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THERMAL PHYSICAL FOUNDATION
OF HIGH TEMPERATURE
TECHNOLOGIES
Knyazeva A.G. (Anna Georgievna)
Institute of Physics of High Technologies
Lection 1
High temperature technology processes is characterized by the
transformation of various energy types into heat energy; here concentration
energy sources are have been used. Energy is used for material treatment
and production
1
EXAMPLES OF HIGH TEMPERATURE TECHNOLOGIES
- Laser and electron beam technologies (welding, cutting, thermal
treatment);
-arc welding and other ways of material conjugation (diffusion soldering,
termite and SHS-welding) ;
-plasmic technologies of coating deposition and surface treatment ;
-ion technologies ;
-oxygen cutting ;
-combined technologies of cutting, welding, building-up ;
-the processes of thin film obtaining and mono crystal growing ;
-many processes of chemical and diffusion treatment of material
surfaces .
-many technologies of new materials development in chemical industry;
-technologies of conversion and burning of natural fuel;
-metallurgical processes
etc.
Each called high temperature process (HTP), in turn, includes many
particular technologies depending on concrete technical solution,
conditions and materials which are used here
2
High temperature technologies modeling is the part of thermal physics.
This field of science has a long history and includes many applications:
The construction of heat engines, gasifies, heat exchangers
Combustion processes of solid, liquid and gaseous fuels
The problems of thermal protection for aircrafts.
The domestic space heating
The heat transfer to long distance
The natural processes in soils
The cooling of working parts and mechanisms
The problems of food keeping and freezing
…….
Besides the basic of thermal physical processes, we will introduce some
models of high technology processes
3
Features of high temperature technologies:
- Essential irreversibility of the processes connecting with inhomogeneous
temperature distribution and their change with time;
- High rates of the heating and cooling of various elements of the system;
- Complex heat exchange;
- Several various phases presence, the correlation between which changes;
-Various physical-chemical phenomena, accompanying the heating and cooling
or forming the basis for the technology.
-Last years HTP using high concentrated energy sources (technology electron
beam, laser irradiation, plasma flows, oxygen stream etc.) are overall used in
electronic industry and mechanical engineering to solve many problems.
Block structure of technology process. 1 –
technology camber; 2 – basic energetic
sources; 3 – additional (accessory)
energetic sources; 4 – material fluxes; 5 –
finally product; 6. – technology waste
products
4
ENERGY SOURCES I
Primary energy sources
Nonrenewable energy
sources
Уголь
нефть
природный газ
сланец
торф
ядерное горючее
Renewable energy
sources
Ветер
солнце
водные ресурсы рек
океаны
моря
древесина
Secondary energy sources
Отработанные горючие
органические вещества
Городские и
промышленные отходы
Горячий отработанный
теплоноситель
Отходы
сельскохозяйственного
производства
Inexhaustible energy sources
Термальные воды Земли
вещества и источники термоядерной
5
энергии
ENERGY SOURCES II
The way of heat
transfer
The mechanisms of energy
transformation
Conductive heating (thermal
conductivity)
Convective heating
Heating by radiation
Fictional heat
kinetic energy dissipation
Joule heating
The heating due to dielectric loss
Heat release from chemical reactions
etc.
6
ENERGY SOURCES III
Heat sources used in HTP can be
surface or volume;
continuous, impulse and impulse-periodic;
concentrated or distributed;
stationary and moving.
Surface sources: technology electron beam; laser irradiation of various wave
length acted on the metals; plasma flows generated by plasmatrones or other
ways; welding arc; optical radiation of wide spectral diapason (for example
focused emission of xenon lamps).
Such classification is conditional !
Depending on situation the same source can be related to different types. It
depends on space-time scales and accompanying processes
For example, when laser acts on some dielectrics, energy release and absorption
occur in a volume, but no in surface. When electron beam power grows, the
energy release maximum moves into a material volume.
7
Classification is conditional:
surface
0
It is typical for surface
source
xT
x max
l  xT
Specific heat scale
Coordinate of maximal heat
release
l
x max
xT
x
r0
L
Traditional volume heat sources are characterized by relatively large heating
time to working temperature (of second portions to minutes or even hour). The
transition to working regime in some high frequency plasmatrons can equal to
thou' of second. The capacity of volume sources achieves to hundreds of kilowatt
or even megawatt; energy concentration is small in comparison with concentrated
sources.
Space-time characteristics of heat sources (energy distribution in a volume or
along a surface; time parameters) play significant role in HTP. Gaussian sources
are the most accepted source types; their emission is distributed along the
surface in accordance with the low of normal distribution
2
  r 2 
 xx



max

q  q0 exp    exp  

8
  r0  
 

l





Energy sources in modern technologies :
Laser energy source. Laser technology (LT)
Electron beam. Technology electron beam (TEB)
high-current beam of particles
The sources of ions and plasma. Ion-plasmous technologies
Electric current. Resistive heating
Our purpose consists in
study thermal physical processes accompanying interrelation of
various energy sources with substances using theoretical
approaches
9
Mathematical modeling in the field of modern technologies includes
- Investigations and development of physical and mathematical models of
technology processes;
- Development of analytical and numerical methods for the solution of thermalphysical problems corresponding to different model of various technologies;
- Engineering relations obtaining to describe temperature and concentration field at
the conditions of material treatments;
- Investigation and development of the solution methods of inverse problems
(including, heat exchange) as the way of technology processes design;
- The study of conjugate and coupling problems to obtain more full information on
heat and mass transfer at the condition of material treatment; the optimization
conditions for technology processes and the methods for their realization;
- The obtaining the conditions for monitoring, controlling and regulation of
technology processes.
Numerical experiment is used as during preliminary analysis of technology
process (for identification of the model parameters; for adequacy checking and
investigation of technology process) as during the synthesis of technology
processes – for testing and comparison of project solutions.
The using necessity of NE as the investigation method connects with following
circumstance. The solution of modern science – technical problems characterizing
extremely complex mathematical description is difficult and sometimes practically
no
10
possible on the base of traditional analytical methods.
thermodynamics
Thermal physics
The model of
technology
process
hydrodynamics
mass exange
Chemical kinetics
engineering
calculation
methods
numerical
methods
11
Quantitative characteristics of heat transfer
The basic role in technology processes belongs to heat and mass transfer.
It is necessary to know the space-time characteristics and units of
measurement
Heat transfer intensity is characterized by the density of the heat flux, that is
by quantity of the heat propagating through unit surface square during time
unit. This value is measured in Watt/cm2 or J/(сm2s).
q
Heat quantity propagating through arbitrary surface F is called in heat
exchange as power of heat flux or simple heat flux - . J/sec or Watt serve as
unit for it measurement.
Q
The heat quantity passed during arbitrary time interval  through arbitrary
surface через is designed as Q . This value is measured in J
All values are connected with each other:
q  Q F  Q F
(1)
12
F
The relations between heat exchange and thermodynamics
The first thermodynamic law for closed system
The heat imposed to the system spends on its internal energy change and work
accomplishment
Q  dU  A
(2)
dU  0
if internal energy increases
A  0
if the work is accomplished by the system .
Measurements units in (2) – J.
For specific values (related to mass unity)
q   du  w
Here the measurement unit J/kg
In thermodynamics, ones understand under internal energy the energy of
chaotic motion of molecules and atoms, including the energy of translation,
rotation and oscillating motions (molecular and inter molecular), and potential
energy of interaction between molecules. Kinetic energy of molecules is single
valued function of the temperature; the potential energy value depends on the
middle distance between molecules, and hence, on occupied volume. As a result,
the internal energy is single valued function of the state.
13
Joule (J, in Russian: Дж, ) — is the unity for measurement of the work and
energy
It is equal to the work accomplished during the displacement of the point of
application of the force equal to 1 Newton in the distance 1 meter in the direction
of force action.
1 J = kg·m²/s² = N·м = Wt·с.
1 J ≈ 6,2415×1018 eV (electron volt).
1 000 000 J ≈ 0,277(7) kilowatt-hour.
1 kilowatt-hour = 3 600 000 J ≈ 859 845
calorie, cal.
1 kilowatt-sec = 1 000 J
1 J ≈ 0,238846 cal.
1 cal = 4,1868 J
1 thermal chemical cal = 4,1840 J.
Electron volt (eV) — non-systemic measurement unit for energy used in atomic
and quantum physics.
1 eV is equals to the energy needed for electron transfer in electrostatic field
between the points with potential difference equal to one volt (V). Because the
work during the charge q transfer equals to qU (where U — is potential difference),
and charge of electron equals to e=1,602 176 487(40)×10−19 coulomb (C), so
1 eV = 1,602 176 487(40)×10−19 J = 1,602 176 487(40)×10−12 erg
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The work in thermodynamics is determined by product of corresponding force
and path of its action. So, the work against the external pressure is the expansion
work
A  pdV ,
J
(3)
A  p dFdn or

F
pdFdn
is elementary work expended on the displacement of each elementary
area forming the square F, restricted the volume V
when dV  0
- The work is accomplished under body
To investigate the reversible processes,
similar diagrams are used in thermodynamics.
The system state corresponds to the points of
this diagram
а
The body expands
б
The body shrinks
The heat and the work are energetic characteristics
of thermal and mechanical interrelation of the
thermodynamical system with environment
15
The examples of other works
The expansion work:
A  pdV ;
The surface tension work
A  d
Elementary work for electric
field (for dielectric)
A  
1
EdD
4
 - Surface tension
D - electric displacement vector
The work of dielectric polarization
(without filed excitation in vacuum)
 E2 
  EdP
Ap  A  d  
 8 


P - polarization vector
Elementary work during change of magnetic field
intensity
magnetization work (without
vacuum magnetization )
Elementary work of deformation for
unit volume of solid body
A  
1
HdB
4
 H2 
  HdJ
A j  A  d  
 8 


3
A  
 ijdij
i, j
16
Отношение количества теплоты , полученного телом при бесконечно малом изменении
его состояния, к связанному с этим изменению температуры называется полной
теплоемкостью тела в данном процессе
C  Q dT
(4)
Обычно величину теплоемкости относят к единице количества вещества и в
зависимости от принятой единицы измерения различают
1.удельную массовую теплоемкость , отнесенную к 1 кг и измеряемую в Дж/(кг.К);
2.удельную объемную теплоемкость , отнесенную к количеству вещества,
содержащемуся в 1 м3 объема при нормальных физических условиях и измеряемую в
Дж/(м3.К);
3.удельную мольную теплоемкость , отнесенную к одному киломолю и c
измеряемую в Дж/(кмоль.К).
c  c  ; c  c 22,4 ; c  c
c
c
(5)
22,4 м3 – объем одного киломоля
Изменение температуры тела при одном и том же количестве сообщаемой
теплоты зависит от характера происходящего при этом процесса, поэтому
теплоемкость является функцией процесса. Это означает, что одно и то же тело
в зависимости от процесса (или в зависимости от условий) требует для своего
нагревания на 1 градус различного количества теплоты.
Теплоемкость и есть такое количество тепла, которое в данных
условиях требуется для изменения температуры тела на один градус
17
(degree, grade).
В термодинамических расчетах большое значение имеют
теплоемкость при постоянном давлении
c p  q dT  p
(6)
и теплоемкость при постоянном объеме
c  q dT v
для удельных величин
u  uT ,v  :
q  du  pd
(7)
du  u T  dT  u  T d
q  u T  dT  u  T  pd
  const
Для изохорного процесса
(9)
q   u T  dT
(10)
c  q dT   u dT 
В изобарном процессе
(11)
p  const
q
dT  p  u T   u  T  pd dT  p
c p  c  u  T  pd dT  p
энтальпия
H  U  pV
dh  du  pd  dp
(8)
или
h  u  p
(12)
(13)
(измеряется в джоулях или
джоулях на кг )
q  dh  dp
c p  q dT  p  h T  p
(15)
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Примеры:
вещество
алюминий
вольфрам
железо
медь
никель
платина
тантал
хром
цирконий
дюралюминий
алюминиевая бронза
асбест
бетон
гранит
дуб
кирпич магнезитовый
кирпич строительный
плексиглас
пробка
стекло оконное
уголь, антрацит
теплоемкость, c p ,
Дж/(кг.К)
896
134
452
383
446
133
138
440
272
833
410
816
837
2390
837
1880
800
1260
плотность,  ,
кг/м3
2702
19300
7870
8933
8900
21450
16600
7160
6570
2787
8666
383
500
2750
609-801
2000
1700
1180
150
2800
1370
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Уравнения первого закона термодинамики мы можем представить в иной форме
d du

dt dt
dT  du 
c
 
dt  dt  
q p


Разность c p  cV mT
m
dh
dp

dt
dt
(16)
dT  dh 
 
dt  dt  p
(17)
q
cp
pV
по определению равна работе внешнего давления по изменению объема
- масса сжимаемого вещества в объеме
V
Второй закон термодинамики устанавливает существование такой
термодинамической функции состояния как энтропия , так что для равновесных
q  Tds
процессов
Q  TdS

ds
d du
p 
dt
dt dt
Для необратимых процессов имеем
.
ds
d du
T
p 
dt
dt dt
T
T
(18)
ds dh
dp


dt dt
dt
(19)
ds dh
dp


dt dt
dt
(20)
T
Второй закон термодинамики может быть сформулирован различными способами. Для
необратимых процессов этот закон только устанавливает возможность и направление
их протекания
Третий закон термодинамики
20
Законы классической термодинамики не могут установить, почему
протекают необратимые процессы, почему все реальные процессы –
необратимы. Для необратимых процессов энтропия не определяется
только как функция состояния.
Для того чтобы определить скорость теплопереноса, мы должны
использовать новые физические принципы, а именно ввести законы
переноса, которые не являются составной частью классической
термодинамики. Это, например, законы теплообмена Фурье, Ньютона,
Стефана-Больцмана и др. Но очень важно помнить, что описание
теплопереноса требует, чтобы новые (дополнительные)
физические принципы не противоречили фундаментальным
термодинамическим законам
конец
21
Mechanisms of heat transfer:
thermal conductivity, convection, Irradiation
There are three basic mechanisms of heat transfer:
Thermal conductivity is the heat transfer due to energy transfer by micro particles
Molecules, atoms, electrons and other micro particles contained in substance move with rates
proportional to their temperature and transfer the energy from zone with high temperature to
zone with low temperature.
Heat transfer together with macroscopic volumes of substance is called convective heat
transfer of convection. It is possible to pass the heat to large distances, from example
from heat electropower station.
It is necessary often to calculate the convective heat transfer between liquid and solid
surface Such process has special name – convective heat exchange. ( The heat goes
from liquid to surface or inversely).
Irradiation is third way of heat transfer. Due to irradiation the heat could be propagate in all
ray-transparent media including in vacuum, outer space, where the irradiation is unique way
of heat exchange between bodies. The photons emitted and absorbed by bodies
participating in heat exchange are energy carrier in this case.
22
TEMPERATURE FIELD CHARACTERISTICS
In any case the heat transfer is accompanied by body temperature change in space and in
time. Analytical investigation of thermal conductivity process comes to the study of spacetime distribution of the temperature, that is to the equation finding
T  T x , y , z , t 
(2.1)
That is mathematical expression of temperature field.
One’s recognize the stationary and no stationary temperature fields.
Stationary temperature field
Two dimensional
temperature field
One dimensional
temperature field
T  f1 x , y , z 
T t  0
(2.2)
T  f 2 x , y , t  T z  0
(2.3)
T  f 3 x , t 
T z  0
T y  0
(2.3)
We choose in solid body the surface so that all their points had
the same temperature Ti in some time moment. That surface is
called as isothermal surface of temperature Ti
These isothermal surfaces can locate any way. But two such surfaces can
not intersect because none part has two temperature simultaneously
Fig.2.1. Isotherms
The intersection of isothermal surfaces by plane gives the
isotherm family.
Temperature in the body changes only in the directions crossing isothermal surfaces. The maximal
23
temperature drop per unit length happens in the direction of the normal to isothermal surface.
Temperature growth in the direction of the normal to the isothermal
surface is characterized by temperature gradient.
Temperature gradient is the vector directed along the normal to the
isothermal surface in the direction of temperature growth and equal
to temperature derivative in this direction
Fig.2.1. Ithorems
 T
T  gradT  n0
n
(2.5)
Projections of vector-gradient to coordinate axis's of Cartesian coordinate system
T x  T  cosn , x   T
n
x
T  y

T
T
 cosn , y  
n
y
T z

T
T
 cosn , z  
n
z
(2.6)
24
Thermal conductivity
The Fourier low is basic law of heat transfer by thermal conductivity. That hypothesis (17681830) is formulated by following way: elementary quantity of the heat dQ (Дж) passing
through element of isothermal surfaces dF during the time dt is proportional to temperature
gradient
T
dQ  
dFdt
(2.7)
n

thermal conductivity coefficient
Heat flux density:

 T
q    n0
n
(2.8)
Heat flux density directs to isothermal surfaces. Its positive
direction coincides with the direction of temperature
decrease, that is the heat is transferred always from hot
points to cold ones.
The lines, the tangents to which coincide with the direction
of the vector of heat flux density, are called as the lines of
heat flux. The lines of the heat flux are orthogonal to
isothermal surfaces (Fig. 2. 2). Scalar value of the heat flux
density is determined by
T
q  
(2.9)
n
The Fourier hypothesis was confirmed experimentally.
Fig.2.2. Isotherms and streamlines
25
Heat quantity through all isothermal surface during time unity :
Heat flux,
capacity
Q


qdF   
F
J/с
(2.10)
J
(2.11)
F

During time 
T
dF
n
Q  


T
dF dt
n
0F
Components of the vector of the heat flux density
q x   T
x
z
q y   T
y
q z   T
z
(2.12)


 
q  i q x  jq y  kq z
T2
T1
T2  T1
x
y
26
THERMAL CONDUCTIVITY COEFFICIENT
Thermal conductivity coefficient equals to the heat quantity which passes during time
unity through isothermal surface unity at the temperature gradient equal to unity


q
T
The concrete mechanism of the heat transfer by thermal conductivity depends on
physical properties of medium
Thermal conductivity of gases:
hydrogen   0,2; carbon dioxide
from 0.006 to 0.6 Vt/(m.К)
  0,025 Vt/(m.К).
  0,02; air
 of gases increases with the temperature, but does not practically with the pressure
The thermal conductivity coefficient of dropping liquids lies in the limits from 0,07 to 0, 7
Vt/(m.К); for the most liquids decreases with the temperature excluding the water and
glycerol and grows with the pressure
Free electrons are basic transmitter for the heat in metals and alloys and are similar to
ideal monoatomic gas. In metals,  decreases with the temperature. Unlike pure metals,
thermal conductivity coefficients of the alloys rise with temperature.
In solid bodies-dielectrics, thermal conductivity coefficient rises with the temperature growth.
As a rule, the materials with greater density have a more high value. This coefficient depends
on material structure..
27
   p   ph  magn
Dielectrics:
It prevail at high
temperature
Prevail at low
temperature
   p  e  b   ph  magn  ex
Semiconductors:
In pure semiconductors in the
region of middle temperatures
In pure specimens:
Metals:
b - bipolar thermal conductivity;
e   p
In alloy crystals
Additional thermal
conductivity due to
excitons diffusion
e  or   p
   p  e
take a place at high T due to
diffusion of pairs
теплопроводность, при высоких
T за счет диффузии пары
«electron-hole»
High thermal conductivity of metals is known from everyday life and connects with high their
electrical conduction. It is assumed in the Drude-Lorentz theory of electrical conduction that
there is some middle distance or middle length of free run l where free electrons are
accelerated by electric field; then they loss the energy owing to some collision with atoms
and molecules. The expression follows from this theory:
ne free electron number
nee2l

2meVT
VT middle rate of heat
motion
28
(more exact treatment gives the value in two time more than above)
If we assume that electrons run at temperature gradient presence the same distance prior to
they return the energy to atoms, we come to the expression for thermal conductivity equation:
ce Heat capacity for 1
electron
1
  neceVT l
3
Ce  nece
Electron heat capacity
From dedicated equations we find:
We have in classical theory where free
electrons are considered as gas :
for unit volume
 2 meVT2ce

 3 e2
2

k 
 3 B  T
  e 
ce  const , VT2 ~ T
In term of quantum statistics, when
electrons are considered as strongly
singular system, the middle rate does not
on temperature and ce ~ T
 2  k B 
   T
 3  e 
Hence bother theories lead to
lСледовательно, обе теории приводят к
Wiedemann-Franz-Lorentz low

 const
T
2
29
FLAT WALL
T1 > T2
dQ  F
Q
dT
dx
dx
Thermal resistance or
resistance of thermal
conductivity
  const
F
T1  T2 
L
q
T1  T2 
L /  
(2.13)
Problem. Let glass shop-window has square 12 m2 and thickness 1 cm.
Fig.2.3. Heat transfer
by thermal conductivity
through flat wall
Thermal conductivity of glass   0,8 Vt/(m.К). Temperature of external
surface of glass in cold day is 272 К (-1 С), and temperature of internal
surface is 296 К (+3 С). It is necessary to find the heat flux through glass and
bundle midplane temperature between external and internal surfaces.
Q
Solution. Heat flux through glass is
Q
Similar to (2.13) for arbitrary x
temperature profile exists in glass
 F
Q 0
L
Vt
F
T1  T 
x
Bundle midplane temperature equals to 274 К, so linear
The problem
   0 1  T  :
can be solved
and fro more
complex
situation
F
T1  T2   0 ,8  12  4  3840
L
0 ,01

T  T1 
Qx
qx
 T1 
F


 2

2  Q   m F T  T 


T

T

T

T
1
2
2
1
2 
 1
L
2


m :
T1  T2  2
(2.13,а)
(2.14)
30
This and other problems can be solved enough rigorous with the
help of modern methods of mathematical physics
31
Теплоемкость смеси – термодинамика;
Теплоемкость в окрестности ФП
Зависит ли она от структуры - ??
Плотность – как определяют??
Теплопроводность пористых материалов и их
структура
32