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Heat transfer
Beam heating
Density reduction
STOP
Heat Transfer and Density Reduction
•
Heat is deposited in the target
material as the beam passes
through it. This heat deposition
has several important
consequences in terms of target
design. In this section, we will
look at how heat can be removed
from the target and how the
temperatures in the target can
affect the target density and other
physical characteristics
Contents
•
•
•
•
•
•
•
Heat Balance
Conduction
Radiation
Convection
Heat transfer in gas targets
Heat transfer in liquid targets
Heat transfer in solid targets
STOP
Heat Balance
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•
Heat Transfer
Contents
Qin = Qout
Heat Balance
Conduction
In order to have a stable radionuclide production, the heat
deposited in the target must be removed.
•
The beam power in watts is the beam energy loss in MeV times
the beam current in microamps
•
There are three modes of heat transfer
– Conduction
– Radiation
– Convection
Conduction is important in target bodies and foils
Radiation can be important in foils and solid metal targets
Convection is important inside gas and liquid targets
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
STOP
•
•
•
Conduction
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Heat Transfer
Contents
The first form of heat transfer to be considered is conduction
since in many ways it is the easiest to model. Heat applied to
one side of a material will be transferred to the other side at a
rate based on the thermal conductivity.
Heat Balance
Heat Source
Conduction
Radiation
Convection
Heat Sink
Heat transfer in gas
targets
Qcond = -kA dT/dx
Heat transfer in liquid
targets
where
Heat transfer in solid
Qcond = heat transferred by conduction (watts)
targets
A = cross-sectional area (cm2)
k = thermal conductivity (watts/cm-°C)
dT = temperature differential (°C)
dx = distance differential (cm)
STOP
Conduction
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Heat Transfer
Contents
Heat Balance
Conduction
In the more usual form of the equation, the heat removed is
directly proportional to the thermal conductivity times the area
times the temperature difference and inversely proportional to the
distance the heat must travel through the substance
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
Qcond
 kA(T1  T2 )

x
targets
Heat transfer in solid
targets
STOP
where
k = coefficient of thermal conductivity (watt/cm-°C)
A = cross-sectional area (cm2)
x = distance (cm)
T1 = temperature of the hotter part (°C)
T2 = temperature of the cooler part (°C)
Conduction Example
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We will take an example of a target generating 600 watts of power
and see how much heat can be removed through two different metal
target bodies of the same thickness and size.
Heat Transfer
Contents
Heat Balance
Conduction
Target
Interior
Metal
Body
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
Beam
Cooling Water
 kA(T1  T2 )
x
If we compare aluminum with nickel for the same thickness, area
and temperature differential
Typical Beam 20 MeV and 30μA = 600 watts Qcond 
QAl =(2.37watt-cm-1°K-1)(2 cm2)(100°K)/(0.5 cm)=948 watts
QNi =(0.91watt-cm-1°K-1)(2 cm2)(100°K)/(0.5 cm)=364 watts
STOP
It is clear that it would be possible to remove the heat through the
aluminum target body, but that the nickel target would continue to
heat up
Radiation
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Heat Transfer
Contents
Heat Balance
The next form of heat transfer is radiation. The amount of heat
transferred is very dependent on the temperature of the material.
The heat transferred is given by the following equation.
Conduction
Qrad = AσT4
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
STOP
where
Qrad = heat emitted as radiation (watts)
A = area of the surface (cm2)
σ = Stefan-Boltzman constant
T = absolute temperature (K)
Radiation Heat Loss
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Heat Transfer
Contents
Heat Balance
Conduction
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
STOP
The table on the right
gives the amount of
heat that can be
transferred at a given
temperature. These
calculations assume a
perfect blackbody. In
reality, the amount of
heat being transferred
must be multiplied by
the emissivity which is a
number less than one
which represents how
close the material is to a
blackbody radiator.
As can be seen, the
amount of heat given off
by this mechanism is
rather low until very high
temperatures are
reached
Temp.(°C)
Temp.(°K)
Qrad (watts)
100
373
0.0001
200
473
0.0023
300
573
0.0117
400
673
0.0371
500
773
0.0906
600
873
0.1878
700
973
0.3479
800
1073
0.5935
900
1173
0.9507
1000
1273
1.449
1100
1373
2.122
1200
1473
3.000
1300
1573
4.138
1400
1673
7.336
1500
1773
9.496
Convection
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Heat Transfer
Contents
Heat Balance
Convection is perhaps the most difficult form of heat transfer to
model accurately. Although the equation is rather simple, the
value of the film coefficient is rather difficult to estimate or
measure and depends on a great number of factors.
Conduction
Radiation
Qconv = hA(T1-T2)
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
where
Qconv = heat transferred by convection
A = surface area (cm2)
h = film coefficient (watt/cm2-K)
targets
T = temperature (K)
STOP
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Convective heat transfer for
laminar flow in tubes
•
Heat Transfer
Contents
Heat Balance
•
The key parameter in convective heat transfer is the film
coefficient h which is usually tabulated in books for various
geometries and materials
More information can be found in texts devoted to heat transfer.
Conduction
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
As an example, we can take the simple case for convective heat
transfer for laminar flow of gas inside tubes. The equation
describing this situation is given below. The equation look more
complicated and the dimensionless quantities of Reynolds
number (Re) and the Prandl modulus (Pr) are made up of
combinations of more fundamental constants. Evaluation of
these quantities and calculations on the heat removal are beyond
the scope of this presentation.
1/ 3
hx
x
 1.86(Re)1/ 3 (Pr)1/ 3  
k
L
STOP
 b

 w



0.14
Heat transfer by convection
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Heat Transfer
Contents
Heat Balance
Conduction
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
STOP
•
A key parameter in the efficiency of heat transfer will be whether
is the flow is laminar or turbulent. Turbulent flow is much more
efficient at removing heat than laminar flow.
Heat Transfer in Gas Targets
Heat Transfer
Contents
Heat Balance
Conduction
Radiation

Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets

Heat transfer in solid
targets


STOP
One of the most common
problems for the
production of
radioisotopes in gas
targets is density
reduction
As the beam is put on
target, the pressure and
temperature increase as
is shown in the figure.
The pressure rise is
correlated with the
temperature rise in the
target
The target comes to
equilibrium fairly quickly
The problem has been
approached in several
different ways.
60
25
C4 N2/O2 Pressure
Target Current
50
20
40
15
30
10
20
5
10
0
12:47
0
12:54
13:01
Time [hh:mm]
13:09
13:16
Beam current [uA]

Target pressure [bar]
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Heat Transfer in Gas Targets
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Heat Transfer
Contents



Heat Balance

Conduction
Radiation

Convection
In small volume targets, this problem is more serious
The small size means that these targets must be run at high
pressure where foil rupture is a distinct possibility
In a typical gas target, the total length is on the order of 10 to 15
cm
In order to produce carbon-11, they must be operated at about
20 atmospheres
Since the volume is small, the pressure rise is large
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
12.5 cm
STOP
Heat Transfer in Gas Targets
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
Heat Transfer
Contents
Heat Balance
Conduction
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets

Heat transfer in solid
targets

STOP
In the section on target
physics, we learned that the
beam deposits its energy in
the target in the form of heat.
This heat raises the
temperature of the target
material which in gas targets
causes an increase in the
pressure. The pressure with
the beam on over the
pressure with the bam off is
called the pressure rise ratio.
The pressure rise ratio
reaches a maximum when
there is just enough gas in
the target to stop the beam
as shown in the figure
As the pressure increases
beyond that point, the ratio
falls as the heat transfer is
improved
Heat Transfer in Gas Targets
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Heat Transfer
Contents
Heat Balance
Conduction



The pressure to stop the beam is dependent on both the energy
and the beam current
The variable is the total power deposited in the gas by the beam
As shown in the figure, the higher the total power deposited in
the target, the higher the pressure needed to stop the beam.
Radiation
Pressure to Stop the Beam
Convection
Heat transfer in gas
700
targets
600
Heat transfer in liquid
targets
Heat transfer in solid
targets
Pressure (psia)
500
400
5.4 MeV
10.7 MeV
14.1 MeV
300
200
100
0
0
STOP
5
10
15
Beam Current (A)
20
25
Heat Transfer in Gas Targets
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Heat Transfer
Contents


The fraction of heat transferred by convection is high except
very close to the wall
The fraction is relatively independent of gas temperature
Heat Balance
Conduction
Radiation
Fraction of Convection
1
Convection
Heat transfer in gas
0.8
targets
Heat transfer in liquid
0.6
targets
Heat transfer in solid
0.4
targets
Figure taken from E. Hugel PhD thesis
0.2
0
0
STOP
1
2
3
4
5
Distance from center of target
6
7
Heat Transfer in Gas Targets
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

Heat Transfer
Contents
Heat Balance
Conduction
Radiation

Density Reduction is a result of target heating
The heating is not uniform in the beam strike area as is shon in
this photograph of the light emission from the beam in a gas
target.
There is spreading of the beam as well as a non-uniform
distribution from the top to the bottom of the target.
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
Beam
0
1
2
Centimeters
STOP
Figure courtesy of S-J Heselius
3
4
5
Heat Transfer in Gas Targets
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
Heat Transfer
Contents
Heat Balance

Conduction
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
STOP

There are
convection flow
patterns set up
inside the target
These currents help
in the convective
heat transfer
The temperature
profile as measured
in a gas target
shows the nonuniform distribution
and suggests the
heat flow pattern as
shown in the figure
below.
Beam Heating in Different Gases
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Heat Transfer
Contents
Heat Balance
The pictures below show proton beams stopping in different
gases. The different colors are due to the electronic excitation of
the gas by the beam. It should also be noted that the beam
areas have different shapes depending on the thermal
characteristics of the gases.
Conduction
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
STOP
Figure courtesy of O. Solin
Liquid Targets
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Heat Transfer
Contents
•
•
Heat Balance
Conduction
•
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
STOP
•
The usual method for the production of fluorine-18 used in FDG
is from an irradiation of oxygen-18 enriched water with a beam of
protons.
The water target used for this production needs to be able to
withstand high beam currents and long irradiation times of about
2 hours.
If the removal of heat is inadequate, there can be boiling in the
target which reduces the yield of fluorine-18
The target itself is usually just a depression cut into a block of
metal or a small volume between two metal foils.
Boiling in the target
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•
Heat Transfer
Contents
Heat Balance
Conduction
•
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
•
•
There is substantial
density reduction in the
water during irradiation if
the target is boiling and if
no provision has been
made for this boiling in the
target design. This has
several consequences
The yield is reduced in the
target
Higher pressures are
created
Mechanical action may
affect surfaces
targets
Heat transfer in solid
•
targets
•
STOP
At right are views of water
targets with insufficient
heat transfer at beam
currents of 5 µA (a) and
10 µA (b)
Note the increase in the
intensity of the boiling at
the higher beam current
Beam
[18O]
H2O
Cooling
Water
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Heat Transfer
Contents
Fluorine-18 Fluoride
Production
•
Heat Balance
Conduction
Radiation
Convection
Heat transfer in gas
targets
•
Heat transfer in liquid
targets
Heat transfer in solid
•
targets
STOP
The boiling in the
water can be reduced
by raising the pressure
on the water,
effectively increasing
the density
In the figure, the light
emission is a measure
of the amount of
boiling in the target.
It deceases with
increasing pressure as
the boiling point of the
water is raised.
Fluorine-18 Fluoride Production
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Heat Transfer
Contents
Heat Balance
Conduction
Radiation
Convection
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
STOP
•
The pressure build up in
the target causes a
deformation of the front
window, increasing the
target volume
• The foil must be supported
or thicker
• The target shown on the
bottom has a support grid
to maintain the shape of the
Cooling Water
foil which keeps the volume
Target Body
constant and allows higher
Foil Support pressures to be applied to
the foil without rupturing.
Fluorine-18 Fluoride Production
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Heat Transfer
Contents
Heat Balance
•
Conduction
Radiation
Convection
•
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
Courtesy of Wake Forest
STOP
If the beam is too tightly
focused, the beam will
cause the water to boil
Use a diffuse beam for
water targets
Fluorine-18 Fluoride Production
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Another Solution: Recirculate the water
through the target
Heat Transfer
Contents
Heat Balance
PRESSURE /VENT
Conduction
Radiation
COOLANT OUT
Convection
Heat transfer in gas
TARGET BODY
BEAM
targets
Heat transfer in liquid
HEAT EXHANGERS
targets
Heat transfer in solid
targets
REGENERATIVE
TURBINE PUMP
COOLANT IN
FILL
DELIVER
REGENERATIVE TURBINE PUMP RECIRCULATING TARGET SYSTEM FOR THE
PRODUCTION OF F-18 AT BEAM POWER OF SEVERAL KILOWATTS
STOP
Heat Transfer in Solid Targets
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•
Heat Transfer
Contents
Heat Balance
Conduction
•
The main operational mode of heat transfer is conduction. Heat
loss by convection and radiation are usually very small in
comparison to loss by conduction.
The thinner the layer between the target and the cooling water,
the better the heat removal.
Radiation
Convection
Heat transfer in gas
Conductive Heat Transfer
targets
Radiative Heat Transfer
(>500°C)
Heat transfer in liquid
targets
Beam
Heat transfer in solid
targets
Convective Heat
Transfer
Backing Plate
Target
Material
Cooling water flow
STOP
Heat transfer in Thallium Target
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•
Heat Transfer
Contents
Heat Balance
Conduction
Radiation
Convection
Heat transfer in gas
•
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
•
STOP
The figure at right
represents a
Thallium Copper Copper
practical situation
Layer
b layer c layer
where there are
several layers of
conduction in the
Incident
target.
30 MeV
The beam passes
Proton
through the thallium
Cooling
layer and part way
Beam
cc Water Flow
into the copper
backing plate before Vacuum
losing all its energy
bb
aa
The temperature
profile for this target
is given on the nest
slide.
ab c
Heat transfer in Thallium Target
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Heat Transfer
Contents
Heat Balance
Tm
Conduction
Radiation
Thallium Copper
Layer
b layer
Copper
c layer
Ti
Heat transfer in gas
targets
Heat transfer in liquid
targets
Heat transfer in solid
targets
Temperature
Convection
Tb
Tc
Tw
STOP
Distance
Cooling
Water
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