions of the KMT. Atmospheric Pressure

CHAPTER 10. Kinetic Molecular Theory. Five Assumptions of the KMT. Atmospheric Pressure Kinetic Molecular Theory CHAPTER 10 States of Matter Kinetikos - Moving Based on the idea that particles of matter are always in motion The motion has consequences Explains the behavior of Gases, Liquids,

More information

Chapter 18 Thermal Properties of Matter

Chapter 18 Thermal Properties of Matter Chapter 18 Thermal Properties of Matter In this section we define the thermodynamic state variables and their relationship to each other, called the equation of state. The system of interest (most of the

More information

An Essential Requirement in CV Based Industrial Appliances.

An Essential Requirement in CV Based Industrial Appliances. Measurement of Flow P M V Subbarao Professor Mechanical Engineering Department An Essential Requirement in CV Based Industrial Appliances. Mathematics of Flow Rate The Scalar Product of two vectors, namely

More information

Fluid Mechanics Testbank By David Admiraal

Fluid Mechanics Testbank By David Admiraal Fluid Mechanics Testbank By David Admiraal This testbank was created for an introductory fluid mechanics class. The primary intentions of the testbank are to help students improve their performance on

More information

Fluid Mechanics II Viscosity and shear stresses

Fluid Mechanics II Viscosity and shear stresses Fluid Mechanics II Viscosity and shear stresses Shear stresses in a Newtonian fluid A fluid at rest can not resist shearing forces. Under the action of such forces it deforms continuously, however small

More information

4.2 Concepts of the Boundary Layer Theory

4.2 Concepts of the Boundary Layer Theory Advanced Heat by Amir Faghri, Yuwen Zhang, and John R. Howell 4.2 Concepts of the Boundary Layer Theory It is difficult to solve the complete viscous flow fluid around a body unless the geometry is very

More information