TECHNICAL FIELD OF THE INVENTION
[0001] This invention relates in general to cooling techniques and, more particularly, to
a method and apparatus for controlling cooling of a system that generates a substantial
amount of heat through use of coolant at a subambient pressure.
BACKGROUND OF THE INVENTION
[0002] Some types of electronic circuits use relatively little power, and produce little
heat. Circuits of this type can usually be cooled satisfactorily through a passive
approach, such as convection cooling. In contrast, there are other circuits that consume
large amounts of power, and produce large amounts of heat. One example is the circuitry
used in a phased array antenna system.
More specifically, a modern phased array antenna system can easily produce 25 to 30
kilowatts of heat, or even more. One known approach for cooling this circuitry is
to incorporate a refrigeration unit into the antenna system. However, suitable refrigeration
units are large, heavy, and consume many kilowatts of power in order to provide adequate
cooling. For example, a typical refrigeration unit may weigh about 200 pounds, and
may consume about 25 to 30 kilowatts of power in order to provide about 25 to 30 kilowatts
of cooling. Although refrigeration units of this type have been generally adequate
for their intended purposes, they have not been satisfactory in all respects.
[0003] In this regard, the size, weight and power consumption characteristics of these known
refrigeration systems are all significantly larger than desirable for an apparatus
such as a phased array antenna system. And given that there is an industry trend toward
even greater power consumption and heat dissipation in phased array antenna systems,
continued use of refrigeration-based cooling systems would involve refrigeration systems
with even greater size, weight and power consumption, which is undesirable. In such
systems, it is often important that stable cooling is achieved during both startup
and when the cooled device is subjected to wide swings in required cooling capacities.
SUMMARY OF THE INVENTION
[0004] According to one embodiment of the invention a method for controlling cooling of
a heat-generating structure disposed in an environment having an ambient pressure
includes providing a fluid coolant and reducing the pressure of the coolant to a subambient
pressure at which the coolant has a boiling temperature less than a temperature of
the heat-generating structure. The method further includes boiling and vaporizing
coolant to absorb heat from the heat-generating structure by bringing the coolant
into thermal communication with the heat generating structure. The method also includes
measuring a parameter indicative of a pressure of the coolant and adjusting the pressure
of the coolant in response to control the cooling of the heat-generating structure.
[0005] Some embodiments of the invention may provide numerous technical advantages. Other
embodiments may realize some, none, or all of these advantages. For example, according
to one embodiment, the temperature of a heat-generating device, such as a phase array
antenna, may be maintained at a desired temperature through a control system that
feeds back an indication of pressure of a coolant. Such an approach avoids complex
control schemes that must take into account thermal delay associated with feeding
back the temperature of the heat-generating device. Such an approach may avoid instability
problems and provides a stable thermal environment during startup and when heat load
environments change.
[0006] Other advantages may be readily ascertainable by those skilled in the art.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] A more complete understanding of embodiments of the invention will be apparent from
the detailed description taken in conjunction with the accompanying drawings in which:
FIGURE 1 is a block diagram of an apparatus that includes a phased array antenna system
and an associated cooling arrangement that embodies aspects of the present invention;
FIGURE 2 is a block diagram of the apparatus of FIGURE 1 showing additional details
related to the control of the system of FIGURE 1;
FIGURE 3 is a block diagram of the system of FIGURE 2 showing yet additional details
related to the control of the system of FIGURE 1; and
FIGURE 4 is a diagram of an example linear actuated bellows that may be used in conjunction
with the teachings of the present invention.
DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS OF THE INVENTION
[0008] Example embodiments of the present invention and their advantages are best understood
by referring to FIGURES 1-4 of the drawings, like numerals being used for like and
corresponding parts of the various drawings.
FIGURE 1 is a block diagram of an apparatus 10 that includes a phased array antenna
system 12. The antenna system 12 includes a plurality of identical modular parts that
are commonly known as slats, two of which are depicted at 14 and 16. A feature of
the present invention involves techniques for controlling cooling the slats 14 and
16, so as to remove appropriate amounts of heat generated by electronic circuitry
therein.
The electronic circuitry within the antenna system 12 has a known configuration, and
is therefore not illustrated and described here in detail. Instead, the circuitry
is described only briefly here, to an extent that facilitates an understanding of
the present invention. In particular, the antenna system 12 includes a two-dimensional
array of not-illustrated antenna elements, each column of the antenna elements being
provided on a respective one of the slats, including the slats 14 and 16. Each slat
includes separate and not-illustrated transmit/receive circuitry for each antenna
element. It is the transmit/receive circuitry which generates most of the heat that
needs to be withdrawn from the slats. The heat generated by the transmit/receive circuitry
is shown diagrammatically in FIGURE 1, for example by the arrows at 18 and 20.
[0009] Each of the slats is configured so that the heat it generates is transferred to a
tube 22 or 24 extending through that slat. Alternatively, the tube 22 or 24 could
be a channel or passageway extending through the slat, instead of a physically separate
tube. A fluid coolant flows through each of the tubes 22 and 24. As discussed later,
this fluid coolant is a two-phase coolant, which enters the slat in liquid form. Absorption
of heat from the slat causes part or all of the liquid coolant to boil and vaporize,
such that some or all of the coolant leaving the slats 14 and 16 is in its vapor phase.
This departing coolant then flows successively through a separator 26, a heat exchanger
28, a pump 30, and a respective one of two orifices 32 and 34, in order to again reach
the inlet ends of the tubes 22 and 24. The pump 30 causes the coolant to circulate
around the endless loop shown in FIGURE 1. In the embodiment of FIGURE 1, the pump
30 consumes only about 0.1 kilowatts to 2.0 kilowatts of power.
[0010] Separator 26 separates the vaporized portion of the liquid coolant flowing through
tubes 22 and 24 from the unvaporized liquid portion. The vaporized portion is provided
to heat exchanger 28, and the liquid portion is provided at separator pump 36.
[0011] Separator pump 36 receives the liquid portion of the coolant that has not vaporized
in tubes 22 and 24 circulates this fluid back through tubes 22 and 24 via orifices
32 and 34.
[0012] The orifices 32 and 34 facilitate proper partitioning of the coolant among the respective
slats, and also help to create a large pressure drop between the output of the pump
30 and the tubes 18 and 20 in which the coolant vaporizes. It is possible for the
orifices 32 and 34 to have the same size, or to have different sizes in order to partition
the coolant in a proportional manner which facilitates a desired cooling profile.
[0013] Ambient air or liquid 38 is caused to flow through the heat exchanger 28, for example
by a not-illustrated fan of a known type. Alternatively, if the apparatus 10 was on
a ship, the flow 38 could be ambient seawater. The heat exchanger 28 transfers heat
from the coolant to the air flow 38. The heat exchanger 28 thus cools the coolant,
thereby causing any portion of the coolant which is in the vapor phase to condense
back into its liquid phase.
The liquid coolant exiting the heat exchanger 28 is supplied to the expansion reservoir
40. Since fluids typically take up more volume in their vapor phase than in their
liquid phase, the expansion reservoir 40 is provided in order to take up the volume
of liquid coolant that is displaced when some or all of the coolant in the system
changes from its liquid phase to its vapor phase. The amount of the coolant that is
in its vapor phase can vary over time, due in part to the fact that the amount of
heat being produced by the antenna system 12 will vary over time, as the antenna system
operates in various operational modes.
[0014] Pressure controller 42 maintains the coolant at a desired subambient pressure in
portions of the cooling loop downstream of the orifices 32 and 34 and upstream of
the pump 30, as described in greater detail in conjunction with FIGURES 2 and 3. Typically,
the ambient air pressure will be that of atmospheric air, which at sea level is 14.7
pounds per square inch area (psia). When antenna system 12 (or any other heat-generating
device) undergoes transient heat loads, this subambient pressure may need to be adjusted
to allow greater or lesser amounts of heat transfer from slats 18 and 20 at a desired
temperature. According to the teachings of the invention, slats 18 and 20 are maintained
at a desired temperature by feeding back the pressure of the coolant as it exits passageways
22 and 24. This pressure is indicative of the temperature at slats 18 and 20. In response,
pressure controller 42 may respond by raising or lowering the pressure of the coolant,
which affects the boiling temperature of the coolant and therefore the rate of heat
transfer. By feeding back the coolant pressure, as opposed to the temperature of the
slats, associated thermal delay is eliminated from the control loop, permitting direct
control of pressure without taking into account the thermal delay.
[0015] Turning now in more detail to the coolant, one highly efficient technique for removing
heat from a surface is to boil and vaporize a liquid which is in contact with the
surface. As the liquid vaporizes, it inherently absorbs heat. The amount of heat that
can be absorbed per unit volume of a liquid is commonly known as the latent heat of
vaporization of the liquid. The higher the latent heat of vaporization, the larger
the amount of heat that can be absorbed per unit volume of liquid being vaporized.
[0016] The coolant used in the disclosed embodiment of FIGURE 1 is water. Water absorbs
a substantial amount of heat as it vaporizes, and thus has a very high latent heat
of vaporization. However, water boils at a temperature of 100ºC at atmospheric pressure
of 14.7 psia. In order to provide suitable cooling for an electronic apparatus such
as the phased array antenna system 12, the coolant needs to boil at a temperature
in the range of approximately 60ºC. When water is subjected to a subambient pressure
of about 3 psia, its boiling temperature decreases to approximately 60ºC. Thus, in
the embodiment of FIGURE 1, the orifices 32 and 34 permit the coolant pressure downstream
from them to be substantially less than the coolant pressure between the pump 30 and
the orifices 32 and 34.
[0017] Water flowing from the pump 30 to the orifices 32 and 34 has a temperature of approximately
60ºC to 65ºC, and a pressure in the range of approximately 15 psia to 100 psia. After
passing through the orifices 32 and 34, the water will still have a temperature of
approximately 60ºC to 65ºC, but will have a much lower pressure, in the range about
2 psia to 8 psia. Due to this reduced pressure, some or all of the water will boil
as it passes through and absorbs heat from the tubes 22 and 24, and some or all of
the water will thus vaporize. After exiting the slats, the water vapor (and any remaining
liquid water) will still have the reduced pressure of about 2 psia to 8 psia.
[0018] When this subambient coolant water reaches the heat exchanger 28, heat will be transferred
from the water to the forced air flow 38. The air flow 38 has a temperature less than
a specified maximum of 55ºC, and typically has an ambient temperature below 40ºC.
As heat is removed from the water coolant, any portion of the water which is in its
vapor phase will condense, such that all of the coolant water will be in liquid form
when it exits the heat exchanger 28. This liquid will have a temperature of approximately
60ºC to 65ºC, and will still be at the subambient pressure of approximately 2 psia
to 8 psia. This liquid coolant will then flow to the pump 30 with a tee connection
prior to the expansion reservoir 40. The pump 30 will have the effect of increasing
the pressure of the coolant water, to a value in the range of approximately 15 psia
to 100 psia, as mentioned earlier.
[0019] It will be noted that the embodiment of FIGURE 1 operates without any refrigeration
system. In the context of high-power electronic circuitry, such as that utilized in
the phased array antenna system 12, the absence of a refrigeration system can result
in a very significant reduction in the size, weight, and power consumption of the
structure provided to cool the antenna system.
[0020] As mentioned above, the coolant used in the embodiment of FIGURE 1 is water. However,
it would alternatively be possible to use other coolants, including but not limited
to methanol, a fluorinert, a mixture of water and methanol, or a mixture of water
and ethylene glycol (WEGL). These alternative coolants each have a latent heat of
vaporization less than that of water, which means that a larger volume of coolant
must be flowing in order to obtain the same cooling effect that can be obtained with
water. As one example, a fluorinert has a latent heat of vaporization which is typically
about 5% of the latent heat of vaporization of water. Thus, in order for a fluorinert
to achieve the same cooling effect as a given volume or flow rate of water, the volume
or flow rate of the fluorinert would have to be approximately 20 times the given volume
or flow rate of water.
[0021] Despite the fact that these alternative coolants have a lower latent heat of vaporization
than water, there are some applications where use of one of these other coolants can
be advantageous, depending on various factors, including the amount of heat which
needs to be dissipated. As one example, in an application where a pure water coolant
may be subjected to low temperatures that might cause it to freeze when not in use,
a mixture of water and ethylene glycol could be a more suitable coolant than pure
water, even though the mixture has a latent heat of vaporization lower than that of
pure water.
[0022] FIGURE 2 is a block diagram of the apparatus 10 of FIGURE 1 showing additional details
related to the control of apparatus 10. FIGURE 2 additionally illustrates a pressure
transducer 44 that measures the pressure of the coolant within tubes 22 and 24. Thus,
pressure transducer 44 measures the pressure at which coolant within tubes 22 and
24 boils. Alternatively, any transducer capable of providing an indication of the
pressure at which coolant within tubes 22 and 24 boils may be utilized. One example
of such an alternative transducer is a temperature transducer, because the pressure
at which coolant in tubes 22 and 24 boils may be determined by the temperature of
such coolant. Temperature transducer 44 provides a signal 46 indicative of the pressure
coolant in tubes 22 and 24 to controller 42. Controller 42 controls pressure of coolant
in tubes 22 and 24 by either introducing additional coolant or removing coolant from
the portion of the control loop between tubes 22 and 24 and heat exchange pump 30.
In this particular example, expansion reservoir 40 includes a pump motor 48 having
a reversible shaft 50 driving a positive displacement charge pump 52. If it is determined
that the pressure in tubes 22 and 24 needs to be increased, controller 42 commands
(via command 60) the pump motor 48 to drive the positive displacement charge pump
52 to provide additional coolant to the coolant loop. If it is desired that the coolant
pressure in tubes 22 and 24 be lowered, controller 42 commands pump motor 48 to drive
positive displacement discharge pump 52 to remove coolant from the coolant loop and
store it in a holding reservoir 54. Controller 42 also receives a level indication
56 indicative of the level of holding reservoir 54. Pump meter feeds back its speed
to controller 42 via signal 62.
[0023] According to the teachings of the invention, either removing or increasing coolant
within the coolant loop effectively changes the pressure of the coolant in tubes 22
and 24. This change in pressure results in a desired change in temperature of phased
array antenna system 12. In one embodiment, controller 42 also receives a signal 58
indicative of the heat load of base array antenna system 12. Because the relationship
between the temperature of antenna array 12 and the pressure within tubes 22 and 24
depends upon the amount of heat being generated by antenna array 12, this signal may
be utilized by controller 42 to determine whether the pressure in the cooling system
loop should be increased or decreased. However, controller 42 may be appropriately
programmed to provide the correct pressure adjustment based upon anticipated heat
loads without receiving an indication of the actual heat load of antenna system 12.
By controlling the temperature of antenna array system 12 through feedback and control
of the pressure of the coolant in tubes 22 and 24, control loop complications associated
with the thermal delay involved in feeding back temperature (and associated stability
problems) can be avoided.
[0024] FIGURE 3 is a block diagram of the system of FIGURE 1 showing yet even further details
related to the control of apparatus 10. In this example, controller 42 receives a
plurality of additional signals. These signals include a slat temperature level set
64, an ambient temperature 66, an ambient air pressure 68, slat temperatures 70, heat
exchanger temperature and pressures 70, and a fan speed 74. In addition, controller
42 also is shown as generating a plurality of additional signals, including a separator
pump control signal 76, a heat exchange pump control signal 78, and a fan control
signal 80. Slat temperature level signal 64 presents a desired temperature for slats
18 and 20. In this particular embodiment, the slat temperature level is set and controller
42 utilizes the desired set level in determining any appropriate changes to the pressure
of the coolant in tubes 22 and 24 to maintain this temperature. Such calculations
may also include the heat load indicator 58. The ambient air temperature signal 66
is used to set the speed of a fan 82 to ensure that the correct air mass flow rate
through heat exchanger 28 occurs for a specific heat load relative to the temperature
of the ambient air entering the heat exchanger 28.
[0025] The ambient air pressure may vary as a function of the operating altitude of apparatus
10. Signal 68, which is indicative of the ambient air pressure is used to set the
fan 82 motor speed to ensure the correct air mass flow through the heat exchanger
regardless of altitude. The ambient air pressure signal 68 is also used to compensate
for pressure variations in the holding reservoir 54 until an optimum pressure is maintained.
[0026] The heat exchanger temperatures, represented by numeral 72, at the heat exchanger
inlet and outlet are provided to controller 42 to indicate the performance of the
heat exchanger and to see if the heat exchanger 28 is reaching its maximum capacity,
as indicated by the outlet temperature being close to or the same as the inlet temperature.
The associated heat exchanger pressures, also represented by reference numeral 72,
is provided to controller 42 on both sides of the heat exchanger 38. These pressures
are used to determine the air mass flow rate through the heat exchanger and determine
the desired fan motor speed. In addition, these pressures are used with the measured
fan speed to assess if the heat exchanger 28 is getting clogged with trash or debris.
[0027] Fan control signal 80 and the associated fan speed 74 are provided by and to controller
42 to control the fan speed to regulate the air mass flow through heat exchanger 28.
Slat temperature level set 64 is a signal provided to controller 42 that informs controller
42 that it should raise the saturation pressure in the loop to raise its boiling temperature
during periods of low heat load. This is performed to hold the temperature of the
slat assembly constant over a range of heat loads.
[0028] Controller 42 also generates halt and status reporting signals, represented collectively
by reference numeral 84. Signals 84 communicate the operational status of the cooling
system and reports whether the cooling system is operating within set limits based
on the heat load being removed. Controller 42 also reports if any alarm or shutdown
limits have been reached.
[0029] FIGURE 4 is a diagram of an example linear actuated bellows-like reservoir 86 that
may be used as an alternative approach for moving fluid into or out of the control
loop to control the loop's pressure. Reservoir 86 includes a linear actuator 88 that
may pull or push on a free end 90 of the bellows 92 to evacuate the loop or to let
coolant flow back into the loop. Reservoir 86 combines the functions of holding reservoir
54 and dispositive displacement charge pump 52.
[0030] Although the present invention has been disclosed in the context of a phased array
antenna system, it will be recognized that it can be utilized in a variety of other
contexts, including but not limited to a power converter assembly, or certain types
of directed energy weapon (DEW) systems. Although the present invention and its advantages
have been described in detail, it should be understood that various changes, substitutions,
and alterations can be made therein without departing from the spirit and scope of
the invention as defined by the appended claims.
1. An apparatus (10), comprising a heat-generating structure (12) disposed in an environment
having an ambient pressure and a cooling system for removing heat from said heat-generating
structure (12), said cooling system including:
a fluid coolant;
structure that reduces a pressure of the coolant to a subambient pressure at which
the coolant has a boiling temperature less than a temperature of the heat-generating
structure (12);
structure that directs a flow of the coolant in the form of a liquid in a manner causing
the liquid coolant to be brought into thermal communication with the heat-generating
structure (12), the heat from the heat-generating structure (12) causing the liquid
coolant to boil and vaporize so that the coolant absorbs from the heat-generating
structure (12) as the coolant changes state;
a pressure transducer (44) disposed within the passageway (22, 24) and operable to
measure a pressure of the coolant in the passageway (22,24);
a controller (42) operable to receive the pressure of the coolant in the passageway
(22, 24) and generate a control signal based at least in part on a desired temperature
of a portion of the heat-generating structure and the amount of heat generated by
the heat-generating structure;
a positive displacement pump (52) responsive to the control signal operable to adjust
a pressure of the coolant to control cooling of the heat-generating structure (12);
wherein the heat-generating structure (12) includes a passageway (22,24) having
a surface that extends along a length of the passageway (22,24); and
wherein heat (18,20) generated by the heat-generating structure (12) is supplied
to the surface of the passageway (22,24) along the length of the surface, the portion
of the coolant flowing through the passageway and engaging the surface so as to absorb
heat from the surface.
2. A method for controlling cooling of a heat-generating structure (12) disposed in an
environment having an ambient pressure, comprising:
providing a fluid coolant;
reducing a pressure of the coolant to a subambient pressure at which the coolant has
a boiling temperature less than a temperature of the heat-generating structure (12);
boiling and vaporizing the coolant to absorb heat from the heat-generating structure
(12) by bringing the coolant into thermal communication with the heat-generating structure
(12);
measuring a parameter indicative of a pressure of the coolant; and
adjusting the pressure of the coolant in response to the measuring to control the
cooling of the heat-generating structure.
3. A method according to claim 2, wherein adjusting the pressure of the coolant comprises
adjusting the pressure of the coolant based at least in part on a heat load of the
heat-generating structure (12).
4. A method according to claim 2, or claim 3, wherein the parameter indicative of a pressure
of the coolant is one of pressure of the coolant and a temperature of the coolant.
5. A method according to any of claims 2 to 4, wherein adjusting the pressure of the
coolant comprises adjusting the pressure of the coolant by a positive displacement
pump (52).
6. A method according to any one of claims 2 to 5, wherein adjusting the pressure of
the coolant comprises adjusting the pressure of the coolant by a linear actuated bellows
(86).
7. A method according to any one of claims 2 to 6, including:
configuring the heat-generating structure (12) to include a passageway (22,24) having
a surface that extends along a length of the passageway (22,24);
supplying the heat (18,20) generated by the heat generating structure to the surface
of the passageway (22,24) along the length thereof; and
causing the portion of the coolant to flow through the passageway (22,24) and engage
the surface.
8. A method according to any one of claims 2 to 7, wherein adjusting the pressure of
the coolant comprises adjusting the pressure of the coolant based in part on a desired
temperature of a portion of the heat-generating structure (12).
9. A method according to claim 7, wherein the parameter indicative of a pressure of the
coolant is a parameter indicative of a pressure of the coolant in the passageway (22,24).
10. A method according to any one of claims 2 to 9, including selecting for use as the
coolant one of water, methanol, a fluorinert, and a mixture of water and ethylene
glycol.
11. A method according to any one of claims 2 to 10, including circulating the coolant
through a flow loop.
12. A method according to claim 11, including configuring the loop to include a heat exchanger
(28) for removing heat from said coolant so as to condense the coolant.
13. A method according to claim 12, including causing the heat exchanger (28) to transfer
heat from the coolant to a further medium having an ambient temperature that is less
than the boiling temperature of the coolant at the pressure of the coolant.
14. An apparatus (10), comprising heat-generating structure (12) disposed in an environment
having an ambient pressure, and a cooling system for removing heat from the heat-generating
structure (12), the cooling system including:
a fluid coolant;
structure that reduces a pressure of the coolant to a subambient pressure at which
the coolant has a boiling temperature less than a temperature of the heat-generating
structure (12);
structure that directs a flow of the coolant in a manner causing the liquid coolant
to be brought into thermal communication with the heat-generating structure (12),
the heat from the heat-generating structure (12) causing the liquid coolant to boil
and vaporize so that the coolant absorbs heat from the heat-generating structure (12)
as the coolant changes state;
a transducer (44) in operative communication with the coolant and operable to measure
a parameter indicative of a pressure of the coolant;
a controller (42) operable to receive the parameter indicative of a pressure of the
coolant and generate a control signal; and
structure responsive to the control signal that is operable to adjust a pressure of
the coolant to control cooling of the heat-generating structure (12).
15. An apparatus (10) according to claim 14, wherein the controller (42) is further operable
to generate a control signal based at least in part on a desired temperature of the
heat-generating structure (12).
16. An apparatus (10) according to claim 14, or claim 15, wherein the controller (42)
is further operable to generate a control signal based at least in part on a heat
load of the heat-generating structure (12).
17. An apparatus (10) according to any one of claims 14 to 16, wherein the transducer
(44) is one of a pressure transducer and a temperature transducer.
18. An apparatus (10) according to any one of claims 14 to 17,
wherein the heat-generating structure (12) includes a passageway (22,24) having
a surface that extends along a length of the passageway (22,24); and
wherein heat (18,20) generated by the heat generating structure (12) is supplied
to the surface of the passageway (22,24) along the length of the surface, the portion
of the coolant flowing through the passageway (22,24) and engaging the surface so
as to absorb heat from the surface.
19. An apparatus (10) according to claim 18, wherein the transducer (44) is a pressure
transducer disposed in the passageway (22,24).
20. An apparatus (10) according to any one of claims 14 to 19, wherein the structure responsive
to the control signal is a positive displacement pump (52).
21. An apparatus (10) according to any one of claims 14 to 19, wherein the structure responsive
to the control signal is a linear actuated bellows (86).
22. An apparatus (10) according to any one of claims 14 to 21, wherein the structure that
directs a flow of the coolant is configured to circulate the coolant through a flow
loop.
23. An apparatus (10) according to Claim 22, including a heat exchanger (28) for removing
heat from the coolant flowing through the loop so as to condense the coolant to a
liquid.
24. An apparatus (10) according to Claim 23, wherein the heat exchanger (28) transfers
heat from the coolant to a further medium having an ambient temperature less than
the boiling temperature of the coolant at the pressure of the coolant.