heat transfer
DESCRIPTION
Heat Transfer. G.Vandoni CERN, AT Division. A detour in basic thermodynamics. W refrigeration work Q heat to extract at T and reject at T a. A refrigerator extracts heat at a temperature T below ambient and rejects it at a Tambient. Second law of thermodynamics :. - PowerPoint PPT PresentationTRANSCRIPT
G.Vandoni, Heat Transfer Academic Training 2005 1
Heat TransferHeat Transfer
G.Vandoni
CERN, AT Division
G.Vandoni, Heat Transfer Academic Training 2005 2
A detour in basic thermodynamicsA detour in basic thermodynamicsA refrigerator extracts heat at a temperature T below ambient and rejects it at a Tambient.
Second law of thermodynamics :
Minimize thermal loads:
W refrigeration work
Q heat to extract at T
and reject at Ta
T
TTQW a )(
Maximize heat extraction:
boundary temperatures fixed, heat transfer rate minimization seeked
heat transfer rate fixed, minimize temperature difference
G.Vandoni, Heat Transfer Academic Training 2005 3
The 3 modes of heat transferThe 3 modes of heat transfer
TgradATkQ )(
Conduction: heat transported in solids or fluids at rest
FOURIER’s law:
)( fw TThAQ
Convection: heat transport produced by flow of fluid
Convection exchange:
)( 44ch TTAQ
Radiation: heat carried by electromagnetic radiation
Stefan-Boltzmann’s law:
G.Vandoni, Heat Transfer Academic Training 2005 4
Electrical analogyElectrical analogy
Valid in the three cases for a small T (linearization of Stefan-Boltzmann’s law)
series/parallel impedances Basis for modelling and numerization above 1D
)( 121 VV
l
SI
S
lRelec
V1 V2I moto
rflow
)( 12 TTl
SkQ
S
l
kRth
1
T1 T2Q
thermal impedance
G.Vandoni, Heat Transfer Academic Training 2005 5
Cryogenic heat transfer Cryogenic heat transfer modesmodes
T3
k~T0.7
increase of Gr for decreasing T, h~T-
1/2
PeakNucleateBoilingFlux
increase of Re for decreasing T
G.Vandoni, Heat Transfer Academic Training 2005 6
Time-independent Time-independent conductionconduction
dx
dTATkQ )( h
c
T
TdTTk
L
AQ )(
1D, constant A
Th
Tc
L
A
property smaterial')( h
c
T
TdTTk
12
1 )(
x
x xA
dxG
0
50
100
150
200
250
300
0 0.2 0.4 0.6 0.8 1
Heat flux reduction by intermediate temperature thermalization:
Temperature profile T(x) of st.steel bar with thermalization 2/3 of length at 80K
Tt
G.Vandoni, Heat Transfer Academic Training 2005 7
Intermediate heat Intermediate heat interceptioninterception
Th
Tc
L
A
TtT
x
pure Copper
300 K
T
x4 K
Stainless steel
77 K
Purely conductive T(x) profile over the whole length
Thermalization (=fixing the temperature) at Tt
Larger Q evacuated at Tt, but smaller at Tc => optimization possible with exergy function
G.Vandoni, Heat Transfer Academic Training 2005 8
Thermal conductivity Thermal conductivity integralsintegrals
Reduction of heat flow to the cold boundary temperature by thermal interception at intermediate temperature
Tc=4 K
G.Vandoni, Heat Transfer Academic Training 2005 9
Time-dependent conduction Time-dependent conduction
difference between heat entering and leaving dv
internal heat source density
rate of temperature increase
(thermal inertia)
Diffusivity D=k/C characterizes the propagation of a thermal transient…
…through a characteristic time depending on the object’s dimension roD
ro2
~
t
TCQ
x
Tk
x h
Energy conservation
dv
G.Vandoni, Heat Transfer Academic Training 2005 10
Diffusivity and time regimesDiffusivity and time regimes
ro
x
xearly
regime
T
D
rt o
2
late regimex
D
rt o
2
0 2 4 6 8 10
)exp()()( tTTTtT o
Late regime: exponential decay
= hS/(C V) time constant of the system
t
D
ro2
G.Vandoni, Heat Transfer Academic Training 2005 11
Internal versus external Internal versus external resistanceresistance
Under some circumstances, the decay is exponential starting from t=0
Biot number:
1k
hrBi o
ro
x
o
volvol
r
Tk
A
Q
ssurf ThA
Q
internal thermal
resistance
surface thermal
resistance
T
x
Lumped capacitance model applies starting t=0
Exponential TtT )(
G.Vandoni, Heat Transfer Academic Training 2005 12
Conductivity of solidsConductivity of solids
-> form for pure and alloyed metals
-> st.steel
-> increase with T
G.Vandoni, Heat Transfer Academic Training 2005 13
Conductivity of solidsConductivity of solids
Heat carriers: phonons (k~T3) and electrons (k~T)
T behaviour well known
Hinder heat transmission at low T ? DEFECTSdifference between pure and alloyed
effect of modification of the defect content: magnetic impurities, annealing, cold work
Good electrical conductors = good thermal conductors (but not the best ones !)
Hinder heat transmission at high T ? Phonon-phonon
Phonon-electronno difference between pure and alloyed metals
G.Vandoni, Heat Transfer Academic Training 2005 14
Metal’s conductivityMetal’s conductivity
TLTkT Lorentz)()( Wiedemann-Franz:
free-electron metal
useful at low
T but wrong
over whole T
range
),()( TRRRkTk RRR parametrization (next slide)
For Cu, Fe, Al, W
Superconductor’s Superconductor’s conductivityconductivity
Electronic above Tc, phononic below Tc:
Pb: knormal/ksupra=45/T2 In : knormal/ksupra=1/T2
=> Thermally switch between conducting and isolating by applying a magnetic field>critical field…
G.Vandoni, Heat Transfer Academic Training 2005 15
RRR parametrization of k(T)RRR parametrization of k(T)
Thermal Conductivity of copper
100
1000
10000
1 10 100 1000T [K]
k [W
/m K
]
RRR=80
RRR=120
RRR=180
RRR=230
i
ii
T
PPP
P
i
r
ioi
WW
WWPW
eTPP
TPW
TW
RRR
K
KRRR
WWWKmWK
P
0
00
5)42(
2
0
10
*7
311
1
634.00003.0
)4(
)273(
)()./(
6
Valid over a broad range of RRR, ~10% exactness
0.634 / RRRr / 0.0003P1 1.7541E-08P2 2.763P3 1.1020E+03P4 -0.165P5 70P6 1.756
P7 0.838 / r0.1661
A similar parametrization also available for (RRR,T)
G.Vandoni, Heat Transfer Academic Training 2005 16
Diffusivity of common Diffusivity of common materialsmaterials
Cv(T) decreases faster than k(T): small equilibration times at low T
Diffusivity larger for conductors than insulators
D=k/Cv
G.Vandoni, Heat Transfer Academic Training 2005 17
Specific heat of structural Specific heat of structural materialsmaterials
Nb: Tc/D=0.04
D Debye temperature, a material’s property
Cv heat capacity per kg mole approximately described by
the
Debye function
T
x
x
Dv dx
e
exTRC
/
0 2
43
)1(9
G.Vandoni, Heat Transfer Academic Training 2005 18
Conductivity of gases: 2 Conductivity of gases: 2 regimesregimes
L
molecular:
P [Pa] 10-2 100
Ar 0.63 cm 6.3 10-5
N21.8 1.8 10-4
He 0.60 6.0 10-5
M
T
p
115
mean free path
vs
wall distance L
[Pa.s],[Pa],[cm]
viscous:
vCM
RTk
2
1
8
3
1
k~T0.7
q proportional to p
q independent from L
q independent from p
q=kST/L
k predicted by kinetic theory of gases
G.Vandoni, Heat Transfer Academic Training 2005 19
Viscous regimeViscous regime
T [K] 4He H2 N2
300 1.56 10-3 1.92 10-3 2.60 10-4
80 0.64 10-3 0.6 10-3 0.76 10-4
20 0.26 10-3 0.16 10-3
5 0.10 10-3
Thermal conductivity k [Wcm-1 K-1] @ 1 atm
G.Vandoni, Heat Transfer Academic Training 2005 20
Molecular regime: Kennard’s Molecular regime: Kennard’s lawlaw
12
2/1
1 81
1TT
MT
pRAQ
Cp/Cv
R ideal gas constant
accomodation coefficient
degree of thermal equilibrium between molecules and wall, ~0.7-1 for heavy gases.
2
1212
21
)1(A
A
for simple geometries, (parallel plates, coaxial
cylinders, spheres)1.E-03
1.E-02
1.E-01
1.E+00
1.E-06 1.E-05 1.E-04p [mmHg]
Q [
mW
/cm
2]
H2
N2
He
300K->77K
G.Vandoni, Heat Transfer Academic Training 2005 21
Contact resistanceContact resistance
Features: Proportional to FORCE, not to pressure
(constant spot area, number of contact points increases with force)
For metals, saturates above 30N @ 300K Hysteresis upon loading cycles (plastic
deformations) Can be reduced by fillers, grease, In, coatings For el. conductors, Rh~Rel Rh-1=Kh increases with T then saturates Approximately proportional to microhardness/k
CH AQ
TR
/
Temperature discontinuity at the interface:
- phonon scattering (Kapitza)
- spot-like contact points
G.Vandoni, Heat Transfer Academic Training 2005 22
Contact resistancesContact resistances
G.Vandoni, Heat Transfer Academic Training 2005 23
Thermal switchesThermal switches
SCOPE: Good thermal contact for cooldown
BUT
Thermal insulation once cold
REALIZATION: Exchanger gas: long time for evacuation Gas heat exchanger: short time for evacuation Superconducting switch (Pb or In) Polycristalline graphite: k~T3 up to 100K
Switch from normal (thermally conducting) to superconducting (thermally insulating) with applied magnetic field
heat sink
device
G.Vandoni, Heat Transfer Academic Training 2005 24
RADIATIONRADIATIONAny surface T>0K absorbs () and emits () energy as electromagnetic radiation:
depending on direction and wavelength
absorbedPtransmittedP
incidentP reflectedP
BLACK-BODY:
The whole incident radiation is absorbed:
=1
Energy conservation
Opaque medium
G.Vandoni, Heat Transfer Academic Training 2005 25
Black-body radiationBlack-body radiation
1)/exp( 2
51
,
TC
CEb
Planck’s law for energy flux emitted by a cavity [W/cm3]
]/[2898
max KmT
Wien’s law
300 K 10 m
80 K 36 m
5500 K (sun)
0.4-0.7 m (visible)
4Tq
Integral over :
Stefan-Boltzmann’s law for black body
=5.67 10-8 W m-2
G.Vandoni, Heat Transfer Academic Training 2005 26
Heat exchange between two Heat exchange between two blackblack surfacessurfaces
Geometrical FORM FACTOR F12
F12= (radiation leaving A1 intercepted by A2) / (radiation leaving A1 in all directions)
= integral of solid angle under which A1 sees A2
A1, T1, A2, T2)( 41
42121 TTFAQ
F12 tabulated for several useful geometries
G.Vandoni, Heat Transfer Academic Training 2005 27
From a blackbody to a real From a blackbody to a real bodybody
4Tq real-body
Definition of (total hemispherical) emissivity :
4Tq black-body
,
),,(),,(
bI
TIT Monochromatic directional
emissivity
grey-body
( independent of )
diffuse-body
(independent of )
APPROXIMATIONS
G.Vandoni, Heat Transfer Academic Training 2005 28
Kirchoff’s lawKirchoff’s law
From energy conservation in a cavity:
For black-body and diffuse grey body: (T)= (T)
Practical use:can be estimated from provided the incident radiation and the surface have the same temperature
In reality, (,T)≠ (,T)
G.Vandoni, Heat Transfer Academic Training 2005 29
Electrical analogy for real (diffuse/grey) Electrical analogy for real (diffuse/grey) surfacessurfaces
q12T14 T2
4
q1 q2
11
11
A
22
21
A
121
1
FA
resistance between two blackbodies
22
2
12111
1
42
41
12 111
AFAA
TTq
Blackbody form factors can be used for real diffuse-grey
surfaces
internal resistance of the surface to
black-body emissionmotor
flux
total thermal impedance
G.Vandoni, Heat Transfer Academic Training 2005 30
Heat transfer between 2 real Heat transfer between 2 real surfaces surfaces
)( 41
42121 TTAq 12 effective emissivity
(emissivities + view factor)
Spheres and long cylindersself-contained, not concentrical/coaxial(A1<A2)
Parallel plates
122
12
21
)1(
AA
122
21
)1(
A2>>A1 equivalent to A2 black: black-body radiation fills the cavity between the two surfaces and is collected by A1 proportionnally to 1
G.Vandoni, Heat Transfer Academic Training 2005 31
Emissivity and materialsEmissivity and materials
Polished metals: small Insulators: large (T): for real metals, ~T at low T Coatings: since related to surface, not bulk, resistance,
=> lower limit on thickness of reflectors (1 above ~40nm)
Real emissivities depend on direction and wavelength
TT 365.0,
Drude law for ideal metal
G.Vandoni, Heat Transfer Academic Training 2005 32
Emissivity and materials –2-Emissivity and materials –2-
G.Vandoni, Heat Transfer Academic Training 2005 33
Radiative heat transfer in Radiative heat transfer in cryogenicscryogenics
Blackbody radiation from 290 K to 4.2 K: 401 W/m2
Blackbody radiation from 80 K to 4.2 K : 2.3 W/m2
)( 44coldwarm TTq
Blackbody radiation from 290 K to 80 K: 399 W/m2
Blackbody radiation from 290 K to 4.2 K : 401 W/m2
negligible effect of Tcold
reduction of heat flux by one cooled screen
G.Vandoni, Heat Transfer Academic Training 2005 34
Floating radiation screensFloating radiation screens
)(2
44cw TTq
Floating = not actively cooled, they operate at a temperature determined by heat balance
T
n
)(22
1 44cw TTq
Tw Tc
)(21
1 44cw TT
nq
)(2
1 444cw TTT
1
4444
i
TTTT cw
ci
G.Vandoni, Heat Transfer Academic Training 2005 35
Multi-layer InsulationMulti-layer Insulation
Reflector: low emittance radiation shield
Stacking of “reflectors” separated by insulating “spacers”
reflector spacer
polyester film, 300-400 A pure Al coating, usually double face
Spacer: insulating, lightweight material
paper, silk, polyester net
1. Heat transfer parallel to the layers ~1000 times greater than normal to the layers
2. Heat transfer very sensitive to layer density
thermal coupling between blanket edges and construction elements may dominate heat rate.
blanket
single local compression affects the T profile over the entire blanket, substantially degradating heat loss (factors 2-3 more !)
G.Vandoni, Heat Transfer Academic Training 2005 36
MLI: effective conductivityMLI: effective conductivity
Effective conductivity k=aT+ bT3
Heat transfer rate q=k/e T, e = thickness
Optimal density: 10-20 cm-1
layers/cm
W/m
2
Low boundary heat transfer rate determined byaT, not by temperature: radiation
1 single aluminized foil is sufficient in high vacuum
in bad vacuum, MLI provides sufficient insulation
77 K-> 4K
High boundary heat transfer rate determined by radiation temperature: important reduction with layer’s number
bad vacuum: radiation dominates anyway300 K-> 77K
G.Vandoni, Heat Transfer Academic Training 2005 37
MLI: number of layersMLI: number of layers
10 layers,
77K-> 4K,
20 mW/m2
30 layers,
300K-> 77K,
0.5 W/m2
N = 15 cm-1
Tc= 4.2K= 0.03
G.Vandoni, Heat Transfer Academic Training 2005 38
MLI and residual pressureMLI and residual pressure
300 K -> 77 K
77 K -> 4.2 K
300 K -> 77 K
77 K -> 4.2 K
300 K -> 77 K
77 K -> 4.2 K
300 K -> 77 K
77 K -> 4.2 K
interstitial gas:
nitrogen
Kennard’s law
MLI constitutes a supplementary protection against vacuum rupture, only at low boundary temperature: at high boundary temperature, radiation dominates anyway
G.Vandoni, Heat Transfer Academic Training 2005 39
Passive cooling by radiatorsPassive cooling by radiators
Radiation cooling to a cold screen -> cool down without contact
Requires large surface-to-volume ratio + large emissivity
Black silicon paints compatible with high vacuum from the space industry (cooling of CERN antiproton collector’s mobile electrodes)
Cooling in space applications towards the cosmic background radiation at 2.7K
Figure: the NGST (next generation space telescope) solar screen
G.Vandoni, Heat Transfer Academic Training 2005 40
Free and forced Free and forced CONVECTIONCONVECTION
)(/ fs TThqAQ
h: heat transfer coefficient, function of fluid properties, flow velocity and channel geometry
TsTf
Free (natural) convection : the fluid movement is due to expansion upon heating, reduction of density and buoyancy (kettle, fireplace)
Forced convection: the fluid is set into movement by external action (pressure difference, mechanical action, elevation difference)
Q transferred heat, A surface area
Scope: determine h
Analysis: dimensionless groups, EMPIRICAL correlations
G.Vandoni, Heat Transfer Academic Training 2005 41
Convection exchange Convection exchange coefficientcoefficient
1 10 102 103 104 105 106
h (W/m2K)
Boiling, water
Condensation, water vapors
Condensation, organic vapors
Liquid metals, forced convection
Water, forced convection
Organic liquids, forced convection
Gases 200atm, forced convection
Gases 1atm, forced convection
Gases, natural convection
Boiling organic liquids
Convective heat transfer in cryogenic fluids not different from any other, except He II
)( fs TThq
Boiling HeI, N2 peak nucleate flux (PNBF):
104 W/m2K
G.Vandoni, Heat Transfer Academic Training 2005 42
Dimensionless groupsDimensionless groupsGroup Name Definition Physical interpretation
Re Reynolds inertia force/viscous force
Pr Prandtlmomentum transport/thermal diffusivity
Nu Nusseltconvection exchange/conduction exchange
Gr Grashof buoyancy force/viscous force
Ra Rayleigh
d=characteristic dimension, ex. tube diameter or hydraulic diameter, =dynamic viscosity, =volume expansivity, k=thermal conductivity, T=temperature difference, =density, Cp=specific heat at constant pressure, h=heat transfer coeff , g= gravity acceleration
/Vd
kC p /
khd /
223 / Tdg
PrGr
fluid characteristic
s
flow character
like Re for free convection
defines convection exchange
G.Vandoni, Heat Transfer Academic Training 2005 43
Reynolds number and flow Reynolds number and flow charactercharacter
Vd
Re density, V fluid average velocity, d hydraulic diameter, dynamic viscosity
Inertia forces compared to viscous forces
Laminar: low heat transfer coefficient
Turbulent: high heat transfer coefficient
Viscous forces are stabilizing:
laminar flow
Inertial forces are de-stabilizing:
turbulent flow
In free convection, Gr plays the role of Re: buoyancy versus viscosity
G.Vandoni, Heat Transfer Academic Training 2005 44
Free (natural) convectionFree (natural) convection
General relation Nu = function(Gr,Pr)
Nu = a (Gr .Pr) n= a . Ra nEmpirical form
Configuration regime limits a n
vertical, free surface laminar 5.103<Ra<109
0.59 ¼
turbulent 109<Ra<101
30.13 1/3
horizontal, free surface
Ra<103 1.18 1/8
laminar 103<Ra<2.107
0.54 ¼
turbulent 2.107<Ra<1013
0.14 1/3d to be used to calculate: diameter (horizontal cylinder), height (vertical plates/cylinders), smallest exchange dimension (horizontal plates), distance between walls (enclosures)
G.Vandoni, Heat Transfer Academic Training 2005 45
Free convection in gases and Free convection in gases and airair
common gases: h~p½, h~T-½.
cold helium gas (80K, 1 bar): Nu~3.65 (laminar)
Air close to ambient conditions
Watt m-2 K-1horizontal plates
Watt m-2 K-1vertical plates4/1
4.1
d
Th
4/1
3.1
d
Th
important increase at low temperature
G.Vandoni, Heat Transfer Academic Training 2005 46
1phase forced convection1phase forced convection
Empirical relation Nu = f (Re,Pr) = aF Rem
Prn
Configuration regime limit a m n F
horizontal plate
laminar 103<Re<105 0.66 ½ 1/3 1
turbulent 3 105<Re 0.036 0.8 1/3 1
horizontal tube annular space
laminar 103<Re<2.1 103
Re Pr D/L >10 1.86 1/3 1/3 (D/L)1/3
turbulent Re Pr D/L >10
RePrD/L>2.4 105 0.023 0.8 0.33 1+(D/L)0.7
Sieder & Tate formula
Colburn formula
G.Vandoni, Heat Transfer Academic Training 2005 47
Steps to solve a convection Steps to solve a convection problemproblem
1. Calulate Re to determine flow character: laminar/turbulent
hydraulic calculation of pressure dropf=Fanning, function of Re
2. Evaluate Pr (fluid characteristics)
3. Choose the appropriate formula for Nu -> h4. In doubt about the importance of free convection:
calculate Gr
d
fv
dx
dp 4
2
2
G.Vandoni, Heat Transfer Academic Training 2005 48
Boiling heat transfer in He IBoiling heat transfer in He I
Increase of heat transfer up to a Peak Nucleate Boiling Flux:
He I: 1 W cm-2 @ 1K superheat
N2: 10 W cm-2 @ 10K
H2O: 100 W cm-2 @ 30K
Positive consequence for safety: limit to the highest flux released by a warm object (quenching magnet, human skin)
Hysteresis: cooling path not the same as warming path
G.Vandoni, Heat Transfer Academic Training 2005 49
Two-phase convectionTwo-phase convectionheat transfer = bubble formation and motion near the walls + direct sweeping of the heated surface by the fluid
Instabilities of density-wave type:
pressure waves increase locally the heat transfer rate, the fluid expands => decrease in conductivity and heat transfer rate
How to avoid them:
-Maintain low vapor quality-Not too large differences in elevation-No downstream flow restrictions -> destabilizing-Introduce upstream flow restrictions -> stabilizing
G.Vandoni, Heat Transfer Academic Training 2005 50
Refrigeration properties of Refrigeration properties of cryogenscryogens
He N2 H2O
Normal boiling point 4.2 77 373
Critical temperature 5.2 126 647
Critical pressure 2.3 34 221
Liquid density/ Vapor density*
7.4 175 1600
Heat of vaporization * [Jg-1] 20.4 199 2260
Liquid viscosity * [poise] 3.2 152 283
Enthalpy increase between T1 and T2
T1 = 4.2 K
T2 = 77 K
384 - -
T1 = 4.2 K 1157 228 -
T2 = 300 K
highly effective for self-sustained vapor cooling!
*at normal boiling point
Working domain close to critical point:
properties of liquid and vapor phase are similar
low vaporization heat
Low viscosity hence excellent leaktightness required for He
G.Vandoni, Heat Transfer Academic Training 2005 51
Shielding potential of cold Shielding potential of cold vapoursvapours
Th
Tc
L
A
Pure conduction heat losses evacuated at
the coldest temperature
2
1
)(T
TdTTk
L
AQ
Self sustained vapour cooling: vapour flow generated only by heat leak is used to cool the
device
Heat evacuation across a small T thermodynamically much
more efficient
G.Vandoni, Heat Transfer Academic Training 2005 52
Shielding potential of cold Shielding potential of cold vapoursvapours
)()( lp TTCmdx
dTATkQ
heat balance, perfect exchange
vLmQ
self-sustained evaporation of fluid
2
/)(1
)(T
Tvpl
l LCTT
dTTk
L
AQ 2
)(T
ldTTk
L
AQ
Th.conductivity integral [W cm-1] [W cm-1]
ETP copper 128 1620
OFHC copper 110 1520
Aluminium 1100 39.9 728
AISI 300 st.steel 0.92 30.6
Q
)()( lp TTCmdx
dTATk
lT
G.Vandoni, Heat Transfer Academic Training 2005 53
Phase diagram of heliumPhase diagram of helium
high HT, low T
dielectric breakdown, sub atm, large gas volume
FORCED FLOW
small inventory, no instabilitybi-variant, high p, JT heating
high HT, low T, large Cv
refrigeration cost, sub-atm pipes
POOL BOILING
constant T, irrespective of q
PNBF, large quantities of cryogenFORCED FLOW
JT cooling, good heat transfer, small liquid inventory
flow instabilities, small (p,T) range
G.Vandoni, Heat Transfer Academic Training 2005 54
Typical heat inleaks in a Typical heat inleaks in a cryostatcryostat
[W/m2]
Black-body radiation from 290 K 400
Black-body radiation from 80 K 2.3
Residual gas conduction (100mPa helium) from 290 K 19
Residual gas conduction (1mPa helium) from 290 K 0.19
Multi-layer insulation (30 layers) from 290 K, residual pressure below 1mPa
0.5-1.5
Multi-layer insulation (10 layers) from 80 K, residual pressure below 1mPa 0.05
Multi-layer insulation (10 layers) from 80 K, residual pressure 100mPa 0.2
Radiation screening
Insulation vacuum
MLI at high (>30 layers) and low (10 layers) boundary temperature
…between flat plates, at vanishingly low temperature
G.Vandoni, Heat Transfer Academic Training 2005 55
Heat inleaks in an acceleratorHeat inleaks in an accelerator
Cryostat heat inleak Resistive dissipation Beam-induced losses
radiation to cold surface superconductor splices synchrotron radiation
cold mass supports wall resistance beam-image currents
warm-to-cold feedthroughs
instrumentation beam-gas inelastic scattering
AC losses beam losses