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WO2017117088A1 - Dispositif de transfert de chaleur fractal - Google Patents

Dispositif de transfert de chaleur fractal Download PDF

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Publication number
WO2017117088A1
WO2017117088A1 PCT/US2016/068641 US2016068641W WO2017117088A1 WO 2017117088 A1 WO2017117088 A1 WO 2017117088A1 US 2016068641 W US2016068641 W US 2016068641W WO 2017117088 A1 WO2017117088 A1 WO 2017117088A1
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Prior art keywords
heatsink
fractal
heat exchange
heat
heat transfer
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Alexander Poltorak
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Priority claimed from US14/984,756 external-priority patent/US10041745B2/en
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F28—HEAT EXCHANGE IN GENERAL
    • F28F—DETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
    • F28F7/00—Elements not covered by group F28F1/00, F28F3/00 or F28F5/00
    • 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
    • F28D21/00—Heat-exchange apparatus not covered by any of the groups F28D1/00 - F28D20/00
    • F28D2021/0019—Other heat exchangers for particular applications; Heat exchange systems not otherwise provided for
    • F28D2021/0028—Other heat exchangers for particular applications; Heat exchange systems not otherwise provided for for cooling heat generating elements, e.g. for cooling electronic components or electric devices
    • F28D2021/0029—Heat sinks
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F28—HEAT EXCHANGE IN GENERAL
    • F28F—DETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
    • F28F2210/00—Heat exchange conduits
    • F28F2210/02—Heat exchange conduits with particular branching, e.g. fractal conduit arrangements
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F28—HEAT EXCHANGE IN GENERAL
    • F28F—DETAILS OF HEAT-EXCHANGE AND HEAT-TRANSFER APPARATUS, OF GENERAL APPLICATION
    • F28F2215/00—Fins
    • F28F2215/10—Secondary fins, e.g. projections or recesses on main fins

Definitions

  • This invention relates to the field of heatsinks or items that transfer heat between a concentrated source or sink and a fluid.
  • a heat sink is a term for a component or assembly that transfers heat generated within a solid material to a fluid or gas medium, such as air or a liquid.
  • a heat sink is typically designed to increase the surface area in contact with the cooling fluid or gas surrounding it, such as the air.
  • Approach air velocity, choice of material, fin (or other protrusion) design and surface treatment are some of the design factors which influence the thermal resistance, i.e. thermal performance, of a heat sink. See, en.wikipedia.org/wiki/Heat_sink.
  • Heatsinks operate by removing heat from an object to be cooled into the surrounding air, gas or liquid through convection and radiation.
  • Convection occurs when heat is either carried passively from one point to another by fluid motion (forced convection) or when heat itself causes fluid motion (free convection). When forced convection and free convection occur together, the process is termed mixed convection.
  • Radiation occurs when energy, for example in the form of heat, travels through a medium or through space and is ultimately absorbed by another body.
  • Thermal radiation is the process by which the surface of an object radiates its thermal energy in the form of electromagnetic waves.
  • Infrared radiation from a common household radiator or electric heater is an example of thermal radiation, as is the heat and light (IR and visible EM waves) emitted by a glowing incandescent light bulb.
  • Thermal radiation is generated when heat from the movement of charged particles within atoms is converted to electromagnetic radiation.
  • a heatsink tends to decrease the maximum temperature of the exposed surface, because the power is transferred to a larger volume. This leads to a possibility of diminishing return on larger heatsinks, since the radiative and convective dissipation tends to be related to the temperature differential between the heatsink surface and the external medium.
  • the heatsink is oversized, the efficiency of heat shedding is poor. If the heatsink is undersized, the object may be insufficiently cooled, the surface of the heatsink dangerously hot, and the heat shedding not much greater than the object itself absent the heatsink.
  • a heat sink transfers thermal energy from a higher temperature to a lower temperature fluid or gas medium, by a process such as radiation, convection, and diffusion.
  • the fluid medium is frequently air, but can also be water or in the case of heat exchangers, oil, and refrigerants.
  • Fourier's law of heat conduction simplified to a one-dimensional form in the direction x, shows that when there is a temperature gradient in a body, heat will be transferred from the higher temperature region to the lower temperature region.
  • the rate at which heat is transferred by conduction, ⁇ 3 ⁇ 4 is proportional to the product of the temperature gradient and the cross-sectional area through which heat is transferred:
  • m is the first derivative of mass over time, i.e., the air mass flow rate in kg/s.
  • the most common heat sink material is aluminum. Chemically pure aluminum is not used in the manufacture of heat sinks, but rather aluminum alloys.
  • Aluminum alloy 1050A has one of the higher thermal conductivity values at 229 W/m » K. However, it is not recommended for machining, since it is a relatively soft material.
  • Aluminum alloys 6061 and 6063 are the more commonly used aluminum alloys, with thermal conductivity values of 166 and 201 W/m » K, respectively. The aforementioned values are dependent on the temper of the alloy.
  • Copper is also used since it has around twice the conductivity of aluminum, but is three times as heavy as aluminum. Copper is also around four to six times more expensive than aluminum, but this is market dependent. Aluminum has the added advantage that it is able to be extruded, while copper cannot. Copper heat sinks are machined and skived.
  • Another method of manufacture is to solder the fins into the heat sink base.
  • Another heat sink material that can be used is diamond. With a thermal conductivity value of 2000 W/m » K, it exceeds that of copper by a factor of five. In contrast to metals, where heat is conducted by delocalized electrons, lattice vibrations are responsible for diamond's very high thermal conductivity. For thermal management applications, the outstanding thermal conductivity and diffusivity of diamond are essential. CVD diamond may be used as a sub-mount for high-power integrated circuits and laser diodes.
  • Composite materials also can be used. Examples are a copper-tungsten pseudoalloy, AlSiC (silicon carbide in aluminum matrix), Dymalloy (diamond in copper-silver alloy matrix), and E-Material (beryllium oxide in beryllium matrix). Such materials are often used as substrates for chips, as their thermal expansion coefficient can be matched to ceramics and semiconductors.
  • Fin efficiency is one of the parameters which make a higher thermal conductivity material important.
  • a fin of a heat sink may be considered to be a flat plate with heat flowing in one end and being dissipated into the surrounding fluid as it travels to the other.
  • the combination of the thermal resistance of the heat sink impeding the flow and the heat lost due to convection, the temperature of the fin and, therefore, the heat transfer to the fluid will decrease from the base to the end of the fin.
  • This factor is called the fin efficiency and is defined as the actual heat transferred by the fin, divided by the heat transfer were the fin to be isothermal (hypothetically the fin having infinite thermal conductivity). Equations 5 and 6 are applicable for straight fins.
  • spreading resistance Another parameter that concerns the thermal conductivity of the heat sink material is spreading resistance.
  • Spreading resistance occurs when thermal energy is transferred from a small area to a larger area in a substance with finite thermal conductivity. In a heat sink, this means that heat does not distribute uniformly through the heat sink base.
  • the spreading resistance phenomenon is shown by how the heat travels from the heat source location and causes a large temperature gradient between the heat source and the edges of the heat sink. This means that some fins are at a lower temperature than if the heat source were uniform across the base of the heat sink. This non-uniformity increases the heat sink's effective thermal resistance.
  • a pin fin heat sink is a heat sink that has pins that extend from its base.
  • the pins can be, for example, cylindrical, elliptical or square/geometric polygonal.
  • a second type of heat sink fin arrangement is the straight fin. These run the entire length of the heat sink.
  • a variation on the straight fin heat sink is a cross cut heat sink.
  • a straight fin heat sink is cut at regular intervals but at a coarser pitch than a pin fin type.
  • Pin fin heat sink performance is significantly better than straight fins when used in their intended application where the fluid flows axially along the pins rather than only tangentially across the pins. See, Kordyban, T., Hot air rises and heat sinks - Everything you know about cooling electronics is wrong, ASME Press, NY 1998.
  • flared fin heat sink Another configuration is the flared fin heat sink; its fins are not parallel to each other, but rather diverge with increasing distance from the base. Flaring the fins decreases flow resistance and makes more air go through the heat sink fin channel; otherwise, more air would bypass the fins. Slanting them keeps the overall dimensions the same, but offers longer fins.
  • Forghan, et al. have published data on tests conducted on pin fin, straight fin and flared fin heat sinks. See, Forghan, F., Goldthwaite, D., Ulinski, M., Metghalchi, M., Experimental and Theoretical Investigation of Thermal Performance of Heat Sinks, ISME, May. 2001. They found that for low approach air velocity, typically around 1 m/s, the thermal performance is at least 20% better than straight fin heat sinks.
  • Lasance and Eggink also found that for the bypass configurations that they tested, the flared heat sink performed better than the other heat sinks tested. See, Lasance, C.J.M and Eggink, H.J., A Method to Rank Heat Sinks in Practice: The Heat Sink Performance Tester, 21st IEEE SEMI -THERM Symposium 2001.
  • the heat transfer from the heatsink is mediated by two effects: conduction via the coolant, and thermal radiation.
  • the surface of the heatsink influences its emissivity; shiny metal absorbs and radiates only a small amount of heat, while matte black is a good radiator. In coolant-mediated heat transfer, the contribution of radiation is generally small.
  • a layer of coating on the heatsink can then be counterproductive, as its thermal resistance can impair heat flow from the fins to the coolant.
  • Finned heatsinks with convective or forced flow will not benefit significantly from being colored.
  • the heatsink surface finish can play an important role. Matte-black surfaces will radiate much more efficiently than shiny bare metal. The importance of radiative vs. coolant-mediated heat transfer increases in situations with low ambient air pressure (e.g. high-altitude operations) or in vacuum (e.g. satellites in space).
  • Frigus Primore in "A Method for Comparing Heat Sinks Based on Reynolds Analogy," available at www.frigprim.com/downloads/Reynolds_analogy_heatsinks.PDF, last accessed April 28, 2010.
  • Frigus Primore in "A Method for Comparing Heat Sinks Based on Reynolds Analogy," available at www.frigprim.com/downloads/Reynolds_analogy_heatsinks.PDF, last accessed April 28, 2010.
  • This article notes that for, plates, parallel plates, and cylinders to be cooled, it is necessary for the velocity of the surrounding fluid to be low in order to minimize mechanical power losses.
  • larger surface flow velocities will increase the heat transfer efficiency, especially where the flow near the surface is turbulent, and substantially disrupts a stagnant surface boundary layer.
  • Frigus Primore discusses the use of parallel plates in chimney heat sinks.
  • One purpose of this type of design is to combine more efficient natural convection with a chimney. Primore notes that the design suffers if there is laminar flow (which creates a re-circulation region in the fluid outlet, thereby completely eliminating the benefit of the chimney) but benefits if there is turbulent flow which allows heat to travel from the parallel plates into the chimney and surrounding fluid.
  • Liu's heatsink includes channels through which fluids would flow in order to exchange heat with the heatsink.
  • Y.J. Lee "Enhanced MicroChannel Heat Sinks Using Oblique Fins," IPACK 2009- 89059, similarly discusses a heat sink comprising a "fractal-shaped microchannel based on the fractal partem of mammalian circulatory and respiratory system.”
  • Lee's idea similar to that of Liu, is that there would be channels inside the heatsink through which a fluid could flow to exchange heat with the heatsink.
  • the stated improvement in Lee's heatsink is (1) the disruption of the thermal boundary layer development; and (2) the generation of secondary flows.
  • Prior art heatsink designs have traditionally concentrated on geometry that is Euclidian, involving structures such as the pin fins, straight fins, and flares discussed above.
  • Electromagnetic Compatibility 1997. 10th (1-3 Sep 1997), pp: 119 - 124, discloses a fractal antenna which also serves as a heatsink in a radio frequency transmitter.
  • a fractal is defined as "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.”
  • fractals involve largely self-repeating patterns, each of which serves to increase the surface area in three-dimensional fractals (perimeter in two-dimensional fractals), three dimensional fractals in theory are characterized by infinite surface area (and two-dimensional fractals are characterized by infinite perimeter).
  • three dimensional fractals in theory are characterized by infinite surface area (and two-dimensional fractals are characterized by infinite perimeter).
  • the scale of the smallest features may be 3-25 iterations of the algorithm. Less than three recursions, and the fractal nature is not apparent, while present manufacturing technologies limit the manufacture of objects with a large range of feature scales.
  • Fractal theory is related to chaos theory. See, en.wikipedia.org/wiki/Chaos_theory, expressly incorporated herein by reference. See, Sui, Y., Teo, C. J., Lee, P. S., Chew, Y. T., & Shu, C. (2010). Fluid flow and heat transfer in wavy microchannels. International Journal of Heat and Mass Transfer, 53(13), 2760-2772; Garibaldi, Dott Ing Pietro. Single-phase natural circulation loops: effects of geometry and heat sink temperature on dynamic behavior and stability. Diss. Ph. D. Thesis, 2008; Fichera, A., and A. Pagano.
  • fractal structures provide a plurality of concave regions or cavities, providing pockets of separated flow which can generate self-sustaining oscillations and acoustic resonance. These pockets serve to reduce the acoustic resonance in turbulent flowing fluid (as compared to flat or Euclidian surfaces), thus allowing for more effective heat transfer between the fractal structure and the surrounding fluid, thereby making the fractal structure ideal for a heatsink.
  • this same wave theory may be applied to fractal heatsinks, especially with respect to the interaction of the heat transfer fluid with the heatsink.
  • the heat conduction within a solid heatsink is typically not modeled as a wave (though modem thought applies phonon phenomena to graphene heat transport), the fluid surrounding the heating certainly is subject to wave phenomena, complex impedances, and indeed the chaotic nature of fluid eddies may interact with the chaotic surface configuration of the heatsink.
  • the efficiency of capturing electric waves in a fractal antenna achieved by Cohen, in some cases can be translated into an efficiency transferring heat out of an object to be cooled in a fractal heatsink as described herein.
  • a phonon is a quasiparticle characterized by the quantization of the modes of lattice vibration of solid crystal structures. Any vibration by a single phonon is in the normal mode of classical mechanics, meaning that the lattice oscillates in the same frequency. Any other arbitrary lattice vibration can be considered a superposition of these elementary vibrations. Under the phonon model, heat travels in waves, with a wavelength on the order of 1 ⁇ . In most materials, the phonons are incoherent, and, therefore, on macroscopic scales, the wave nature of heat transport is not apparent or exploitable.
  • thermodynamic properties of a solid are directly related to its phonon structure.
  • the entire set of all possible phonons combine in what is known as the phonon density of states which determines the heat capacity of a crystal.
  • a crystal lattice lies in its ground state, and contains no phonons.
  • a lattice at a non-zero temperature has an energy that is not constant, but fluctuates randomly about some mean value. These energy fluctuations are caused by random lattice vibrations, which can be viewed as a gas-like structure of phonons or thermal phonons.
  • thermal phonons can be created and destroyed by random energy fluctuations.
  • phonon transport phenomena are apparent at macroscopic levels, which make phonon impedance measurable and useful.
  • a graphene sheet were formed to resonate at a particular phonon wavelength, the resonant energy would not be emitted.
  • the graphene sheet were configured using a fractal geometry, the phonon impedance would be well controlled over a broad range of wavelengths, with sharp resonances at none, leading to an efficient energy dissipation device.
  • a thermally responsive technology such as a memory metal actuator (which may be passive or active), or other active or passive element, to change the configuration of the heatsink under various conditions.
  • a thermostat is provided to shunt flow around the radiator when the engine is cool.
  • a variable geometry heatsink according to the present technology may have an external surface exposed to an unconstrained heat transfer medium, such as air. See, Baurle, R. A., and D. R. Eklund. "Analysis of dual-mode hydrocarbon scramjet operation at Mach 4-6.5.” Journal of
  • thermodynamic model of the system For example, in one embodiment, a thermodynamic model of the system
  • the heat sink may operate passively, without flows induced by an active device to induce flow in the thermal transfer medium.
  • radiative heat transfer may be important, as well as thermally-induced convection.
  • the active device to induce flow in the thermal transfer medium may induce maximum flows, and the heatsink configured for minimal turbulence with laminar flows where possible.
  • the system may assume a configuration which is optimized according to a cost function, which may involve the effect of heat/temperature on the heat source, energy consumed by the active device to induce flow in the thermal transfer medium, noise resulting from induced flow, etc.
  • a cost function which may involve the effect of heat/temperature on the heat source, energy consumed by the active device to induce flow in the thermal transfer medium, noise resulting from induced flow, etc.
  • efficiency may be improved by allowing the heatsink to assume a variable configuration. Since the optimum heatsink configuration depends on, e.g., ambient temperature, humidity, atmospheric pressure, heat load, air flow rate, gravitational vector with respect to the heatsink, etc., the model should explore the range of combinations of the device to induce thermal transfer medium flow, the variable geometry, and to a lesser extent, control over the heat source.
  • An example of the later is that for a given power dissipation, it may be more efficient to have thermal cycles reaching a maximum temperature than a constant temperature. During the cycles, the geometry may change
  • the geometry may optimally change during or in anticipation of temperature changes.
  • An example here is that as the heat source produces a heat peak, the heat diffuses over time through a solid heatsink material. There is a lag, and so the temperature of the heat source is different that the temperature of the heatsink, and the heatsink itself has variations in temperature at different positions.
  • there is a single actuator which controls the entire heatsink though this is not a limitation, and there may be multiple actuators to control different parts of the heatsink independently or semi- independently.
  • the device to induce thermal transfer medium flow may have a variable flow rate, and also may have multiple independently controlled portions.
  • the device to induce thermal transfer medium flow may also increase activity. This, in turn, can reduce the temperature of various portions of the heatsink, depending on the relationship of the device to induce thermal transfer medium flow and the variable geometry heatsink.
  • the entire system may operate in a phased cyclic or dynamic manner, with asynchronous maxima and minima of the various functions.
  • a heatsink may be provided for a microprocessor having multiple cores.
  • the device to induce thermal transfer medium flow may be off, or at a low flow rate.
  • the heatsink in this case optimally has the greatest spread for radiative and passive convective cooling.
  • the processor itself may have the option of distributing the load over multiple cores, and spatially spreading the heat dissipation, or concentrating the load in a single core which may get hot. Since temperature differentials increase heat flow, the concentrated heat source may selectively transfer heat to sub-portion of the heatsink, and thus that portion may be able to efficiently shed the heat under the passive or low energy cost state.
  • the processor As the load further increases, the processor as a whole typically becomes thermally limited, and as a result, the entire die or processor complex is treated as a unitary source, spreading heat to all elements of the heatsink.
  • the temperature is low, and the system would seek to operate in the most efficient state of the device to induce thermal transfer medium flow. This may include laminar flow over the heat dissipating elements of the heatsink.
  • the heat increases, and as a result, the device to induce thermal transfer medium flow must increase its flow rate. At this point, a compromise may be made, between minimum energy cost (and thus a minimization of the energy to drive the device to induce thermal transfer medium flow), and effective heat dissipation.
  • the heatsink may be configured to induce turbulence in the medium flow around it. This, in turn, increases the resistance to flow, but reduces the boundary layer effect.
  • a fractal physical relationship of element of the heatsink may act to reduce peak acoustic emission with respect to frequency.
  • the interaction of the elements of the heatsink may be further optimized to achieve higher efficiency.
  • this mode is one traditionally analyzed as the maximum capacity of the heatsink and device to induce thermal transfer medium flow system, and as such would typically assume or nearly assume a traditional optimized geometry.
  • the maximum heart dissipation configuration may be somewhat different than a parallel plate heatsink, for example. Note that not all regions of the heatsink need to operate within the same regime at the same time, and even under a steady state heat load, may vary cyclically, randomly or chaotically (over a relevant timescale).
  • the term "chaotically” is intended to assume its technical meaning under chaos and fractal theory, and not adopt a lay interpretation.
  • randomly is intended to encompass true randomness, pseudorandom variations, and deterministic changes that over the relevant timescale have statistical characteristics that model randomness within an acceptable margin of error, the acceptability relating to achieving a suitable regime of operation.
  • the random features may be used to advantage.
  • the device to induce thermal transfer medium flow may be subject to a tinsel type flow disruptor, which in some regimes appears to be a random variation in air flow speed, direction, vortex, etc. While this may increase noise, it also can create persistent disruptions in boundary layers, even on smooth and regular heatsink elements. That is, either the heatsink geometry and the device to induce thermal transfer medium flow, or both, may have fractal or chaotic tendencies.
  • the geometry involves branching elements, to increase surface area of the elements.
  • An actuator may be used to alter angles or even to open and close branches.
  • a heatsink formed of a shape memory alloy (SMA) (such as Nitinol)
  • SMA shape memory alloy
  • Such a device may be thermally processed to have characteristic shape changes at temperature transitions, and indeed, the composition of the alloy may be controlled during fabrication to produce a variety of transition temperatures. Therefore, a 3D heatsink may be provided which inherently changes shape through a series of transitions as the temperature is increased and decreased.
  • the changes tend to be monotonic with increasing temperature, though by engineering the angles and physical configuration, the actual physical shape and heat dissipation properties may assume a non-monotonic function.
  • the branch points are formed of SMA, and the bulk be formed of a high thermal conductivity material, such as copper and/or silver, or to a lesser extent, aluminum.
  • actuators which may be SMA, solenoids, or otherwise, are controlled to change the position of repositionable elements.
  • independent control can be exercised which is not dependent on temperature, but typically, the number of controlled elements is more constrained due to manufacturing and control feasibility issues.
  • the actuators may alter a spacing, angle, position, or engagement of heat sink elements. When a set of regularly spaced and sized elements are controlled according to a constant or spectrally-defined distribution, this can be controlled to operate within highly predictable regimes.
  • the resulting fluid dynamics will likely require a statistical flow (e.g., Monte Carlo) analysis, rather than a simplifying presumption of static function. This will especially be the case if the thermal timeconstants of the heat flow from the heat source, to the heatsink, and then to the heat transfer fluid, are near or within the range of timeconstants of the turbulence or chaotically varying flows of the heat transfer fluid.
  • a statistical flow e.g., Monte Carlo
  • the thermal heat transfer timeconstants are longer than the turbulent or chaotic variation timeconstants, and therefore this meeting this presumption requires either generating low frequency turbulent or chaotic variations of the heat transfer fluid medium, or making the heatsink (and perhaps other elements) with short timeconstants, such as using short/thin/small elements, using phonon transport phenomena, or other means.
  • the timeconstant(s) of the thermal transfer medium flow is much shorter than the relevant thermal timconstants of the heat source and heatsink, and the purpose of the turbulent or chaotic disruption is to alter the convective heat transfer characteristics of the heatsink, such as reducing the boundary layers or making them dynamically changing over time and space.
  • planar heatsinks such as used in antenna designs.
  • the present technology may have corresponding effect to that discussed above, especially where a device to induce thermal transfer medium flow is provided to cool a generally planar heatsink system.
  • any heatsink in actuality must be considered in three dimensions, and the fact that it may have expanses of a thin uniform thickness layer does not defeat use of three dimensional analysis to understand its functioning and optimization.
  • a variable geometry is typically infeasible.
  • there a planar heatsink structure serves a secondary purpose, such as an antenna, the physical configuration is constrained by this other purpose.
  • the device to induce thermal transfer medium flow is typically not so constrained, and therefore provides a controllable variable. Further, in many cases, the requirement for "thinness" of a 2D heatsink does not preclude texturing on an exposed surface, which itself may have a fractal variation.
  • a variable geometry may be achieve by altering flow characteristics of thermal transfer medium flow, and for example, a deflector may be controlled to change a direction of impingement.
  • a surface of a heatsink can have anisotropic features, which respond differently to different flow direction.
  • the efficiency of the fan can be optimized other than by fan speed alone, to provide another control variable. This may have particular importance where the fan itself is highly constrained, and cannot simply be made oversized, or where energy efficiency is an overriding concern.
  • the technology is not limited to cooling gas fluids, and may encompass liquids. Typically, cooling liquids are recycled, and therefore operate within a physically closed system.
  • Use of fractal branching fluid networks is known, but various principles discussed above, such as variable geometry, variations in flow rate over different regimes of operation, different directions of flow over surfaces, and intentional induction of chaotic flow patterns may be adopted top advantage.
  • Many fractal designs are characterized by concave regions or cavities. See, for example, Figs. 2 and 3. While sets of concavities may be useful in improving aerodynamics and fluid dynamics to increase turbulence, if they are disposed in a regular array, they will likely produce an acoustic resonance, and may have peaks in a fluid impedance function.
  • the multiscale nature of a fractal geometric design will allow the system to benefit from the concavities, while avoiding a narrowly tuned system.
  • a fractal-shaped heatsink for the purpose of dissipating heat.
  • Benefits of a fractal heatsink, over a traditional heatsink having a Euclidian geometry may include: (1) the fractal heatsink has a greater surface area, allowing for more exposure of the hot device to the surrounding air or liquid and faster dissipation of heat; and (2) due to the plethora of concave structures or cavities in fractal structures, the fractal heatsink is better able to take advantage of turbulent flow mechanics than a traditional heatsink, resulting in heat entering and exiting the heatsink more quickly (3) acoustic properties, especially in forced convection systems.
  • the technology provides, according to various embodiments, a heatsink to cool an object through conduction (diffusion), convection and radiation. See,
  • a fractal branching network can advantageously be used to reduce reflections at discontinuities and decrease complex impedance.
  • a fractal geometry may assist in optimizing the cross-section area and surface area (for radiation and convective transfer) under given constraints.
  • a fractal geometry may provide acoustic benefits, by distributing acoustic energy across a wide band, and thus ensuring "whiteness" of a noise spectrum and absence of sharp resonances. Further, a fractal geometry may provide high or maximum surface area, and produce turbulent cooling medium flows to reduce boundary later effects. Depending on the constraints imposed, a fractal geometry may also provide chimneys or defined flow paths through a network of elements, and thus control an impedance of coolant flow, though generally, a fractal branching network will produce higher flow impedance than corresponding smooth regular surfaces.
  • a textured surface or configuration (as might be achieved by a fractal geometry) can actually increase laminar flow some distance away from the surface, by creating a controlled disturbed intermediate layer.
  • a fractal geometry can avoid parallel surfaces which can limit radiative dissipation.
  • a parallel plate heatsink will radiatively transfer heat between the plates, and thus limit the effectiveness of radiation from the bulk of the surfaces as an effective dissipation mechanism.
  • irregular angles and surface branches may help to avoid reabsorption of thermal radiation by the elements of the heatsink, and thus enhance radiative dissipation.
  • heatsink elements For the smallest heatsink elements, on the order of 10-100 nm, the focus of the heat transfer may be on radiation rather than convection. Electron emission and ionization may also be relevant. Larger heatsink elements, approximately >1 mm in size, will generally rely on convection as the primary form of heat transfer. In a fractal geometry system, elements spanning these regimes may be provided in a single system.
  • the heatsink comprises a heat exchange device with a plurality of heat exchange elements having a fractal variation therebetween.
  • a heat transfer fluid such as air, water, or another gas or liquid, is induced to flow through the heat exchange device.
  • the heat transfer fluid has turbulent portions.
  • the fractal variation in the plurality of heat exchange elements substantially reduces the narrow band acoustic resonance resulting from fluid flow around the heatsink elements as compared to a heatsink having a linear or
  • a heat transfer fluid air, gas or liquid
  • the fractal shape of the heatsink would generally provide a range of physical size parameters, and thus for any given flow rate, would typically induce turbulent flow over some portion of a fractal geometry array.
  • a fractal geometry facilitates optimization over a range of parameters.
  • turbulence or turbulent flow is a flow regime characterized by chaotic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and flow velocity in space and time. See, en. wikipedia. org/wiki/Turbulence; www. scholarpedia. org/article/Turbulence, expressly incorporated herein by reference.
  • Flow in which the kinetic energy dies out due to the action of fluid molecular viscosity is called laminar flow. While there is no theorem relating the non-dimensional Reynolds number (Re) to turbulence, flows at Reynolds numbers larger than 5000 are typically (but not necessarily) turbulent, while those at low Reynolds numbers usually remain laminar.
  • turbulence can first be sustained if the Reynolds number is larger than a critical value of about 2040; moreover, the turbulence is generally interspersed with laminar flow until a larger Reynolds number of about 4000.
  • Reynolds number a critical value of about 2040
  • unsteady vortices appear on many scales and interact with each other. Drag due to boundary layer skin friction increases. The structure and location of boundary layer separation often changes, sometimes resulting in a reduction of overall drag.
  • laminar-turbulent transition is not governed by Reynolds number, the same transition occurs if the size of the object is gradually increased, or the viscosity of the fluid is decreased, or if the density of the fluid is increased.
  • Turbulence is characterized by the following features: Irregularity: Turbulent flows are always highly irregular. For this reason, turbulence problems are normally treated statistically rather than deterministically. Turbulent flow is chaotic. However, not all chaotic flows are turbulent. Diffusivity: The readily available supply of energy in turbulent flows tends to accelerate the homogenization (mixing) of fluid mixtures. The characteristic which is responsible for the enhanced mixing and increased rates of mass, momentum and energy transports in a flow is called "diffusivity”. Rotationality: Turbulent flows have non-zero vorticity and are characterized by a strong three-dimensional vortex generation mechanism known as vortex stretching.
  • turbulent flow can be realized as a superposition of a spectrum of flow velocity fluctuations and eddies upon a mean flow.
  • the eddies are loosely defined as coherent patterns of flow velocity, vorticity and pressure.
  • Turbulent flows may be viewed as made of an entire hierarchy of eddies over a wide range of length scales and the hierarchy can be described by the energy spectrum that measures the energy in flow velocity fluctuations for each length scale (wavenumber).
  • the scales in the energy cascade are generally uncontrollable and highly non-symmetric. Nevertheless, based on these length scales these eddies can be divided into three categories.
  • Integral length scales Largest scales in the energy spectrum. These eddies obtain energy from the mean flow and also from each other. Thus, these are the energy production eddies which contain most of the energy. They have the large flow velocity fluctuation and are low in frequency. Integral scales are highly anisotropic. The maximum length of these scales is constrained by the characteristic length of the apparatus.
  • Kolmogorov length scales Smallest scales in the spectrum that form the viscous sublayer range. In this range, the energy input from nonlinear interactions and the energy drain from viscous dissipation are in exact balance. The small scales have high frequency, causing turbulence to be locally isotropic and homogeneous.
  • Taylor microscales The intermediate scales between the largest and the smallest scales which make the inertial subrange. Taylor microscales are not dissipative scale but pass down the energy from the largest to the smallest. Taylor microscales play a dominant role in energy and momentum transfer in the wavenumber space.
  • the Russian mathematician Andrey Kolmogorov proposed the first statistical theory of turbulence, based on the aforementioned notion of the energy cascade (an idea originally introduced by Richardson) and the concept of self-similarity (e.g., fractal relationships).
  • the small scale turbulent motions are statistically isotropic (i.e. no preferential spatial direction could be discerned).
  • the large scales of a flow are not isotropic, since they are determined by the particular geometrical features of the boundaries (the size characterizing the large scales will be denoted as L).
  • Kolmogorov introduced a second hypothesis: for very high Reynolds numbers the statistics of small scales are universally and uniquely determined by the kinematic viscosity (v) and the rate of energy dissipation ( ⁇ ). With only these two parameters, the unique length (Kolmogorov length scale)that can be formed by dimensional analysis is
  • a turbulent flow is characterized by a hierarchy of scales through which the energy cascade takes place. Dissipation of kinetic energy takes place at scales of the order of Kolmogorov length ⁇ , while the input of energy into the cascade comes from the decay of the large scales, of order L. These two scales at the extremes of the cascade can differ by several orders of magnitude at high Reynolds numbers. In between there is a range of scales (each one with its own characteristic length r) that has formed at the expense of the energy of the large ones. These scales are very large compared with the Kolmogorov length, but still very small compared with the large scale of the flow (i.e., ⁇ « ⁇ « ⁇ ).
  • the efficiency of heat transfer may be increased as compared to a heat exchange device having a linear or Euclidian geometric variation between several heat exchange elements, at least over certain regimes of operation.
  • the heat exchange device may include a highly conductive substance whose heat conductivity exceeds 850 W/(m K). Examples of such superconductors include graphene, diamond, and diamond-like coatings. Altematively, the heat exchange device may include carbon nanotubes. At such high thermal conductivities, phonon heat transport may be at play.
  • the heatsink could include a heat transfer surface that is connected to the heat exchange device and is designed to accept a solid to be cooled.
  • a connector that is designed to connect with a solid to be cooled in at least one point.
  • there are at least three connectors serving to keep the solid and the heatsink in a fixed position relative to one another.
  • the connector could be a point connector, a bus, a wire, a planar connector or a three-dimensional connector.
  • the heatsink has an aperture or void in the center thereof designed to accept a solid to be cooled.
  • the heatsink may also be integral to the heat source, or attached by other means.
  • This heatsink is typically intended to be used to cool objects, and may be part of a passive or active system.
  • Modern three-dimensional laser and liquid printers can create objects such as the heatsinks described herein with a resolution of features on the order of about 16 ⁇ , making it feasible for those of skilled in the art to use such fabrication technologies to produce objects with a size below 25 cm.
  • larger heatsinks such as car radiators, can be manufactured in a traditional manner, designed with an architecture of elements having a fractal configuration.
  • a liquid-to-gas heat exchanger may be provided in which segments of fluid flow conduit have a fractal relationship over three levels of recursion, i.e., paths with an average of at least two branches.
  • Other fractal design concepts may be applied concurrently, as may be appropriate.
  • Yet another embodiment of the invention involves a method of cooling a solid by connecting the solid with a heatsink.
  • the heatsink comprises a heat exchange device having a plurality of heat exchange elements having a fractal variation therebetween.
  • a heat transfer fluid having turbulent portions is induced to flow with respect to the plurality of heat exchange elements.
  • the fractal variation in the plurality of heat exchange elements serves to substantially reduce narrow band resonance as compared to a corresponding heat exchange device having a linear or Euclidean geometric variation between a plurality of heat exchange elements.
  • a preferred embodiment provides a surface of a solid heatsink, e.g., an internal or external surface, having fluid thermodynamical properties adapted to generate an asymmetric pattern of vortices over the surface over a range of fluid flow rates.
  • the range may comprise a range of natural convective fluid flow rates arising from use of the heatsink to cool a heat-emissive object.
  • the range may also comprise a range of flow rates arising from a forced convective flow (e.g., a fan) over the heatsink.
  • the heatsink may cool an unconstrained or uncontained fluid, generally over an external surface of a heatsink, or a constrained or contained fluid, generally within an internal surface of a heatsink.
  • Fig. 1 shows a set of governing equations for a parallel plate heatsink.
  • Fig. 2 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is placed adjacent to the object to be cooled.
  • Fig. 3 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is placed either adjacent to or surrounding the object to be cooled.
  • Fig. 4 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a Quadratic Koch Island.
  • Fig. 5A illustrates the basis for the Quadratic Koch Island.
  • Fig. 5B illustrates a Quadratic Koch Island obtained after application of one iteration.
  • Fig. 5C illustrates a Quadratic Koch Island obtained after application of several iterations.
  • Fig. 6 illustrates the total length of all the fractal segments of a Quadratic Koch
  • Fig. 7A illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a modified Koch Snowflake.
  • Fig. 7B illustrates the basis for generating the modified Snowflake.
  • Fig. 8A illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a Sierpinski Carpet.
  • Fig. 8B illustrates the basis for generating the Sierpinski Carpet.
  • Fig. 9 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a Mandelbox.
  • Fig. 10 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a Sierpinski tetrahedron.
  • Fig. 11 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a Dodecaedron fractal.
  • Fig. 12 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a Icosahedron flake.
  • Fig. 13 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on an Octahedron flake.
  • Fig. 14 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a 3D Quadtratic Koch.
  • Fig. 15 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a Jerusalem cube.
  • Fig. 16 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a von Koch surface.
  • Fig. 17 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a Menger sponge.
  • Fig. 18 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a 3D H fractal.
  • Fig. 19 illustrates a fractal heatsink that is an exemplary embodiment of the invention.
  • the heatsink is based on a Mandelbulb.
  • Fig. 2 illustrates a heatsink implementing a first embodiment of this invention. Note that the illustration is in two dimensions, but a three dimensional embodiment is both possible and preferred.
  • a heat transfer surface 100 that allows the heatsink to rest comfortably on a surface, such as the solid to be cooled 190.
  • the heat transfer surface 100 is roughly planar, having a closed Euclidian cross-section on the bottom. However, it might also have another shape, for example if the solid to be cooled does not have a planar face.
  • a fractal-shaped heat exchange device begins at point 110. Note that the heatsink has three branches leaving from point 110 - branch 120, branch 140, and branch 160.
  • the branch structure initiating from point 110 is nearly identical to that at point 122 and 142, even though only point 110 is a true starting point.
  • the fractal property of self-similarity is present.
  • the structure that begins at point 110 the "first motif”
  • the structure from point 122 the "second motif”
  • the structure that begins from point 142 the "third motif.”
  • the replication from first to second motif and from second to third motif involves a linear displacement (upward) and a change of scale.
  • the second motif and third motif are a smaller, similar copy of the first motif.
  • the fractals designed here are generally finite and the second motif will thus be an inexact copy of the first motif, i.e. if there are N levels starting from the first motif, the second motif level will have N-l levels, if N is very large, the difference is insignificant.
  • the self-similarity element required in fractals is not preserved perfectly in the preferred designs due to the limitations of available machinery, other feasibility constraints, and various design issues.
  • the benefits are achieved without requiring fractal relationships over more than a few "orders" of magnitude (iterations of the fractal recursive algorithm). For example, in the embodiment illustrated in Fig.
  • the fractal heatsink has a much larger surface area than the heat transfer surface alone, or a regular array of heatsink because all of the "branches" and “leaves” of the fernlike fractal shape serve to increase the surface area.
  • the turbulent portions of the heat transfer fluid near the surface will be increased by the textures inherent in the fractal variation in the heat exchange element 110.
  • the fractal patterns is itself non-identically repeating within the fractal design, this will serve to substantially reduce narrow band acoustic resonance as compared to a corresponding heat exchange device having a repeating design, e.g., a linear or geometric variation between several heat exchange elements, thereby further aiding in the heat transfer process.
  • the heat transfer surface 100 and the roughly fractal- shaped heat exchange element 110 are all made out of an efficient heat conductor, such as copper or aluminum, or more preferably, having a portion whose heat conductivity exceeds 850 W/(m*K), such as graphene with a heat conductivity of between 4840 and 5300
  • the heatsink is formed, at least in part, of carbon nanotubes, which display anisotropic heat conduction, with an efficient heat transfer along the long axis of the tube.
  • Carbon nanotubes are submicroscopic hollow tubes made of a chicken-wire-like or lattice of carbon atoms. These tubes have a diameter of just a few nanometers and are highly heat conductive, transferring heat much faster than diamond, and in some cases comparable to graphene. See web.mit.edu/press/2010/thermopower-waves.html (last accessed April 15, 2010) incorporated herein by reference.
  • this exemplary embodiment provides a plethora of openings, e.g. 124 and 126, between the branches or fractal subelements to ensure that all of the branches are exposed to the surrounding air, gas or liquid and to allow the heat to escape from the heatsink into the surroundings.
  • at least two of these openings are congruent, as are openings 124 and 126 illustrated here.
  • An embodiment of the invention allows the openings to be filled with the air or liquid from the surrounding medium. Due to the limitation imposed by the solid's flat shape, it is not possible to increase the exposure of the fem-like fractal to the solid. However, the air or liquid outside of the solid are perfect for the fractal's exposure.
  • the fractal shape is advantageous to ensure the escape of the phonons into the surrounding fluid medium because the fractal configuration may avoid peaked internal reflection of waves, and provide high surface exposure to the fluid heat transfer medium. Skilled persons in the art will realize that this could be achieved through many known structures. For example, graphene, which is one-atom-thick carbon and highly heat conductive, would be an advantageous material to use to build a 2D implementation of the fractal heatsink herein described.
  • Convex regions When a turbulently flowing fluid passes around an obstacle, concave regions or cavities in the obstacle create pockets of separated flow which generates self-sustaining oscillations and acoustic resonance. Convex regions may also be provided. These regions may be provided in a fractal arrangement. In this aspect of the technology, fractal is meant to signify self-similar but with differences in scale and optionally another attribute. The regions may produce substantially reduced narrow band acoustic resonance as compared to regularly spaced and arranged disruptions in the flow partem. Likewise, the presence of disruptions disturbs the surface layer and may enhance convective heat transfer.
  • Fig. 3 illustrates another embodiment of the invention.
  • a solid to be cooled that has an arbitrary shape 290 is located inside (illustrated) or outside (not illustrated) a two- dimensional or three-dimensional roughly fractal shaped 210 heatsink.
  • the heatsink 210 has an aperture 270 designed to hold the solid.
  • the fractal heat exchange element has multiple motifs, starting with the large triangle at 210, to progressively smaller triangles at 220 and 230. However, note that the fractal does not keep extending infinitely and there are no triangles smaller than the one at 230.
  • the fractal heatsink 210 has multiple recursive fractal iterations 220 and 230, but the fractal iterations stop at level 230 for simplicity of design and manufacturability.
  • the fractal submotifs 220 and 230 are of different dimensional sizes from the original fractal motif 210 and protrude from the original fractal shape 210.
  • the first motif is a large triangle, and the latter motifs are smaller triangles, which involve a rotation, linear displacement, and change of scale of the prior motif.
  • the fractal shape has some apertures in it (not illustrated) to allow the solid to be cooled to connect with other elements.
  • the solid to be cooled is connected to the fractal shape at point connector 240 and through bus wires at 250 and 260.
  • the solid should be connected to the fractal heatsink in at least one point, either through a point connection, a bus wire connection, or some other connection. If it is desired that the solid be fixed inside the heatsink, there may be at least three connection points, as illustrated. However, only one connection point is necessary for conduction between the solid to be cooled and the heatsink.
  • the point or bus wire connection is built using a strong heat conductor, such as carbon nanotubes or a diamond-like coating.
  • the fractal structure 210 in Fig.2 has multiple concave regions or cavities. When a turbulently flowing fluid passes around this fractal heatsink, the concave regions or cavities substantially reduce the narrow band acoustic resonance as compared to a flat or Euclidian structure. This allows for more energy to be available to for heat transfer.
  • the heatsink 210 in Fig. 3 could be constructed without the connections at points 240, 250, and 260.
  • a liquid or gas would fill the aperture 270 with the intent that the liquid or gas surround the solid to be cooled, hold it in place, or suspend it.
  • the liquid or gas surrounding the solid would conduct heat from the solid to the heatsink, which would then cause the heat to exit.
  • the heatsink comprises a heat exchange device which is structurally configured based on a Quadratic Koch Island as illustrated in Fig. 4.
  • Fig. 5A illustrates a square with dimension x 0 that forms the basis for the Quadratic Koch Island.
  • Fig. 5B illustrates a Quadratic Koch Island obtained after application of one fractal on the square. The fractal with section lengths of / is applied to each side of the square in the first iteration. Similarly, after several such iterations, a Quadratic Koch Island as illustrated in FIG. 5C may be obtained.
  • Fig. 6 illustrates the length of the fractal //which is the total length of all the fractal segments.
  • the length of each fractal section, /( «), decreases with each iteration of the fractal.
  • the fractal section length is described by eq. 7.
  • n is the number of iterations
  • the fractal section length decreases after each iteration.
  • the section length tends towards being negligible.
  • the overall length L of the fractal may be obtained from eq. 8.
  • o is the length of the side of the original square
  • n is the number of iterations
  • o is the length of the side of the original square
  • n is the number of iterations
  • the number of iterations corresponding to the Quadratic Koch Island may be greater than 5. Consequently, the heat exchange device functions as a compact heat exchanger. In other words, the heat exchange device has a large heat transfer area per unit exchanger volume. As a result, several advantages are obtained such as, but not limited to, reduction in space, weight, power requirements and costs. In another embodiment, the number of iterations corresponding to the Quadratic Koch Island may be less than or equal to 5. Consequently, the heat exchange device may function as a non-compact heat exchanger.
  • heat transfer and heat transfer coefficient increase independently of each other with every application of the fractal. Further, the increase may be double, or greater, with every fractal iteration. In general, the increase in heat transfer follows a trend of 2". Moreover, pumping power increases at almost one and a half the rate. Pumping power is the power needed to pump the heat transfer fluid through the heat exchange device.
  • the heatsink comprises a heat exchange device which is structurally configured based on a modified Koch Snowflake as illustrated in Fig. 7A.
  • the basis for generating the modified Snowflake is an equilateral triangle of width w as illustrated in Fig. 7B.
  • two smaller equilateral triangles of width 1/3 of the base width w are added onto two sides of the base triangle.
  • the modified Koch Snowflakes as illustrated in Fig. 7A may be obtained.
  • the surface area, A s (ri), of the modified Koch Snowflake may be obtained from eq.
  • w is the width of the base triangle
  • n is the number of iterations
  • t is the thickness of the modified Koch Snowflake
  • w is the width of the base triangle
  • n is the number of iterations
  • t is the thickness of the modified Koch Snowflake
  • p is the density of the material making up the modified Koch Snowflake
  • a heat transfer effectiveness ( ⁇ ) of the modified Koch Snowflake may be defined as the ratio of heat transfer achieved to heat transfer that would occur if the modified Koch Snowflake was not present, ⁇ may be calculated from eq. 13.
  • A is the area
  • a heat transfer efficiency ( ⁇ ) of the modified Koch Snowflake may be defined as the ratio of heat transfer achieved to the heat transfer that would occur if the entire modified Koch Snowflake was at the base temperature, ⁇ may be calculated from eq. 12.
  • A is the area
  • the heat transfer effectiveness ( ⁇ ) increases with each iteration.
  • the modified Koch Snowflake corresponding to three iterations may be used to form the heat exchange device. Accordingly, in this case, the heat transfer effectiveness ( ⁇ ) may increase by up to 44.8%. Further, the increase in heat transfer effectiveness ( ⁇ ) per mass may be up to 6%.
  • the material used to make the modified Koch Snowflake may be aluminum. Consequently, heat transfer effectiveness ( ⁇ ) per mass of approximately two times larger than that obtained using copper may be achieved.
  • the heat transfer effectiveness ( ⁇ ) per mass depends on the thickness of the modified Koch Snowflake.
  • the ratio of width (w) to thickness (t) corresponding to the modified Koch Snowflake may be 8. Accordingly, an increase in heat transfer effectiveness ( ⁇ ) per mass of up to 303% may be achieved at the fourth iteration.
  • the heatsink comprises a heat exchange device which is structurally configured based on a Sierpinski Carpet as illustrated in Fig. 8a.
  • the Sierpinski Carpet is formed by iteratively removing material from a base geometry such as, but not limited to, a square as illustrated in Fig. 8b. In the first iteration, a square with 1/3 of the base width (w) is removed. Similarly, by performing second and third iterations, the Sierpinski Carpets as illustrated in Fig. 8a may be obtained.
  • the surface area, A s (ri), of the Sierpinski Carpet may be obtained from eq. 13.
  • w is the width of the base square
  • n is the number of iterations t is the thickness of the Sierpinski Carpet
  • the surface area of the Sierpinski carpet initially reduces before reaching a minimum. However, after reaching the minimum, the surface area increases with each subsequent iteration. For example, at a width (w) of 0.0508 m an increase in surface area of 117% may be obtained after five iterations. Similarly, at a width (w) of 0.0254 m, a surface area increase of 265% may be obtained after five iterations.
  • the mass of the Sierpinski Carpet may be obtained using eq. 14.
  • w is the width of the base square
  • n is the number of iterations
  • t is the thickness of the Sierpinski carpet
  • p is the density of the material making up the Sierpinski carpet
  • the heat transfer effectiveness ( ⁇ ) corresponding to the Sierpinski carpet increases with each iteration.
  • the Sierpinski carpet corresponding to three iterations may be used to form the heat exchange device. Accordingly, in this case, the heat transfer effectiveness ( ⁇ ) may increase by up to 11.4%. Further, the increase in heat transfer effectiveness ( ⁇ ) per mass corresponding to the Sierpinski carpet may be up to 59%.
  • the material used to make the the Sierpinski carpet may be aluminum.
  • the heat transfer effectiveness ( ⁇ ) per mass corresponding to the Sierpinski carpet depends on the thickness of the corresponding to the Sierpinski carpet.
  • the ratio of width (w) to thickness (t) corresponding to the corresponding to the Sierpinski carpet may be 8. Accordingly, an increase in heat transfer effectiveness ( ⁇ ) per mass of up to 303% may be achieved at the fourth iteration.
  • the heatsink may comprise a heat exchange device which is structurally configured based on, but not limited to, one or more fractals selected from the group comprising:
  • the heatsink may comprise a heat exchange device which is structurally configured based on a Mandelbox as exemplarily illustrated in Fig. 9.
  • a Mandelbox is a box-like fractal object that has similar properties as that of the Mandelbrot set. It may be considered as a map of continuous, locally shape preserving Julia sets. Accordingly, the Mandelbox varies at different locations, since each area uses a Julia set fractal with a unique formula.
  • the Mandelbox may be obtained by applying eq. 15 repeatedly to every point in space. That point v is part of the Mandelbox if it does not escape to infinity.
  • v s*ballFold(r, f boxFold(v)) + c (15) where boxFold(v) means for each axis a:
  • the heatsink may comprise a heat exchange device which is structurally configured based on a Sierpinski tetrahedron.
  • the Sierpinski tetrahedron also called as tetrix, is a three-dimensional analogue of the Sierpinski triangle.
  • the Sierpinski tetrahedron may be formed by repeatedly shrinking a regular tetrahedron to one half its original height, putting together four copies of this tetrahedron with corners touching, and then repeating the process. This is illustrated in Fig. 10 for the first four iterations.
  • the Sierpinski tetrahedron constructed from an initial tetrahedron of side-length L has the property that the total surface area remains constant with each iteration.
  • the initial surface area of the (iteration-0) tetrahedron of side-length L is 2 V3.
  • the side-length is halved and there are 4 such smaller tetrahedra. Therefore, the total s
  • the heatsink may comprise a heat exchange device which is structurally configured based on a dodecaedron fractal.
  • the heatsink may comprise a heat exchange device which is structurally configured based on an icosahedron flake, also called as a Sierpinski icosahedron.
  • the icosahedron flake may be formed by successive flakes of twelve regular icosahedrons, as exemplarily illustrated in Fig. 12 for third iteration.
  • the heatsink may comprise a heat exchange device which is structurally configured based on an octahedron flake.
  • the octahedron flake, or Sierpinski octahedron may be formed by successive flakes of six regular octahedrons, as exemplarily illustrated in Fig. 13 for third iteration. Each flake may be formed by placing an octahedron scaled by 1/2 in each comer.
  • the heatsink may comprise a heat exchange device which is structurally configured based on a 3D Quadtratic Koch. As exemplarily illustrated in Fig. 14, the 3D Quadratic Koch may be obtained by growing a scaled down version of a triangular pyramid onto the faces of the larger triangular pyramid with each iteration. Fig. 14 illustrates the first four iterations.
  • the heatsink may comprise a heat exchange device which is structurally configured based on a Jerusalem cube, as exemplarily illustrated in Fig. 15.
  • the Jerusalem cube may be obtained by recursively drilling Greek cross-shaped holes into a cube.
  • the Jerusalem Cube may be constructed as follows:
  • Each iteration adds eight cubes of rank one and twelve cubes of rank two, a twenty- fold increase.
  • the heatsink may comprise a heat exchange device which is structurally configured based on a von Koch surface, as exemplarily illustrated in Fig. 16.
  • the von Koch surface may be constructed by starting from an equilateral triangular surface. In the first iteration, the midpoints of each side of the equilateral triangular surface are joined together to form an equilateral triangular base of a hollow triangular pyramid. This process is repeated with each iteration.
  • the heatsink may comprise a heat exchange device which is structurally configured based on a Menger sponge, as exemplarily illustrated in Fig. 17.
  • the Quiltr sponge may be constructed as follows:
  • the heatsink may comprise a heat exchange device which is structurally configured based on a 3D H fractal, as exemplarily illustrated in Fig. 18.
  • the 3D H fractal is based on an H-tree which may be constructed by starting with a line segment of arbitrary length, drawing two shorter segments at right angles to the first through its endpoints, and continuing in the same vein, reducing (dividing) the length of the line segments drawn at each stage by V2. Further, by adding line segments on the direction perpendicular to the H tree plane, the 3D H fractal may be obtained.
  • the heatsink may comprise a heat exchange device which is structurally configured based on a Mandelbulb, as exemplarily illustrated in Fig. 19.
  • the Mandelbulb is a three-dimensional analogue of the Mandelbrot set.
  • the heatsink comprises a heat exchange device having a plurality of heat exchange elements which are perforated.
  • a heat exchange device having a plurality of heat exchange elements which are perforated.
  • an enhanced heat transfer may be achieved.
  • use of perforations may increase heat transfer by up to a factor of two per pumping power.
  • the plurality of heat exchange elements may be hollow. The combination of hollow heat exchange elements with perforations can result in increases in heat transfer greater than that of a solid heat exchange element of the same diameter. Additionally, increases in heat transfer per pumping power of up to 20% could be achieved by varying the inclination angle and diameter of the perforations in aligned arrays of the plurality of heat exchange elements.
  • one or more of the number of perforations and shape of perforations may be configured in order to control the heat transfer. For instance, under natural convection, heat transfer is directly proportional to the number of square perforations. In another instance, circular and square perforations may be used to obtain higher Nusselt number. Since heat transfer is proportional to Nusselt number, greater heat transfer may be achieved with such an arrangement. In yet another instance, the Nusselt number corresponding to the plurality of heat exchange elements may be varied based on one or more of a pitch, a hole diameter, a surface area and flow velocity. In particular, by modifying the pitch of the perforations, the Nusselt number and hence heat transfer may be increased.
  • the heat transfer effectiveness of the plurality of heat exchange elements may be greater than or equal to a minimum value such that addition of the plurality of heat exchange elements is justified.
  • the minimum value may be ten.
  • a spacing between the plurality of heat exchange elements is determined based on a height of the plurality of heat exchange elements.
  • an optimal spacing between the plurality of heat exchange elements may decrease with an increase in height of the plurality of heat exchange elements.
  • a shape corresponding to the plurality of heat exchange elements may be configured to provide enhanced heat transfer.
  • the plurality of heat exchange elements may be fluted. As a result, an increase in heat transfer by up to 9% may be achieved.
  • the plurality of heat exchange elements may be wavy providing an increase in heat transfer by up to 6%.
  • the corresponding to the plurality of heat exchange elements may be triangular, circular, elliptical, rectangular and trapezoidal.
  • the plurality of heat exchange elements may be elliptically annular.
  • an elliptical aspect ratio corresponding to the plurality of heat exchange elements may be varied in order to obtain greater heat transfer efficiency.
  • the elliptical aspect ratio may be increased in order to obtain higher heat transfer efficiency.
  • the plurality of heat exchange elements may be trapezoidal with an optimal aspect number of 1.5.
  • the plurality of heat exchange elements may be diamond shaped pin fins.
  • the pitch corresponding to the plurality of heat exchange elements may be varied to obtain enhanced heat transfer.
  • the pitch may be varied in proportion to the required heat transfer coefficient. As a result, increase in heat transfer up to 340% beyond that of flat pin fins may be achieved.
  • the surface geometry of the plurality of heat exchange elements may be varied in order to provide enhanced heat transfer.
  • square ribs along the plurality of heat exchange elements may be used.
  • thermal performance may increase by up to 30%.
  • diamond shaped surface protrusions may be provided over the plurality of heat exchange elements. Consequently, thermal performance may be increased by up to 38% while also leading to better flow distribution.
  • grooves may be created on the surfaces of the plurality of heat exchange elements.
  • heat transfer could increase by up to 25%.
  • dimples may be placed on the flat base of the plurality of heat exchange elements forming a pin fin. Consequently, an increase in heat transfer by up to 8% may be achieved while also reducing the friction factor by up to 18%.
  • convex shaped dimples may be used to obtain greater heat transfer.
  • an orientation of the plurality of heat exchange elements may be varied in order to enhance heat transfer. For instance, in case the number of the plurality of heat exchange elements is large, the plurality of heat exchange elements may be oriented vertically with respect to the flat base of the plurality of heat exchange elements. In another instance, in case the plurality of heat exchange elements are short with a finning factor of less than 2.7, a horizontal orientation may be used in order to provide better heat transfer.
  • the plurality of heat exchange elements may be configured in order to control an amount of heat transfer by radiation.
  • the height of the plurality of heat exchange elements may be maintained short. As a result, up to 55% of the heat transfer may take place by radiation.
  • the height of the plurality of heat exchange elements may be increased in order to reduce the amount of heat transfer by radiation.
  • the plurality of heat exchange elements may be circular around an annular heat pipe.
  • a ratio of spacing between the plurality of heat exchange elements and diameter of the plurality of heat exchange elements may be controlled in order to vary the amount of heat transfer by radiation. For instance, the ratio may be decreased in order to decrease the amount of heat transfer by radiation. Similarly, the ratio may be increased in order to increase the amount of heat transfer by radiation.
  • the number of iterations corresponding to the fractal variation between respective branches of the plurality of heat exchange elements may be configured in order to control heat transfer. For instance, the number of iterations may be increased in order to obtain greater heat transfer. However, beyond a certain limit, heat transfer may not be directly proportional to the number of iterations. Additionally, varying the number of iterations may also control diffusion rate across the surfaces of the plurality of heat exchange elements based on the fact that diffusion rate is directly proportional to the number of iterations. However, a certain number of iterations such as, but not limited to, four to five iterations, the diffusion rate may converge.
  • a dimension corresponding to the fractal variation between respective branches of the plurality of heat exchange elements may be configured in order to control heat transfer.
  • the heat transfer is directly proportional to the fractal dimension. However, this relationship is valid only till a limited number of iterations.
  • the number of branches corresponding to the plurality of heat exchange elements may be configured to control the heat transfer. Under natural convection, heat transfer effectiveness is found to be directly proportional to the number of branches. However, after a certain number of branch generations, heat transfer effectiveness saturates. Further, a branching ratio may be configured in order to obtain minimum resistance to heat conduction and hence greater heat transfer. In a non-limiting example, a branching ratio of 0.707 or 0.7937 may be used.
  • heat transfer may be controlled based on the velocity of fluidic heat exchange medium flowing over the plurality of heat exchange elements.
  • the heat transfer is directly proportional to the velocity of fluidic heat exchange medium under forced convection.
  • the optimal number of branches required to maximize heat transfer has been found to reduce with increase in velocity of fluidic heat exchange medium. Accordingly, under forced convection with higher velocity, less number of branches may be required to achieve a required amount of heat transfer.
  • heat transfer by the plurality of heat exchange elements in the form of an array of perforated fins may be controlled by varying a pumping power. In this case, the heat transfer can be inversely proportional to the pumping power with small increase for turbulent cross-flow but significant increase for parallel flow.
  • the heat sink may be manufactured using manufacturing techniques such as, but not limited to, inj ection molding, die casting, extrusion, forging, gravitational molding, CNC milling, CNC punching, stamping, wire cut machine and wire cut Electrical Discharge Machining (EDM), additive manufacturing (e.g., 3D printing, 2.5D printing, etc.
  • manufacturing techniques such as, but not limited to, inj ection molding, die casting, extrusion, forging, gravitational molding, CNC milling, CNC punching, stamping, wire cut machine and wire cut Electrical Discharge Machining (EDM), additive manufacturing (e.g., 3D printing, 2.5D printing, etc.
  • the heatsink may be manufactured by a machining processing employing cutting tools and controlled slicing techniques to construct the plurality of heat exchange elements from a solid block of material such as, but not limited to, copper or aluminum. This technique is preferable to construct the plurality of heat exchange elements with smaller thickness than is possible by other techniques such as extrusion.
  • Advantages of the heatsink manufactured using this technique include high aspect ratio, thin fin, low tooling cost, easy and inexpensive to prototype, unidirectional flow and single piece construction.
  • the heatsink may be manufactured by bending sheets made of, but not limited to, copper or aluminum into fins to form the plurality of heat exchange elements. The fins are then bonded to the flat base of the heatsink.
  • This technique allows the flat base and the fins to be made of different materials. Advantages of this manufacturing technique include light weight of fins, lower tooling cost and differing materials for the flat base and the fins.
  • the heatsink may be manufactured from sheets of material such as, but not limited to, copper or aluminum bonded onto the flat base using one or more of epoxy, soldering and brazing. This technique of manufacturing is suitable for high power application with low thermal resistance and where forced air cooling is available.
  • the heatsink may be manufactured using die casting.
  • material such as, but not limited to, liquid aluminum is forced under high pressure into re-usable steel molds. This technique is specially suited when the plurality of heat exchange elements are of complex shapes.
  • modem three-dimensional laser and liquid printers can create objects such as the heatsinks described herein with a resolution of features on the order of 16 ⁇ .
  • US Patent Application No. 2006/0037177 expressly incorporated herein by reference, describes a method of controlling crystal growth to produce fractals or other structures through the use of spectral energy patterns by adjusting the temperature, pressure, and electromagnetic energy to which the crystal is exposed. This method might be used to fabricate the heatsinks described herein.
  • traditional manufacturing methods for large equipment can be adapted to create the fractal structures described herein.

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Thermal Sciences (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Cooling Or The Like Of Electrical Apparatus (AREA)

Abstract

La présente invention concerne un dissipateur thermique comprenant un dispositif d'échange de chaleur comportant une pluralité d'éléments d'échange de chaleur ayant chacun une surface limite à par rapport à un fluide de transfert de chaleur, comportant des éléments ou régions successifs variant selon une relation fractale. Selon un mode de réalisation, un spectre de bruit dû à l'écoulement de fluide est à large bande. Selon un autre mode de réalisation, les couches de limites de surface sont interrompues pour augmenter le transfert de chaleur. Des tourbillons induits par l'écoulement peuvent être générés à des emplacements non correspondants de la pluralité d'éléments d'échange de chaleur variant de façon fractale.
PCT/US2016/068641 2015-12-30 2016-12-27 Dispositif de transfert de chaleur fractal Ceased WO2017117088A1 (fr)

Applications Claiming Priority (2)

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US14/984,756 2015-12-30
US14/984,756 US10041745B2 (en) 2010-05-04 2015-12-30 Fractal heat transfer device

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WO2017117088A1 true WO2017117088A1 (fr) 2017-07-06

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Cited By (10)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108745214A (zh) * 2018-07-11 2018-11-06 江苏揽山环境科技股份有限公司 一种实现混沌状态气液传质传热的反应系统
EP3483543A1 (fr) * 2017-11-14 2019-05-15 The Boeing Company Échangeurs de chaleur dendritiques et leur procédés d'utilisation
WO2019239141A1 (fr) * 2018-06-15 2019-12-19 H2Go Power Ltd Dispositif de stockage d'hydrogène et procédé de production d'un dispositif de stockage d'hydrogène
CN110944472A (zh) * 2018-09-25 2020-03-31 苹果公司 外壳构造
US11060480B2 (en) 2017-11-14 2021-07-13 The Boeing Company Sound-attenuating heat exchangers and methods of utilizing the same
US11143170B2 (en) 2019-06-28 2021-10-12 The Boeing Company Shape memory alloy lifting tubes and shape memory alloy actuators including the same
US11168584B2 (en) 2019-06-28 2021-11-09 The Boeing Company Thermal management system using shape memory alloy actuator
US11525438B2 (en) 2019-06-28 2022-12-13 The Boeing Company Shape memory alloy actuators and thermal management systems including the same
US12259196B2 (en) 2022-06-16 2025-03-25 The Boeing Company Sound-attenuating heat exchangers and methods of exchanging heat and attenuating sound within sound-attenuating heat exchangers
CN120161501A (zh) * 2025-02-13 2025-06-17 湖北省地震局(中国地震局地震研究所) 一种基于科赫分形曲线的微动勘探方法

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
RU2347952C1 (ru) * 2007-10-16 2009-02-27 Вера Семеновна Рождественская Электрогидравлический следящий привод объемного регулирования
WO2011138670A2 (fr) * 2010-05-04 2011-11-10 Alexander Poltorak Dispositif de transfert thermique fractal
RU134358U1 (ru) * 2013-05-30 2013-11-10 Федеральное государственное бюджетное образовательное учреждение высшего профессионального образования "Саратовский государственный технический университет имени Гагарина Ю.А." (СГТУ имени Гагарина Ю.А.) Фрактальный радиатор для охлаждения полупроводниковых и микроэлектронных компонент

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
RU2347952C1 (ru) * 2007-10-16 2009-02-27 Вера Семеновна Рождественская Электрогидравлический следящий привод объемного регулирования
WO2011138670A2 (fr) * 2010-05-04 2011-11-10 Alexander Poltorak Dispositif de transfert thermique fractal
RU134358U1 (ru) * 2013-05-30 2013-11-10 Федеральное государственное бюджетное образовательное учреждение высшего профессионального образования "Саратовский государственный технический университет имени Гагарина Ю.А." (СГТУ имени Гагарина Ю.А.) Фрактальный радиатор для охлаждения полупроводниковых и микроэлектронных компонент

Cited By (18)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US10619570B2 (en) 2017-11-14 2020-04-14 The Boeing Company Dendritic heat exchangers and methods of utilizing the same
EP3483543A1 (fr) * 2017-11-14 2019-05-15 The Boeing Company Échangeurs de chaleur dendritiques et leur procédés d'utilisation
US11060480B2 (en) 2017-11-14 2021-07-13 The Boeing Company Sound-attenuating heat exchangers and methods of utilizing the same
WO2019239141A1 (fr) * 2018-06-15 2019-12-19 H2Go Power Ltd Dispositif de stockage d'hydrogène et procédé de production d'un dispositif de stockage d'hydrogène
US12061020B2 (en) 2018-06-15 2024-08-13 H2Go Power Ltd Hydrogen storage device and method of producing a hydrogen storage device
CN108745214A (zh) * 2018-07-11 2018-11-06 江苏揽山环境科技股份有限公司 一种实现混沌状态气液传质传热的反应系统
KR102229665B1 (ko) 2018-09-25 2021-03-18 애플 인크. 하우징 구성
US10667426B2 (en) 2018-09-25 2020-05-26 Apple Inc. Housing construction
KR20200035200A (ko) * 2018-09-25 2020-04-02 애플 인크. 하우징 구성
US10966343B2 (en) 2018-09-25 2021-03-30 Apple Inc. Housing construction
CN110944472B (zh) * 2018-09-25 2021-06-18 苹果公司 外壳构造
EP3629684A1 (fr) * 2018-09-25 2020-04-01 Apple Inc. Construction de boîtier
CN110944472A (zh) * 2018-09-25 2020-03-31 苹果公司 外壳构造
US11143170B2 (en) 2019-06-28 2021-10-12 The Boeing Company Shape memory alloy lifting tubes and shape memory alloy actuators including the same
US11168584B2 (en) 2019-06-28 2021-11-09 The Boeing Company Thermal management system using shape memory alloy actuator
US11525438B2 (en) 2019-06-28 2022-12-13 The Boeing Company Shape memory alloy actuators and thermal management systems including the same
US12259196B2 (en) 2022-06-16 2025-03-25 The Boeing Company Sound-attenuating heat exchangers and methods of exchanging heat and attenuating sound within sound-attenuating heat exchangers
CN120161501A (zh) * 2025-02-13 2025-06-17 湖北省地震局(中国地震局地震研究所) 一种基于科赫分形曲线的微动勘探方法

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