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Non-Continuum Energy Transfer: Overview Non-Continuum Energy Transfer: Overview

Non-Continuum Energy Transfer: Overview - PowerPoint Presentation

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Uploaded On 2017-04-11

Non-Continuum Energy Transfer: Overview - PPT Presentation

Topics Covered To Date Conduction transport of thermal energy through a medium solidliquidgas due to the random motion of the energy carriers Fourier s law circuit analogy 1D lumped capacitance unsteady separation of variables 2D steady 1D unsteady ID: 536520

thermal energy scale continuum energy thermal continuum scale length conductivity heat carriers transport carrier kinetic description particles direction law particle due gas

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Presentation Transcript

Slide1

Non-Continuum Energy Transfer: OverviewSlide2

Topics Covered To Date

Conduction -

transport of thermal energy through a medium (solid/liquid/gas) due to the

random motion of the energy carriers

Fourier

s law, circuit analogy (1-D), lumped capacitance (unsteady), separation of variables (2-D steady, 1-D unsteady)

Convection

transport of thermal energy at the interface of a fluid and a solid due to the

random interactions at the surface

(conduction) and

bulk motion of the fluid

(advection)

Netwon

s law, heat transfer coefficient, energy balance, similarity solutions, integral methods, direct integration

Radiation

– transport of thermal energy to/from a solid due to the emission/absorption of

electromagnetic waves

(photons)

We studied these topics by considering the phenomena at the

continuum-scale

macroscopic

Slide3

Continuum Scale

The

continuum-scale

is a length/time scale where the medium of interest is treated as

continuous

individual or discrete effects are not considered

Properties can be defined as continuous and

averaged

over all the energy carriers

thermal conductivity

viscosity

density

When the

characteristic dimension of the system

is comparable to the

mechanistic length

of the energy carrier, the energy carriers behave

discretely

and

cannot be treated continuously

non-continuum

the mechanistic length is the

mean length of transport

or

mean free path of the energy carrier between collisions

even at large length scale this is possible (gas dynamics in a vacuum!)Slide4

Continuum Scale

At the continuum-scale,

local thermodynamic equilibrium

is assumed

temperature is

only defined at local thermodynamic equilibrium

Ultrafast processes may induce

non-equilibrium

during the timescale of interest (

e.g.

, laser processing)

At the non-continuum scale (both time and length) we treat energy carriers

statisticallySlide5

Four Energy Carriers

Phonons – bond vibrations between adjacent atoms/molecules in a solid

not a true

particle

can often be treated as a particle

can be likened to mass-spring-mass

primary energy carrier in insulating and semi-conducting solids

Electrons – fundamental particle in matter

carries charge (electricity)

and

thermal energy

primary energy carrier in metals

Photons

electromagnetic waves or

light particles

radiation

no charge/no mass

Atoms/Molecules

freely (random) moving energy carriers in a gas/liquidSlide6

Appreciating Length Scales

Consider length in meters:

10

-9

nano

10

-6

micro

10

-3

milli

10

0

10

3

kilo

10

6

mega”

109“giga”

simple molecule

(caffeine)

You Are HereSlide7

The Scale of ThingsSlide8

The Importance of Non-Continuum

Technology Perspective

scaling down of devices is possible due to advances in technology

take advantage of non-continuum physics

potential for high impact in essential fields (healthcare, information, energy)

in order to

control the transport

at these small scales we must understand the

nature of the transport

Scientific/Academic Perspective

study non-continuum phenomena helps us understand the physical nature of the principles we

ve come to accept

we can define, from first principles,

entropy

,

specific heat, thermal conductivity, ideal gas law, viscosityby understanding non-continuum physics we can better appreciate our worldSlide9

mems.sandia.govSlide10

mems.sandia.govSlide11

Kinetic Description of Thermal Conductivity

Conduction is how

thermal energy is

transported through a medium

solids: phonons/electrons; fluids: atoms/molecules

We will use the

kinetic theory approach

to arrive at a relationship for thermal conductivity

valid for any energy carrier that

behaves and be described like

a

particle

T

hot

T

coldSlide12

Kinetic Description of Thermal Conductivity

Consider a box of particles

G. Chen

Consider the small distance:

If each “particle” carries with it thermal energy, the total heat flux across the face is the difference between particles moving

in the

forward direction and those moving in the reverse direction.

The ½ assumes only half of the particles in the distance

v

x

τ

move in the positive directionSlide13

Kinetic Description of Thermal Conductivity

We can Taylor expand this relationship just as we did in the derivation of the heat equation:

If

the speed in the

x

-direction is 1/3 of the total speed & we use the chain rule

Specific heat defined as how much the temperature increases for a given amount of heat transfer Slide14

Kinetic Description of Thermal Conductivity

c

ompare to

Fourier’s

Law

To determine thermal conductivity we need to understand how heat is stored and how energy carries collide