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
© Aalto University, 2014
9/19/2014 Special Course on Molecular Eng. 2
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
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Focus – heat transfer theory, models and applications in solid and
molecular nanostructures
9/19/2014 Special Course on Molecular Eng. 3
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)
Lecture 1: Part I – Course description
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
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
9/19/2014 Special Course on Molecular Eng. 4
Lecture 1: Part I – Course description
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
9/19/2014 Special Course on Molecular Eng. 5
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)
Lecture 1: Part I – Course description
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Course description
Hot Plate: 10 W/cm3
Nuclear Reactor: 100 W/cm3
Sun Surface: 7000 W/cm3
9/19/2014 Special Course on Molecular Eng. 6
Lecture 1: Part I – Course description
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
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
9/19/2014 Special Course on Molecular Eng. 7
Lecture 1: Part I – Course description
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
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
9/19/2014 Special Course on Molecular Eng. 8
Lecture 1: Part I – Course description
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Course contents – theory (1)
9/19/2014 Special Course on Molecular Eng. 9
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
Lecture 1: Part I – Course description
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Course contents – theory (2)
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
9/19/2014 Special Course on Molecular Eng. 10
Lecture 1: Part I – Course description
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Course contents – theory (3)
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
9/19/2014 Special Course on Molecular Eng. 11
Lecture 1: Part I – Course description
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
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
9/19/2014 Special Course on Molecular Eng. 12
Lecture 1: Part I – Course description
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Course contents – applications / experimental techniques
Experimental techniques for heat transfer� Scanning thermal microscopy / optical & hybrid techniques
9/19/2014 Special Course on Molecular Eng. 13
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
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Laws of thermodynamics (1)
9/19/2014 Special Course on Molecular Eng. 14
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)
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
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
9/19/2014 Special Course on Molecular Eng. 15
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
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
9/19/2014 Special Course on Molecular Eng. 16
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
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Classical definition of temperature and heat (2)
This definition implies an important concept:� Temperature describes thermal equilibrium
9/19/2014 Special Course on Molecular Eng. 17
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.
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Classical definition of temperature and heat (3)
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
9/19/2014 Special Course on Molecular Eng. 18
Heat conduction is usually studied using Fourier’s law relating
local heat flux density to the local temperature gradient.
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Macroscopic heat transfer: conduction (1)
9/19/2014 Special Course on Molecular Eng. 19
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:
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Macroscopic heat transfer: conduction (2)
9/19/2014 Special Course on Molecular Eng. 20
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
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Macroscopic heat transfer: conduction (3)
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.
9/19/2014 Special Course on Molecular Eng. 21
�When fluid molecules move from one place to another,
they carry internal energy
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Macroscopic heat transfer: convection (1)
9/19/2014 Special Course on Molecular Eng. 22
)( 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
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
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
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
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:
9/19/2014 Special Course on Molecular Eng. 24
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
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
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
9/19/2014 Special Course on Molecular Eng. 25
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Macroscopic heat transfer: energy balance (1)
9/19/2014 Special Course on Molecular Eng. 26
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
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Macroscopic heat transfer: energy balance (2)
9/19/2014 Special Course on Molecular Eng. 27
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 =∇∇
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Macroscopic heat transfer: energy balance (3)
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
9/19/2014 Special Course on Molecular Eng. 28
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Macroscopic heat transfer: local equilibrium (1)
9/19/2014 Special Course on Molecular Eng. 29
�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?
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Macroscopic heat transfer: local equilibrium (2)
9/19/2014 Special Course on Molecular Eng. 30
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
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…).
9/19/2014 Special Course on Molecular Eng. 31
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Thermodynamics vs. Statistical Mechanics (2)
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.
9/19/2014 Special Course on Molecular Eng. 32
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Thermodynamics vs. Statistical Mechanics (3)
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...
9/19/2014 Special Course on Molecular Eng. 33
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Thermodynamics vs. Statistical Mechanics (4)
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
∂∂=
9/19/2014 Special Course on Molecular Eng. 34
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.
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Limits of the macroscopic approach at short scales (1)
9/19/2014 Special Course on Molecular Eng. 35
� 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..)
Lecture 1: Part II– Heat transfer in Macroscopic/Bulk systems
Lecturer: Dr. Toufik Sadi
© Aalto University, 2014
Limits of the macroscopic approach at short scales (2)