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
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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