Heat Transfer at Cryogenic Temperatures · December 7th, 2007 HT at Cryogenic Temperatures 11/21 HT...

Heat Transfer at Cryogenic Temperatures

Considerations and Aspects of LowTemperature Devices

Kai SchwarzwälderFriday TalkDecember 7th, 2007

December 7th, 2007 HT at Cryogenic Temperatures 2/21

Heat Transfer – be aware !

„Heat transfer is the crux of most cryogenic designs.“ –Jack W. Ekin

„If you do not look at any other chapter in this book, this isthe place where it pays to spend a little time…“ – Jack W. Ekin p.49

„If you get it right on paper, it‘ll be right when you build it.“– Susan Wright, p.49

„Der Teufel liegt im Detail“ – Jack W. Ekin / german adage„Der Teufel ist ein Eichhörnchen.“ – german adage


Outline

Heat Transferwithin one material

across material interfaces

miscalleneous

Practical considerationsother properties

miscalleneous phenomena

heat switches

Part I:Physics of Heat transfer


Conductance in solids / liquids

Thermal conductivity λ

Wiedemann-Franz-law:T<10K, T>200K

λρ = LT L = 2.44 · 10−8 V 2

K2

q̇cond =A

L

T2ZT1

λ(T )dT

=A

Lλ̄∆T A 6= A(x)

Ther

mal

con

duct

ance

λ/ W

/cm

K


Conductance in gases

Mean free pathIdeal gas:

Real gas:

→ Two cases:Ballistic regime ℓ >>dHydrodynamic regimeℓ<<d

` = 2.87 · 10−3 cm Pa

Kj+1T j+1

Pj = 1.147 for He

= 60μm(Atm., RT)

` =kT

Pσ= 60nm (Atm.,RT)

Heat switch

Thermal uniformity q̇A∆T

/W

m2K


Conductance in gases

hydrodynamic regime

liquid 3-15 times more conductivefor gases:

ballistic regime

q̇cond = λ̄Ad∆T

λ ∼ N ∼ P ⇒ λ ∼ P

q̇cond = ka0PAi∆T

λ ∼ `N ` ∼ 1P

N ∼ P

¾⇒ λ = λ(6P )

k = 2.1 He

= 4.4 H

= 2.1 air

a0 = a1a21

a2+A1a2(1−a2)a1

λ = cCV c = 1.5...2.5 for cryo. gases


Convection

free convection(buoyant forces)

convection in liquidsmuch strongerforced convection

q̇conv = hAsurf∆T


Radiation

Stefan-Boltzmann

wave length0,9IMI 7031

varnish

0,07Stainless steal

commonHighlyoxidisedPolished

Material

0,60,03Brass

0,60,02Cu

0,30,03Al

Emissivity, λ=10μm

q̇rad = σEA¡T 42 − T 41

¢E effective Emissivity

E½¿ 1 specular/polished≈ 1 diffuse

λmT = 2900μmK ⇒ λ =

½10μm RT700μm 4K


Radiation Shielding

avoid scratches, finger prints, oil drops,..(emissivity)N „floating“ baffles → HT reduced byHelically twisted strips:better pumpingMultilayer Insulation (MLI):

30-80 layers of aluminised MylarMLI can be adsorber → virtual leaklong time to get into eqilibrium„apparent mean thermal conductivity“:10-5 W/mK in OVC at 10-2Pahandle MLI blanket with care(no crinkling or pushing, solid HT)

1N+1


HT across liquid-solid interface

Non-boiling regime:Convection dominates, strong influence of surface orientation

Nucleate boilingweaker influence of surface orientationHe:

N:

Film boilinggas blankets the surfaceΔT jumps abruptly at constant heat flux

„...,the Achilles heel for liquid cooling is not heat conduction through theliquid, but heat transfer across the liquid-solid interface ....“

q̇A = X · 104(∆T )2.5 W

K2.5m2

q̇A = 5 · 102...3(∆T )2.5 W

K2.5m2


HT across solid-solid interfaces

Ranking1. solder joint2. glue/varnish/grease3. pressed

Ther

mal

Con

duct

ance

W/K

q̇(T ) = q̇445N ;4.2K ·F

445N

µT

4.2K

¶γγ = 1.3...3 Mat. property

gold plating

In foil(0.05…0.1mm)

grease(ApiezonTM N)

Main methodto improve HT

high pressure

moderate, P≥Pin=1MPa

low pressure

Type of pressurecontact

q̇ = q̇(A)

q̇ = q̇(A)

q̇ = q̇(6A,F )


Miscalleneous HT I

Thermoacoustic Oscillations(Taconis)

one open, one closed (RT) endthermally excited pressurewavesspontaneous start100s ml/hinterrupt by pulling outavoid by drilling holesTell-tale humrather in thin tubes(D≤1cm)

superfluid-He creepHeII climbes up walls, evaporated at warmer stagescreep rate:

On glass: 3 times lower(clean surface) to 3 timeshigher (adsorbed air)limits evaporative coolingavoid by small perimeter

V̇ = · 0−7 ls cm2 1


Miscalleneous HT II

Ad-/Desorption of gasgas desorbed on hot wall → adsorbed on cold walltransport of latent heat of evaporisation/meltingimportant in low T calorimetry and demagnetisation

Others: (T≤1K)mechanical vibrations (eddycurrent)radioactive heatingneighbourhood radio station

Part II:Practical Considerations


Intuition

„Metals feel colder to the touch than ceramics and therefore have a greater heat capacity.“ → speed of equilibration

„Copper provides great cooling power at lowtemperatures.“→ C drops al low T, better: LHe

„Materials become brittle when frozen.“ → not fccmetals, Kapton or Teflon, but epoxy!

„Solder is fairly soft.“→ stronger at 77K, like fccmetals, mostly no change at lower T

3.2.1 Room-temperature intuition generally does not work


Other Properties I

Matthiessen‘s rule:

Residual Resistance Ratio

ρ(T ) ∼= ρres + ρi(T )

RRR≡ RRTR4K

= ρRTρ4K

RRR= ρiRT+ρresρres

⇔ ρres =ρiRTRRR−1

Res

istiv

ity/ μ

Ωcm


Other Properties II


Other Properties III

Fracture toughness:good: fcc materials (Cu, Al, stainless, alloys thereof)bad: bcc (Nb), hpc (Ti)

Yield strengthmaterial starts to deform plastically

Magnetic susceptibilitystainless-steel can have phase transition from para- to ferromagnetic, welding/machining can induce that property

SuperconductivityAl, solder,…; no HT, no resistance


Miscalleneous Phenomena & Heat Switches

Joule Heatingideal cross-sectionvapor-cooled leadssuperconductors

Eddy currentsslit geometry: interrupt loopsinsulators

Heat switchesgasessuperconductorsboiling noise

Thank you

for your attention !

Heat Transfer at Cryogenic Temperatures · December 7th, 2007 HT at Cryogenic Temperatures 11/21 HT...

Documents

Transcript of Heat Transfer at Cryogenic Temperatures · December 7th, 2007 HT at Cryogenic Temperatures 11/21 HT...