Classifications

• • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
  • F28—HEAT EXCHANGE IN GENERAL
  • F28F—DETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
  • F28F13/00—Arrangements for modifying heat-transfer, e.g. increasing, decreasing
  • F28F13/18—Arrangements for modifying heat-transfer, e.g. increasing, decreasing by applying coatings, e.g. radiation-absorbing, radiation-reflecting; by surface treatment, e.g. polishing
• • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
  • F28—HEAT EXCHANGE IN GENERAL
  • F28D—HEAT-EXCHANGE APPARATUS, NOT PROVIDED FOR IN ANOTHER SUBCLASS, IN WHICH THE HEAT-EXCHANGE MEDIA DO NOT COME INTO DIRECT CONTACT
  • F28D15/00—Heat-exchange apparatus with the intermediate heat-transfer medium in closed tubes passing into or through the conduit walls ; Heat-exchange apparatus employing intermediate heat-transfer medium or bodies
• • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
  • F28—HEAT EXCHANGE IN GENERAL
  • F28F—DETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
  • F28F1/00—Tubular elements; Assemblies of tubular elements
• • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
  • F28—HEAT EXCHANGE IN GENERAL
  • F28D—HEAT-EXCHANGE APPARATUS, NOT PROVIDED FOR IN ANOTHER SUBCLASS, IN WHICH THE HEAT-EXCHANGE MEDIA DO NOT COME INTO DIRECT CONTACT
  • F28D15/00—Heat-exchange apparatus with the intermediate heat-transfer medium in closed tubes passing into or through the conduit walls ; Heat-exchange apparatus employing intermediate heat-transfer medium or bodies
  • F28D15/02—Heat-exchange apparatus with the intermediate heat-transfer medium in closed tubes passing into or through the conduit walls ; Heat-exchange apparatus employing intermediate heat-transfer medium or bodies in which the medium condenses and evaporates, e.g. heat pipes
  • F28D2015/0225—Microheat pipes
• • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
  • F28—HEAT EXCHANGE IN GENERAL
  • F28F—DETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
  • F28F2260/00—Heat exchangers or heat exchange elements having special size, e.g. microstructures
  • F28F2260/02—Heat exchangers or heat exchange elements having special size, e.g. microstructures having microchannels

Definitions

• Materials, components, and methods consistent with the present disclosure are directed to the fabrication and use of micro-scale channels with a fluid, where the micro-scale channels are arranged according to certain macroscopic configurations so as to at least partially control the temperature and flow of the fluid.
• a volume of fluid such as air
• a temperature and pressure When considered as a collection of constituent particles, comprising, for example, molecules of oxygen and nitrogen, the volume of fluid at a given temperature can also be characterized as a distribution of constituent particle speeds. This distribution can be characterized, generally, by an average speed which is understood to bear a relationship with the temperature of the fluid (as a gas, for example).
• the internal thermal energy of a fluid can provide a source of energy for applications related to heating, cooling, and the generation of fluid flow.
• embodiments can provide a system that utilizes one or more micro-scale channels (a "micro channel") configured to accommodate the flow of a fluid, and where the walls of the micro channel and the constituent particles in the fluid are configured such that collisions between the constituent particles and the walls of the micro channel are substantially specular.
• a micro channel configured to accommodate the flow of a fluid
• the micro channel can be arranged in a macroscopic configuration to provide at least one wall with at least a first wall portion that is at least approximately planar, a second wall portion that is at least approximately planar, a third wall portion that is approximately planar, a first intermediate wall portion, and a second intermediate wall portion, where a boundary of the first wall portion is contiguous with a first boundary of the first intermediate wall portion, a first boundary of the second wall portion is contiguous with a second boundary of the first intermediate wall portion, a second boundary of the second wall portion is contiguous with a first boundary of the second intermediate wall portion, and a boundary of the third wall portion is contiguous with a second boundary of the second intermediate wall portion, such that the first wall portion, the first intermediate wall portion, the second wall portion, the second intermediate wall portion, and the third wall portion form a contiguous wall of a portion of the micro channel.
• embodiments can provide that a first normal to the approximate plane defined by the first wall portion is not parallel to a second normal to the approximate plane defined by the second wall portion, and is also not parallel to a third normal to the approximate plane defined by the third wall portion, and where the second normal is also not parallel to the third normal. Further still, embodiments can provide that the angle offset between the first normal and the second normal is less than 90 degrees, and is approximately the same as the angle offset between the second normal and the third normal. Where the separation between the first wall portion and the second wall portion is at least N times the largest width of the micro channel over that separation
• the angle offset between the first normal and the second normal can be less than N/10 degrees.
• the angle offset between the second normal and the third normal can be less than N/10 degrees.
• the angle offset between the first normal and the second normal can be less than 2.5 degrees.
• the angle offset between the first normal and the second normal can be less than 5 degrees.
• embodiments can provide for the manipulation of flow and temperature of a volume of fluid, where the fluid can comprise molecules, and can allow for the population of molecular vibrational levels through enhanced heating of a volume of the fluid. Where such vibrationally-excited molecules are allowed to relax, embodiments can allow for the creation and manipulation of electromagnetic radiation emitted thereby.
• embodiments can provide for the manipulation of flow and temperature of a volume of fluid, and can provide for practical applications ranging from heating and cooling, refrigeration, electricity generation, coherent and non-coherent light emission, gas pumping, plasma and particle beam production, particle beam acceleration, chemical processes, and others.
• Figure 1 depicts an exemplary heat exchange system consistent with the present disclosure
• Figure 2 is an exemplary view of the micro channels within an accelerating element of the system of FIG. 1 ;
• Figure 3 is an exemplary illustration of a specular collision consistent with the present disclosure
• Figure 4 is an exemplary view of the micro channels within a decelerating element of the system of FIG. 1 ;
• Figure 5 depicts an exemplary view of an interface and a connection channel connecting an accelerating element and a decelerating element of the system of FIG. 1 ;
• Figure 6 depicts exemplary normal vectors to the walls of the micro channels and the angular offsets within an accelerating element of the system of FIG. 1.
• FIG. 1 depicts a view of exemplary heat exchange system 100 consistent with the present disclosure.
• Pump 150 is configured to generate and/or maintain a flow of fluid (such as air, for example) from channel 152 to channel 151.
• Arrow 1 18 indicates an exemplary fluid flow into channel 151
• arrow 128 indicates an exemplary fluid flow from channel 152.
• sub-system 1 10 can include a plurality of accelerating elements 1 15, where each accelerating element 1 15 includes micro channels (to be described further below) in fluid communication with channel 151.
• sub-system 120 can include a plurality of decelerating elements 125, where each decelerating element 125 also includes micro channels (to be described further below) in fluid communication with channel 152.
• each of micro channel of each accelerating element 1 15 can be a one-to-one correspondence between each of micro channel of each accelerating element 1 15 and each of micro channel of each decelerating element 125, where the one-to-one correspondence can be realized by ensuring that the micro channel of each accelerating element 115 is in fluid communication with a micro channel of a decelerating element 125 through interface 130.
• each pair of accelerating element 1 15 and decelerating element 125 can transfer 100 watts from the cold side (accelerating element 1 15) to the hot side (decelerating element 125).
• the dimensions of such an accelerating element 115 within such a 100 watt pair of accelerating and decelerating elements can be 100 millimeters by 100 millimeters.
• an additional heat exchange element (not shown) may be affixed to each accelerating element 1 15 and decelerating element 125.
• the additional heat exchange element can be substantially planar (such as accelerating element 1 15 and decelerating element 125 are planar) and serve to conduct heat away from decelerating element 125 into the ambient air (by providing additional surface area to dissipate such energy) or serve to conduct heat to accelerating element 115 from the ambient air (again, by providing provide additional surface area for cooling purposes).
• the additional heat exchange element can be 100 millimeters by 100 millimeters, thereby making the dimensions of the combined accelerating element 1 15 and additional heat exchange element 100 millimeters by 200 millimeters, and making the dimensions of the combined decelerating element 125 and additional heat exchange element 100 millimeters by 200 millimeters in one embodiment. In the embodiment depicted in FIG.
• system 100 can be capable of transferring 2 kilowatts from sub-system 1 10 to sub-system 120.
• the height, H, of a 3.5 kilowatt system can be approximately 300 millimeters.
• interface 130 is 10 millimeters wide (and taking into account the additional heat exchange elements described above), the overall dimensions of such a 3.5 kilowatt system can be 300 millimeters by 210 millimeters by 200 millimeters.
• the exemplary diameter of channel 151 and channel 152 can be 25 millimeters or more.
• pump 150 can be a 300-500 watt air pump.
• the air to be circulated through system 100 can be drawn from the immediate environment of system 100.
• Channel 151 is in fluid communication with channel 152 through a plurality of micro channels within the plurality of accelerating elements 1 15, interface 130, and decelerating elements 125.
• Arrow 138 depicts the flow of fluid from accelerating element 1 15 to decelerating element 125 through interface 130.
• FIG. 2 is a schematic view of micro channel 210 within an exemplary accelerating element 1 15 of FIG. 1.
• Channel 1 1 is depicted as an opening in accelerating element 1 15, and in fluid communication with micro channel 210.
• the scale of micro channel 210 as depicted in FIG. 2 is for illustration purposes.
• Micro channel 210 can be engineered to be small (i.e., with an internal surface area that may be as small as approximately 3e-l 1 m A 2 per linear micron to 6e-10 m A 2 per linear micron in a preferred embodiment, which can correspond, respectively, to a channel with an approximate diameter of 9 microns to 180 microns). As depicted in FIG.
• micro channel 210 is approximately confined to a planar region (i.e. , accelerating element 1 15) and exhibits a spiral such that a fluid entering from channel 151 enters micro channel 210, describing arcs of increasing radius until the fluid enters entering linear channel 220.
• the total length of micro channel 210 from channel 151 until reaching linear channel 220 can be approximately 10 mm to more than 1 meter.
• the width W can be 100 millimeters.
• the walls of micro channel 210 can be substantially specular, FIG.
• FIG. 3 depicts a portion of FIG. 2 in more detail.
• arrow 325 represents a velocity component of constituent particle 310 before constituent particle 310 collides with wall 305.
• Wild 305 is an enlarged view of an exemplary wall of micro channel 210, and constituent particle 310 corresponds to a constituent particle in an exemplary fluid flowing through micro channel 210 according to a preferred embodiment.
• Normal 306 represents an axis that is perpendicular to the plane defined by wall 305.
• Arrow 335 represents a velocity component of constituent particle 310 after constituent particle 310 collides with wall 305.
• a specular collision between constituent particle 310 and wall 305 is a collision in which the velocity component of constituent particle 310 parallel to plane 302 determined by local portion 301 of wall 305 proximal to the collision between constituent particle 310 and wall 305, is substantially the same before and after the collision. Moreover, during a specular collision, the speed of constituent particle 310 associated with the velocity component perpendicular to the plane of wall 305 can be substantially the same before and after the collision.
• specular collision should not be interpreted to apply to elastic collisions only.
• any one particular specular collision between constituent particle 310 and wall 305 can increase or decrease the kinetic energy of constituent particle 310 relative to the kinetic energy it possessed prior to the collision. For example, if there is a transfer of energy from wall 305 to constituent particle 310, then one would expect that the acute angle between constituent particle 310 and the plane parallel to wall 305 would be larger after the collision than before the collision. Likewise, if there is a transfer of energy from constituent particle 310 to wall 305, then one would expect that the acute angle between constituent particle 310 and the plane parallel to wall 305 would be smaller after the collision than before the collision.
• the temperature of the fluid comprising a plurality of constituent particles is different from the temperature of the wall, there can be a transfer of internal energy from the fluid to the wall, or from the wall to the fluid (depending upon which is at the higher temperature).
• a transfer of energy from a fluid flowing through micro channel 210 to wall 305 or from wall 305 to the fluid flowing through micro channel 210 can occur predominantly through the average change in the speed of constituent particle 310 associated with the change in its velocity component perpendicular to the plane of wall 305 during the collision.
• a change in the velocity component of constituent particle 310 during the collision can change the overall speed of constituent particle 310 as a result of the collision process.
• the surface of the walls of micro channel 210 can include any suitable material configured for specular collisions, such as silicon, tungsten, gold, platinum, and diamond. Such a surface may be deposited onto micro channel 210 using any of a variety of MEMs fabrication techniques, including, but not limited to, sputtering and evaporative deposition.
• diamond smooth films with grains as small as 100 nm and 20nm Ra roughness can be grown onto channel walls.
• diamond can be preferable as a result of its melting point (i.e., approx. 4000 K at one atmosphere) and as a result of its hardness (i.e., alO in Mohs scale for hardness).
• the surface of the walls of micro channel 210 can also include tungsten carbide, glass and pyrolytic graphite— in part at least because of its high thermal conductivity of 1700 W/mK.
• Micro channel 210 can also include a diamond nanoparticle film on pyrolytic graphite substrate.
• FIG. 4 is a schematic view of micro channel 410 within an exemplary decelerating element 125 of FIG. 1.
• Channel 152 is depicted as an opening in decelerating element 125, and in fluid communication with micro channel 410.
• the scale of micro channel 410 as depicted in FIG. 4 is for illustration purposes.
• Micro channel 410 can be engineered to be small (i.e., with an internal surface area that may be as small as approximately 3e-l 1 m A 2 per linear micron to 6e-10 m A 2 per linear micron in a preferred embodiment, which can correspond, respectively, to a channel with an approximate diameter of 9 microns to 180 microns).
• FIG. 1 As depicted in FIG.
• micro channel 410 is approximately confined to a planar region (i.e., accelerating element 125) and exhibits a spiral such that a fluid entering from linear channel 420 enters micro channel 410, describing arcs of decreasing radius until the fluid enters entering channel 152.
• the total length of micro channel 410 from linear channel 420 until reaching channel 152 can be approximately 10 mm to more than 1 meter.
• the width W can be 100 millimeters.
• the walls of micro channel 410 can be substantially specular.
• the surface of the walls of micro channel 410 can include any suitable material configured for specular collisions, such as silicon, tungsten, gold, platinum, and diamond. Such a surface may be deposited onto micro channel 410 using any of a variety of MEMs fabrication techniques, including, but not limited to, sputtering and evaporative deposition.
• diamond smooth films with grains as small as 100 nm and 20nm Ra roughness can be grown onto channel walls.
• diamond can be preferable as a result of its melting point (i.e., approx. 4000 K at one atmosphere) and as a result of its hardness (i.e., alO in Mohs scale for hardness).
• the surface of the walls of micro channel 410 can also include tungsten carbide, glass and pyrolytic graphite— in part at least because of its high thermal conductivity of 1700 W/mK.
• Micro channel 410 can also include a diamond nanoparticle film on pyrolytic graphite substrate
• FIG. 5 depicts connection 510 between linear channel 220 and linear channel 420 through interface 130.
• channel 151 can be kept at a relatively high pressure, and channel 152 can be kept at a relatively low pressure, so as to allow for the flow of fluid through the plurality of accelerating elements 1 15 and decelerating elements 125.
• the channel 151 can exhibit a pressure of approximately 1 atm or more, and channel 152 can exhibit a pressure that is approximately 0.528 of the pressure of channel 151.
• FIG. 6 depicts an expanded view of micro channel 210
• fluid that is at the inner portion of micro channel 210 i.e., proximal to inflow opening 601
• Tj the temperature of the fluid at inflow opening 601
• the constituent particles can be represented by a distribution of speeds, the average speed of which is proportional to temperature.
• the constituent particles of a fluid moving through inflow opening 601 into micro channel 210 can exhibit a velocity that has its component parallel to direction 650 larger than its component perpendicular to direction 650. Consequently, the fluid passing through micro channel 210 acquires a flow velocity that is predominantly parallel to direction 650.
• the kinetic energy that is associated with the flow of fluid in direction 650 is drawn from the internal thermal energy of fluid, which was at Ti before it entered inflow opening 601.
• Tj the temperature of fluid (in a frame that is stationary with the velocity of flow) in micro channel 210 can be lower than Tj, which we will designate as T ⁇ - Where T2 is also less than the temperature of wall 610 (which we will designate as T w ) of micro channel 210, then the fluid in micro channel 210 can cool the material comprising accelerating element 1 15.
• Micro channel 210 is configured to enhance the effect this temperature change has on the fluid passing through micro channel 210 in at least three ways. Specifically, where wall 610 and the constituent particles in the fluid are configured such that collisions between wall 610 and the constituent particles are substantially specular, then such collisions—which are a means of transferring energy between wall 610 and the fluid— will have a minimal effect on the overall flow of fluid through micro channel 210.
• Micro channel 210 is configured to enhance the effect of cooling by selectively avoiding the effect of non- specular collisions.
• the outer wall of micro channel 210 is configured as a generally increasing spiral
• the specular scattering of a constituent particle off of successive portions of the wall of micro channel 210 can convert a portion of the velocity component which was perpendicular to the direction of flow through micro channel 210 (i.e., a radial velocity component) to a component parallel to the direction of flow through micro channel 210.
• a radial velocity component a portion of the velocity component which was perpendicular to the direction of flow through micro channel 210
• the spiral grows larger along the path of micro channel 210, the constituent particles can undergo less and less collisions with the wall (along the path of micro channel 210) as the fluid travels towards linear channel 220.
• micro channel 210 is engineered to be small (i.e., with an internal surface area that may be as small as approximately 3e-l 1 m A 2 per linear micron to 6e-10 m A 2 per linear micro in a preferred embodiment), then the ratio of the surface area presented by the wall of micro channel 210 to a given volume of fluid in any region within micro channel 210 is relatively large (i.e., where the volume of the fluid enclosed by the above surface is approximately 8e-17 m A 3 per linear micron to 3e-15 m A 3 per linear micron). Because the surface area presented by the wall of micro channel 210 to a volume of fluid is a primary means of energy exchange between the walls and the fluid 115, this can tend to maximize the overall energy exchange interaction between the fluid and micro channel 210.
• a constituent particle can enter inflow opening 601 with a component predominantly parallel to direction 650, and undergoes a specular collision with local region 610 of the wall of micro channel 210, and acquires a velocity component in direction 651.
• the constituent particle may now undergo a specular collision with local region 615 of the wall of micro channel 210, and acquires a velocity component in direction 652.
• the constituent particle can undergo a specular collision with local region 620 of the wall of micro channel 210, and acquire a further velocity component along the general direction of micro channel 210.
• Angle ⁇ corresponds to the angular offset between normal 625 and normal 630.
• Angle a corresponds to the angular offset between normal 630 and normal 635.
• the angle offset between the first normal and the second normal can be less than N/10 degrees.
• the angle offset between the second normal and the third normal can be less than N/10 degrees.
• the angle offset between the first normal and the second normal is less than 2.5 degrees.
• the angle offset between normal 625 and normal 630 can be less than 5 degrees.
• the angle offset between normal 630 and normal 635 can be less than 5 degrees.
• accelerating element 1 15 can be cooled by the passage of a fluid, where the fluid is configured to exhibit specular collisions with the walls of micro channel 210. Moreover, a fluid passing through accelerating element 115 can be accelerated: i.e., when the fluid arrives at linear channel 220, the velocity components of the fluid's constituent particles are predominantly along the direction of linear channel 220 leading to connection 510.
• TKE translational kinetic energy
• the translational kinetic energy (TKE) of the constituent particles in a fluid i.e., molecules in a molecular beam
• the percentage of TKE transferred from the fluid to the surface can be dependent upon the velocity of the fluid, the smoothness of the surface, the internal kinetic energy of the constituent particles in the fluid and the kinetic energy density of the surface.
• a fluid as a molecular beam
• RMS root mean square
• micro channel 410 is configured as a spiral that presents successively smaller radii to a fluid passing from linear channel 420 to channel 152.
• a high velocity fluid arriving from connection 510 to linear channel 420 can undergo more and more collisions with the wall (along the path of micro channel 210) as the fluid travels towards channel 152.
• micro channel 410 in decelerating element 125 are configured to cause the constituent particles in the fluid passing through micro channel 410 to undergo specular collisions.
• a molecular beam in a MEMS device (such as accelerating element 1 15 and decelerating element 125) that can be used for cooling electronics, refrigeration, air conditioning and other applications can exhibit high RMS velocities.
• a molecular beam composed of room air with an RMS velocity of 2,000 meters per second has the translational kinetic energy of still air at over 4,000 K, a temperature that is well beyond the melting point of most materials.
• a refrigeration system's hot-side heat exchanger preferably would have the ability to extract precise quantities of both translational and internal kinetic energy from the accelerated molecular beam without damage to a heat exchanger composed of conventional materials, such as aluminum and thermally conductive plastics with a melting point of only 933 K or less.
• a gradual reduction in the translational kinetic energy level of a fast molecular beam with a high energy density relative to that of the surface allows for energy transfer to the surface to occur over an extended surface length. This is a desirable method of extracting the energy from a molecular beam when a more concentrated extraction would damage the channel or raise the temperature of a device beyond practical limits.
• a hot side heat exchanger in a refrigeration system that is made of aluminum with a melting point of 933 K can be used to transfer extracted energy from a high energy molecular beam with an RMS velocity of 2,000 m/s or more to the outside environment without damaging the channels of the heat exchange device and not overheating any portion of the outer surface of the heat exchanger device.
• virtually any conformal channel material including ceramics and thermally conductive polymers can be used as channels and thermal packaging in hot-side heat exchanger applications.
• MEMS device channel designs can permit a molecular beam to experience such a series of collisions with an arc of gradually decreasing radius.
• channels configured as spirals with an initially large radii that gradually reduce over length to a smaller radii, and a spiraling molecular beam progressing through an attenuated channel using the centrifugal force of the spiral motion to remain in close proximity to the surface at all diameters of the channel are two examples of such designs.
• Any gradual energy extraction design would serve to facilitate the conversion of the beams kinetic energy to infrared and optical wavelengths of light even when the average energy content of the beam, if abruptly slowed or stopped could produce higher frequency emissions.
• designs that facilitate more abrupt energy extraction methods can of course be applied and are within the scope of this disclosure.
• a heat exchanger consistent with the present disclosure that gradually absorbs the kinetic energy from a high energy molecular beam can be heated as kinetic energy from the molecular beam is absorbed by the heat exchanger's inner channel surfaces.
• the heat exchanger and molecular beam channel surfaces can be maintained with any desired delta T (change in temperature) with the ambient surroundings with conventional means of heat transfer from the heat exchanger to the ambient environment.
• Heat exchangers that evenly extract energy from a molecular beam along a channel surface can very nearly approximate nearly isothermal conditions.
• Energy extracted from an equilibrated molecular beam can be used to precisely quantize the modes of energy in a channel cavity. Emissions of light with a predictable energy are provided by Plank's radiation formula that is equal to Planck's constant times the frequency. Plank's radiation formula can be used to calculate the average energy of any desired frequency of light emitted from a MEMS device channel.
• Continuous coherent spontaneous emission can also occur when a collimated and equilibrated molecular beam transfers highly resolved quantities of energy to the surface of a channel.
• Channel transparency to the emitted frequency of light can allow for the light to escape the channel for practical purposes that include any laser application and conversion of light energy to electric current as would occur by a photodiode array in the flux path of the photonic emissions from the channels.
• the voltage of the current can be related to the bandgap energy of the channel material.
• Coherent emissions can permit photodiodes with a narrow bandwidth to efficiently convert extracted energy from a molecular beam to an electric current of a desired voltage.
• Coherent and in-phase emissions from several channels can be readily achieved from a series of parallel channel surfaces on a MEMS device using ultra-flat wafer surfaces. Energy density of coherent emissions can be accomplished with sub- micron gaps between parallel channels.
• MEMS devices with optically and UV transparent channels with excellent optical homogeneity can be fabricated using a variety of materials. Silicon can provide suitable transparent optical homogeneity to some infrared frequencies, as can germanium and Amtir. Sapphire, yttria, and yttrium alumina garnet provide excellent optical transmission of infrared as well.
• Optical glass can be used for UV and optical wavelengths.
• the architecture or micro channel 210 and micro channel 410 can reduce pumping power requirements. Due at least in part to such architecture, the values associated with the coefficient of performance (“COP") can be 10 or higher.
• values of COP can be 10 or higher by operating at different pressures.
• the power required per constituent particle (or molecule) is a function of the pressure ratio, and not the pressure.
• a pumping cost per constituent particle will remain the same, but a higher density flow if constituent particles (i.e., a higher density molecular beam) can provide higher heat transfer rates and could produce a COP of 10 or more.

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