becs-114 6400 lecture 1 notes

9/19/2014 Special Course on Molecular Eng. 1

Lecture 1: Part I – Course description; Part II– Heat transfer in Macroscopic/Bulk systems

Lecturer: Dr. Toufik Sadi

© Aalto University, 2014

Special Course on Molecular Engineering

Lecture 1

Heat Transfer in Macroscopic and

Bulk Systems

By

Dr. Toufik SadiContact: toufik.sadi (at) aalto.fi



BECS-114.6400 Special Course on Molecular EngineeringFall 2014 – Heat transfer in solid and molecular nanostructures

Level – Graduate course P (5cr)

Lecturer

Dr. Toufik SadiEmail: toufik.sadi (at) aalto.fi Mobile: +358 50 512 4353

Visiting address: Room F302, F Building, Rakentajanaukio 2 C

Other contributors

Dr. Jani Oksanen Dr. Teppo HäyrynenEmail: Jani.Oksanen (at) aalto.fi Email: Teppo.Hayrynen (at) aalto.fi

Prof. Jukka Tulkki Mr. Mikko PartanenEmail: Jukka.Tulkki (at) aalto.fi Email: Mikko.Partanen (at) aalto.fi

Lecture 1: Part I – Course description



Focus – heat transfer theory, models and applications in solid and

molecular nanostructures


Basic knowledge – quantum mechanics/solid-state physics/

statistical physics/mathematical modeling/scientific programming

Teaching –� Lectures – theory of the topic (2hrs/wk)

Periods: 19.09.–17.10.2014 & 31.10.–05.12.2014

Time: Fridays at 12:15-14:00 Place: Room 3F254 (Eng. Physics)

� Exercises – modeling phenomena using MATLAB (2hrs/wk)

Periods: 26.09.–17.10.2014 & 31.10.–05.12.2014

Time: Fridays at 11:15-12:00 Place: Room 3F254 (Eng. Physics)




BECS-114.6400 Special Course on Molecular EngineeringFall 2014 – Heat transfer in solid and molecular nanostructures

Course description

Objectives1) Presenting a theoretical review of selected heat transfer

phenomena in nanoscale/molecular solid structures

2) Discussing relevant computational models and tools

3) Pointing out potential engineering applications

Audience� Master and graduate students:� passionate about the field of nanoscale/molecular science & technology

� with basic knowledge in at least one of the following areas:

� quantum mechanics, solid-state physics, mathematical modeling and

scientific programming






Scope� Room temperature phenomena

� Landauer-Büttiker formalism used where needed

Recomended course books1) G. Chen, Nanoscale energy transport and

conversion, Oxford University Press, 2005. (Theory)

2) S. Volz, Microscale and Nanoscale Heat Transfer.

Springer, 2007. (computational and experimental techniques)




Course description

Hot Plate: 10 W/cm3

Nuclear Reactor: 100 W/cm3

Sun Surface: 7000 W/cm3





Heat transfer in nanostructures : increased importance

Miniaturization consequences� Hot-spots: localized areas of high power

density

� Reduced thermal conductivity in

confined structures, such as

superlattices, nanowires and

nanoparticles

� Influence of thermal resistance at

interfaces, considering the

high surface/volume ratio

� Transfer dominated by new kind of

quasi-particles (phonon polaritons)

Source: Pop et al., Proceedings of the

IEEE, vol. 94, 1587, 2006

Scientific: Formulating a consistent theory of heat transfer

at the nanometer and mesoscopic scale

Technological: Nanostructures

High power densitiesLow thermal conductivity &

high electrical conductivityThermal interface resistance

� Thermal interface materials (using e.g. CNTs)

� Energy recycling exploiting thermoelectric effects (using e.g. nanowires)

� Radical change in nanostructure composition and design

� Significant improvements in cooling systems





Heat transfer in nanostructures : opportunities

Heat transfer in macroscopic systems/bulk crystals

� Classical definition of temperature and heat

� Macroscopic heat transfer

� Laws of thermodynamics

� Conduction / Convection / Radiation

� Energy Balance

� Local equilibrium

� ‘Thermodynamics’ vs. ‘Statistical Mechanics’

� Limits of the macroscopic approach at short scales





Course contents – theory (1)


Heat transfer in micro-/nano-crystals� Heat carriers / dynamics / statistics / size effects

� Electronic mechanisms� Free electrons / Electron transport in solids / Ballistic and

diffusive transport regimes / Semi-classical & quantum electron

transport models

� Phononic mechanisms� Vibrational modes in a lattice / Phonon transport / Heat flux and

thermal conductivity / Semi-classical & quantum phonon

transport models

� Molecular/atomistic mechanisms





Radiative heat transfer in nano-crystals� Radiative transfer equation

� Electromagnetic approach to thermal emission

� Thermal emission mechanisms

� Fluctuation-dissipation theorem

� Radiative transfer on short length scales

� Review of electromagnetism concepts and equations

� Calculation of thermal emission from a nanoparticle

� Thermal near-field emission from surfaces

� Near-field radiative transfer between two planes

� Coupling of radiative and phononic mechanisms: quasiparticles






Semi-classical Boltzmann approach� The Monte Carlo model / potential applications

� Electron transport in nano-transistors, thin layers and nanowires

� Thermal conductivity calculations in confined nanostructures

Atomistic approach� The molecular dynamics model / potential application

� Vibrational properties / thermal conductivity / thermal interface resistance

Quantum approach� Quantum fields & Green's functions / Landauer-Büttiker formalism





Course contents – methods

Fluctuational electrodynamics� Fluctuation-dissipation theorem / Dyadic Green's functions

Thermal transport� Energy recycling using thermoelectricity

� Thermal devices

� Super-insulating nanoporous materials

Optoelectronic / photonic / photovoltaic applications�Light-emitting diodes

�Plasmonic nanostructures

�Solar cells





Course contents – applications / experimental techniques

Experimental techniques for heat transfer� Scanning thermal microscopy / optical & hybrid techniques


Zeroth law of thermodynamics If two systems are in thermal equilibrium with a third system, they

must be in thermal equilibrium with each other

� This law contributes to the definition of the notion of temperature.

First law of thermodynamics Considering heat and work as forms of energy transfer, change in

the internal energy of an isolated (closed) system is given by the

amount of heat supplied to the system minus the amount of work

done by the system

� Energy conservation law the energy of an isolated system is

constant.

Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems



Laws of thermodynamics (1)


Second law of thermodynamics The entropy of any isolated system not in equilibrium

almost always increases�Isolated systems spontaneously evolve towards thermal

equilibrium

�Entropy is the property towards equilibrium

Third law of thermodynamics The entropy of a system approaches a constant value

as the temperature approaches zero (typically zero)




Laws of thermodynamics (2)

Heat Transfer

In classical thermodynamics, heat transfer is defined

as the energy flow across the boundaries of a system

experiencing a temperature difference





Classical definition of temperature and heat (1)

This definition implies three important points: 1) Heat transfer is a form of energy flow

2) Heat transfer is associated with a temperature difference

3) Heat transfer is a boundary phenomenon


Temperature

In classical thermodynamics, it is defined on the basis

of the concept of thermal equilibrium � if systems A

and B are in thermal equilibrium with each other, then

both systems have the same temperature





This definition implies an important concept:� Temperature describes thermal equilibrium


The definitions of temperature and heat transfer are

independent of the material, contributing to establishing the

universality of classical thermodynamics.

However, these definitions do not consider the physical

microscopic description underlying heat transfer processes

and the meaning of temperature.

This course aims to go beyond the classical understanding of

heat transfer, and address the link between thermal

transport/processes and temperature at the nanoscale level.





Heat conductionIs the energy transfer through a medium/material, caused by

a temperature difference due to the random motion of heat

carriers in the material

� Heat is the part of the energy that is carried out around through

random motion of heat carriers, such as electrons, phonons or

molecules


Heat conduction is usually studied using Fourier’s law relating

local heat flux density to the local temperature gradient.




Macroscopic heat transfer: conduction (1)


Fourier’s law for

conduction

T∇−= κq

� Heat flux density (q) is the amount of energy

flowing through a unit area per unit time

� κ is the thermal conductivity, a temperature

dependent material propertySource: G. Chen, Nanoscale energy transport

and conversion, Oxford University Press, 2005

)( ∧

∂∂+

∧∂∂+

∧∂∂−=

∧+

∧+

∧

zyxzyx

zT

yT

xT

zqyqxq κ

Or, in Cartesian coordinates:






Example Assuming a semi-infinite silicon die, with a

300K heat-sink placed at the bottom

surface, calculate the temperature at the

following positions: 100nm, 1μm, 10μm

from the heat-sink (points a, b, c in the

corresponding figure)? Use the following

information:

� The thermal conductivity of Si is 150 S.I.

at 300K.

� The heat flux is assumed to be constant

at 1.5x109 S.I. along the x-direction, and

zero along the y- and z-directions.

300K heat-sink

Si

a

b

c

100nm

1μm

10μm

A semi-infinite silicon die wirh a

300K heat-sink at the surface





ConvectionIt occurs when a bulk fluid motion is coupled with a

temperature gradient

Example: heat transfer between a solid surface and a fluid

The convection heat rate transfer rate Q (in Watts) between the

solid surface (at temperature Ts) and the fluid (at temperature Tf) is

given by Newton’s law of cooling.


�When fluid molecules move from one place to another,

they carry internal energy




Macroscopic heat transfer: convection (1)


)( fs

TTAhQ −=� ‘h’ is the heat transfer coefficient and ‘A’ is the surface area

� ‘h’ is not a material property. It is a flow property that depends on the flow

field, fluid properties and the geometry.

� This coefficient also plays a role when heat transfer occurs between a solid

surface and a liquid undergoing a phase change (e.g. condensation)

� Reliable models are needed to estimate this coefficient.

Newton’s law of cooling

Natural convection: the fluid is set into motion by the buoyancy force due to

the difference in the densities of hot and cold fluids

Forced convection: the motion is created externally e.g. by a fan




Macroscopic heat transfer: convection (2)

RadiationHeat transfer in this mode does not require a medium and can

propagate in vacuum. The energy is carried by electromagnec waves.

)}1(/{ /251,

−= TCb

eCE λλ λ

� Real-life objects radiate less than a black-body. The surface is

characterized by the emissitivity:

λλλε,

/b

EE=9/19/2014 Special Course on Molecular Eng. 23




Macroscopic heat transfer: radiation (1)

� A blackbody is an ideal object emitting maximum amount of

radiation, in equilibrium. It radiates according to Planck’s law:


Since the propagation of thermal radiation is a form of electromagnetic

wave, it can be described by Maxwell’s equations.

However, calculating radiative heat transfer may be considerably

simplified, by treating thermal radiation as incoherent photon particles,

or bundles of rays propagating in straight lines. These rays can be

scattered, absorbed, or enhanced by emission. When reaching a surface,

these rays may be reflected, absorbed or transmitted.

Using this philosophy, the radiation heat transfer per unit area (q)

between two surfaces may be calculated as follows:

214

24

1 where,)( TTTTq >−=σ




Macroscopic heat transfer: radiation (2)

Constitutive and conservation equations � The (constitutive) equations reviewed previously (Fourier’s

Law, Newton’s Law, etc…) for different transfer modes

relate the heat flux (q) to temperature (T)

→ Another (conservation) equation is needed to solve

for the heat flux and temperature

→ This is derived from the first law of thermodynamics,

which is the most important conservation principal

for heat transfer





Macroscopic heat transfer: energy balance (1)


The first law of thermodynamics gives:

dtdUWQ /=−

� ‘Q’ is the rate of heat transfer into the system

� ‘W’ is the power output

� ‘U’ is the system (internal, kinetic and potential) energy

NOTE: Constitutive equations relate to specific materials and

processes but may not valid in all cases. Conservation

equations are universal






Let us consider an arbitrary system

with given boundaries, as illustrated

in the figure shown in this slide,

where conduction is the only

mechanism present. Fourier’s law

and the conservation equation give

the familiar heat diffusion equation:

� ρ and C are the density and the specific

heat of the material, respectively

dtdTCT / )( ρκ =∇∇





Q WClosed

system

Heat conduction through a

closed system

In thermodynamics, we define equilibrium as a state

of an isolated system in which no macroscopic change

is observed with time

� Temperature and pressure are quantities defined only

under equilibrium conditions

�Heat transport phenomenon occurs when the system is

driven out of equilibrium

�A system at thermal steady-state is not necessarily at an

equilibrium state





Macroscopic heat transfer: local equilibrium (1)


�At steady-state, a system may be out of equilibrium

globally, but the deviation from equilibrium at each point is

usually small. A small area around these points may be

assumed as being in equilibrium

→This allows the definition of the local temperature,

pressure, chemical potential, etc…

� An important discussion point

How small a region should be to assume local

equilibrium?




Macroscopic heat transfer: local equilibrium (2)





Thermodynamics vs. Statistical Mechanics (1)

Classical thermodynamics investigates the

relation between heat/temperature and work.

In thermodynamics, temperature is a

macroscopic variable, independent of the bulk

amount of elements contained inside (atoms,

electrons, etc…).






In real-life, systems are typically not in

thermodynamic equilibrium. A practical approach in

classical thermodynamics involves dividing an object

conceptually into “cell-like elements” of smaller sizes

(both in space and time). If thermodynamic

equilibrium conditions are reasonably satisfied in each

“cell”, then a temperature exists for it, and local

equilibrium is said to prevail throughout the body.






Statistical mechanics provides a microscopic explanation of

temperature, based on macroscopic systems' being composed

of many particles. It explains macroscopic phenomena in

terms of dynamics of molecules, ions, etc… Thermodynamics

formulation uses degrees of freedom instead of particles.

On the molecular level, temperature is a result of the motion

of particles constituting the material. Temperature increases

as this motion, and hence the resulting kinetic energy,

increase. The energy may result from atomic vibrations

(phonons), the excitation of electrons, etc...






In statistical mechanics, the entropy of a system (S) is

given by:

� kb is the Boltzmann constant, and Γ is the number of states

The temperature (T) is defined to be:

� E is the total kinetic energy of the system

)log( Γ=b

kS

SET

∂∂=


In microscopic terms, the main limitation of the macroscopic

approach to heat conduction corresponds to the length and

time scales comparable to the phonon “mean free path” and

the “phonon relaxation time”, respectively.

For radiative problems, relevant length scales include the

“wavelength”, “skin depth”, and “coherence lengths”.

Similar consideration must be accounted for in the case of

convection: the “mean free path”, “collision time” and “time-

of-flight” of the molecules.




Limits of the macroscopic approach at short scales (1)


� In solids, the characteristic length scales at which

classical theories discussed in this lecture fail are

typically on the order of submicrons.

� However, the exact sizes depend on the material

properties, the type of heat carriers and ambient

temperature.� E.g. in silicon field-effect transistors (FETs), the characteristic

length is around 100-200nm at room temperature. This

significantly increases at other lower (typical) operating

ambient temperatures (4K, 77K,etc..)




Limits of the macroscopic approach at short scales (2)

becs-114 6400 lecture 1 notes

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