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Heat Transfer and Cooling Temperatures at Low Temperatures - Coggle Diagram
Heat Transfer and Cooling Temperatures at Low Temperatures
Introduction
Fundamental laws of heat transfer
conduction
convection
radiation
Leads to cryogenic condition
thermal contact resistance
total emissivity of materials
heat transfer correlation in forced or boiling flow
Main cooling techniques at low temperature
with cryogen
without cryogen
Thermal stability in the steady state regime in the cooling system design :
temperature of the system must remain constant in the nominal working condition
the system can be maintained at a temperature lower than room temperature
Requires certain levels of thermal protection against transient events :
the temperature of the system must stay below a certain value to avoid problematic situations
Objective : To minimize the heat load from the surroundings and to maximize the heat transfer with a cooling device using the knowledge of :
identification of the different heat loads to the system
the fundamental laws of heat transfer
thermo-physical properties of materials and fluids
The heat trasnfer
Thermal radiation
Radiation exchange between two surfaces :
The heat transfer by radiation between two enclosed surfaces; from one at temperature T1 with an emissivity ε1 and a surface A1, to another at T2 with ε2 and A2 :
EQN (19-23)
PAGE 339
Shielding and multilayer insulation :
using the blackbody relation
an intermediate surface held at intermediate temperature is required to
reduce the heat load at low temperature
Using Eq. (22) with
the assumption that the surfaces and emissivities are identical for the different reflecting surfaces
, the
heat flux density q as a function of the number of intermediate surfaces for passive shielding
can be calculated
General laws :
Any surface at finite temperature absorbs, reflects, and emits electromagnetic radiation
When describing the radiation characteristics of real surfaces, it is useful to start with the concept of an ideal surface: the blackbody.
The blackbody is a perfect emitter and absorber. It absorbs
all incident radiation regardless of the wavelength and direction.
At a given temperature and wavelength, the emission is maximum and the blackbody is a diffuse emitter (no directional dependence)
The emissive power (W·m–3) of the blackbody per unit wavelength and per surface (hemispherical) as a function of wavelength is described by Planck’s law:
EQN (15 - 18)
PAGE (336 & 337)
Convection
Natural convection :
the simplest correlations are expressed as
Nu = c × (Gr × Pr)^n
n = 1/4 for a laminar regime and n = 1/3 for a turbulent regime
Boiling convection :
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, and the bubble hydrodynamics
The heat transfer process depends on the bubble growth rate, the detachment frequency, the number of nucleation sites, and the surface conditions
film boiling
: the heat is primarily transferred by conduction through the vapour film, explaining the large increase of the wall temperature
Before the onset of boiling, natural convection takes place; and since the boiling heat transfer is extremely efficient, when boiling is activated, the wall temperature increase is slowed down
After the onset of boiling, the evolution of nucleate boiling is encountered; that is, from partially to fully developed nucleate boiling, where the vapour content and structure are continuously increasing
At one point, called the ‘critical point’, the vapour production is so high that the vapour structures coalesce and form a blanket of vapour at the heating surface
This results in a new regime called ‘film boiling’,
Introduction :
basic notion of the physics of convection to extract the useful information on cryogenic design
convection heat transfer : heat can be transferred in the fluid by movement of matter, a quantity of energy that is advected within the fluid, thus movement of matter can be created externally by a
pump or a pressurization system
Force convection :
the equations of motion in the
Boussinesq approximation
are useful to
present the
dimensionless numbers and their physical significance
to evaluate heat transfer coefficients and flow regimes.
EQN (24 - 30)
PAGE (341 & 342)
A laminar flow in pipes is very rare, except in porous media, and it is too specific for details to be given here
Thermal conduction
liquid
bad thermal conductors, at room temperature and at low temperature alike
thermal conductivity usually decreases with temperature
gas
to evaluate the heat leak or to characterize
thermal switches, devices that exchange heat with gas in certain conditions
-λ ≫ L : free molecular regime
-λ ≪ L : hydrodynamic regime
EQN (13 & 14)
PAGE 335
solid
heat transfer w/o mass transfer in solid
Fourier law : relationship between heat flux density and temperature gradient
EQN (1-3)
PAGE (329 & 330)
Principles uses for the thermal conductivity integral :
determination of heat losses and heat interception between room temperature and the low temperature of the system under consideration
Example : the heat input into a liquid helium bath cooled system
EQN (4-6)
PAGE (331)
The thermal design at low temperature need the
calculation of thermal resistance Rth
EQN (7-9)
PAGE (332)
In the treatment of the
thermal resistace Rc
Rc :
proportional to the force applied at the contact but not to the pressure
reduces with the increasing force but increases with decreasing temperature by several orders of magnitude from 200 to 20 K
at low temperatures can be the largest thermal resistance source
Include the transient conduction process in a cryostat design at low temperature
EQN (10-12)
PAGE (334)
Cooling techniques at low temperature
Introduction :
cooling a device to low temperature can be achieved with or without cryogenic fluids
A cooling method called
WET METHOD
when a cryogenic fluid is used in contact with the device
or
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
Different methods of cooling
Forced flow :
one of the methods used to reduce the amount of cryogen, especially in indirect cooling
composed of a network of peripheral tubes
Advantages :
the adjustable heat transfer rate with
mass flow rate
Cooling in the supercritical state can be grouped in the single-phase category and one of its main
advantages is a heat transfer coefficient comparable to that of pool boiling in helium
Another advantage of cooling with supercritical fluid is the lack of
hydraulic instabilities in the single-phase flow compared to a two-phase flow
two-phase forced flow cooling :
The first is the guarantee of having an almost isothermal flow due to the high heat transfer, even at high vapour quality, in this flow regime
DRAWBACKS OF 2 PHASES
the limited
range of temperature cooling and the non-uniform cooling if the vapour and the liquid are not homogeneous in their motion.
Moreover, if the heat flux q > qcr, then there is film boiling and the heat transfer rate becomes an order
of magnitude smaller.
Disadvantages for a single-phase
flow :
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; and the temperature range limitation due to finite sub-cooling
Natural and two-phase circulation loops :
Circulation loops are 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
Advantages :
there is no need for a circulating system (centrifugal pump, forced pressure differential, etc.)
two types of circulation loops:
the ‘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
the ‘Closed Loop’, where the vapour is re-condensed in a closed reservoir with a heat exchanger.
Baths :
most common cooling method is to use a liquid bath in which the system is immersed
the fluid at the free surface is at saturation
(T ≈ Tsat)
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
Main advantages :
the simplicity of the cryogenic design and operation, the high heat transfer due to nucleate boiling
Therefore, an almost constant surface temperature
If there is sub-cooling due to a hydrostatic pressure head, as is depicted for the helium cooling bath then there is an extra ΔTsub that can be used before boiling is reached
Disadvantages :
t a large quantity of cryogen has to be handled, particularly in case of a quench of a cryomagnetic system (risk of pressure rise)
If q > qcr, then the heat transfer coefficient in film boiling is an order of magnitude smaller than that in a nucleate boiling case and non-uniform cooling can result due to film vapour formation.
Cryogen-free cooling and the coupled system :
Cyogen-free method
: use a conductive thermal link between the cold source (the cryocooler) and the low-temperature device
Advantages :
easy implementation (no liquid, no heat exchanger, no transfer line, etc.) are very attractive,
Disadvantages :
one has to be very accurate in the thermal design, since these cryocoolers provide a finite cooling power at a prescribed temperature
Therefore if the real power to be extracted exceeds the maximum power of the cryocooler, the working temperature will inevitably be higher than expected
The 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
For a fully conductive thermal link, the thermal diffusion in the thermal link limits the
cooling for transient events
Overcome :
use a thermal link with a fluid
Capillary-pumped devices
Oscillating Heat Pipe (OHP)
Small natural circulation loop coupled with a cryocooler can be used to serve as a self-sustaining thermal link at cryogenic temperatures