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HEAT TRANSFERR AND COOLING TECHNIQUES AT LOW TEMPERATURE, image, image,…
HEAT TRANSFERR AND COOLING TECHNIQUES AT LOW TEMPERATURE
Heat transfer
Thermal Radiation
Exchange between two surfaces
The heat transfer by radiation between two enclosed surfaces can be written as follows :
where q12 is the heat transfer rate from surface 1 to surface 2. F12 is the ‘view factor’, which is the fraction of the heat leaving surface 1 that is intercepted by surface 2.
Shielding and multilayer insulation
To understand the philosophy of ‘passive’ thermal shielding from room temperature to low temperature, simple evaluation using the blackbody relation is sufficient, without knowledge of the emissivities and view factors
An intermediate surface held at intermediate temperature is required to reduce the heat load at low temperature.
Passive thermal shielding is implemented using a multilayer insulation (MLI) system (also called superinsulation), assembly of reflective films (usually aluminium or aluminized polyester film) separated by insulating interlayers (polyester, glass-fibre nets, or paper), operated under vacuum.
The reflecting layers reduce heat transfer by radiation, the insulating interlayers reduce heat transfer by conduction between reflecting layers, and the high vacuum reduces convection and residual gas conduction.
General laws
Any surface at finite temperature absorbs, reflects, and emits electromagnetic radiation.
The emitted radiation, Φ, consists of a continuous non-uniform distribution of monochromatic components.
Thermal conduction
Liquids
Liquids are bad thermal conductors.
Thermal conductivity usually decreases with temperature.
In most heat transfer situations, the thermal conduction in a liquid negligible except superfluid helium
Gas
The heat transfer between two surfaces in a gas is of interest to evaluate the heat leak or to characterize thermal switches, devices that exchange heat with gas in certain conditions
Two different heat transfer regimes depending on the ratio between the mean free path of the gas molecules, λ, and the distance L between the two surfaces involved in the heat transfer.
λ ≫ L, corresponds to the free molecular regime, obtained at low residual pressure, and the heat transfer depends on the residual gas pressure and is independent of L. Described by Kennard’s law.
λ ≪ L, corresponds to the hydrodynamic regime, obtained at high residual gas pressure and the heat transfer is independent of pressure and described by a Fourier law.
Solids
Relationship between the heat flux density and the temperature gradient :
q = −k(T)∇T
One of the principal uses for the thermal conductivity integral is in the determination of heat losses and heat interception between room temperature and the low temperature of the system under consideration.
To reduce the heat load on the helium bath, heat interception by another cold source at an intermediate constant temperature is used.
In the treatment of the thermal resistance, assumed a perfect thermal contact between the different components.
The rugosity creates an imperfect contact, generating a temperature drop due to the local contact creating constriction of the flux lines.
The phonon scattering at the solid–solid contact and the heat transfer via eventual interstitial elements increase the contact thermal resistance.
Convection
Boiling
Heat is transferred between a surface and the fluid by the conjunction of a phase change and the vapour bubble movement in the vicinity of the surface.
Heat transfer combines :
Natural convection in the liquid
Latent heat to be absorbed for the bubble formation
The bubble hydrodynamics.
Forced
As for natural convection, the correlations used for non-cryogenic fluids are suitable at low temperature in the forced convection regime.
The heat transfer coefficients can go up to several kW·m–2·K–1.
Natural
The heat flux at the wall is computed with correlations of the type Nu = f(Gr, Pr, L)
The heat transfer coefficients are of the order of 10–100 W·m–2·K–1.
Few data exist for cryogenic fluids, since two-phase phenomena take over even at low heat fluxes.
Cooling Techniques
Introduction
Dry method when a cryocooler is used without any fluid as coolant.
Indirect cooling method, when a cryogenic fluid is used without direct contact with the device but only through intermediate components
Wet method when a cryogenic fluid is used in contact with the device
Method of cooling
Force flow
Methods used to reduce the amount of cryogen, especially in indirect cooling composed of a network of peripheral tubes.
Advantage is the adjustable heat transfer rate with mass flow rate
Single phase
Disadvantanges
Include:
the pressurization system, or the implementation of the circulation pump and its maintenance at low temperature
The implementation of the heat exchanger system to sub-cool the fluid
The temperature range limitation due to finite sub-cooling
Supercritical phase
Advantages
A heat transfer coefficient comparable to that of pool boiling in helium.
The lack of hydraulic instabilities in the single-phase flow compared to a two-phase flow.
Disadvantages
Needs to have a ‘heavier’ cryogenic installation to ensure a periodic re-cooling for operation and to maintain a pressure above Pcrit (2.25 bars Absolute for He) in the system.
Two phase
Advantages
The guarantee of having an almost isothermal flow due to the high heat transfer, even at high vapour quality, in this flow regime.
Disadvantages
The limited range of temperature cooling and the non-uniform cooling if the vapour and the liquid are not homogeneous in their motion.
Baths
Use a liquid bath in which the system is immersed
It is a direct or indirect cooling method with no net liquid mass flow and where the main heat transfer process is essentially due to latent heat of vaporization
Disadvantages
Large quantity of cryogen has to be handled, particularly in case of a quench of a cryomagnetic system (risk of pressure rise).
Advantages
The simplicity of the cryogenic design and operation, the high heat transfer due to nucleate boiling, and, therefore, an almost constant surface temperature.
Natural and two-phase circulation loops
An auto-tuned mass flow rate system in which the flow is created by the weight unbalance between the heated branch and the feeding branch of the loop due to vaporization or decreased vapour density
Type
Open loop : where the boil-off goes out of the system to be re-liquefied somewhere else before refilling the reservoir permanently to avoid a dry-out.
Closed loop : where the vapour is re-condensed in a closed reservoir with a heat exchanger
Advantanges
No need for a circulating system
Confirguration
Horizontal confirguration, the heat transfer is as high as that for the vertical case, but there are flow instabilities at low heat flux flow
Vertical configuration, two-phase flow circulation loops also have high heat transfer rates
Cryogen-free cooling and the coupled system
Cryocoolers can provide sufficient power to cool down and maintain a small cryomagnetic system at low temperature.
The obvious advantages of easy implementation are very attractive, one has to be very accurate in the thermal design, since these cryocoolers provide a finite cooling power at a prescribed temperature.
Other technical issue to keep in mind is that a thermal link is necessary to distribute the cooling power over the entire system with this ‘point-source’ of cold that is the cryocooler.
To overcome disadvantages use a thermal link with a fluid.
Capillary Pump
Have been used for many temperature ranges
The operating principle is identical whatever the temperature range.
A flow is created by capillary pressure in a porous
medium at the liquid/vapour interface
Masnah
