System and method for maintaining efficiency of a fractal heat sink

Abstract

A heatsink comprising a heat exchange device having a plurality of heat exchange elements each having a surface boundary with respect to a heat transfer fluid, having successive elements or regions having varying size scales. According to one embodiment, an accumulation of dust or particles on a surface of the heatsink is reduced by a removal mechanism. The mechanism can be thermal pyrolysis, vibration, blowing, etc. In the case of vibration, adverse effects on the system to be cooled may be minimized by an active or passive vibration suppression system.

Claims

1. A method of heat transfer, comprising: providing a base structure configured to interface with a heat source; receiving heat through the base structure into a heat exchange device configured to emit the received heat from a heat exchange surface, into a surrounding heat exchange medium; and reducing an accumulation of particles on the heat exchange surface with at least one of a particle-degrading device and a particle dislodging device, wherein the heat exchange surface comprises an actuator controlled by an automated electronic processor in dependence on a computational heat exchange model to alter a spatial relationship of a first portion of the heat exchange surface respect to a second portion of the heat exchange surface.

2. The method according to claim 1, wherein the particle-degrading device degrades particles by at least one of pyrolysis, heat-induced oxidation, photo-induced oxidation, laser ablation, induced electrical discharge-induced oxidation, and plasma oxidation.

3. The method according to claim 1, further comprising vibrating the heat exchange surface relative to the accumulation of particles to reduce the accumulation of particles.

4. The method according to claim 3, wherein the vibrations are induced by at least one of a piezoelectric transducer and an electromagnetic transducer.

5. The method according to claim 1, further comprising at least one of inducing a time-varying vector flow of heat exchange media over the heat exchange surface, wherein the time-varying vector is altered in dependence on at least one control input.

6. The method according to claim 5, wherein the induced flow of heat exchange media comprises entrained particles comprising at least one of liquid droplets and solid particles.

7. The method according to claim 1, wherein the accumulation of particles on the heat exchange surface is reduced by altering at least one electrostatic charge.

8. The method according to claim 1, wherein the accumulation of particles on the heat exchange surface is reduced by heating and cooling at least one shape memory alloy.

9. The method according to claim 1, wherein the particle dislodging device comprises an electrostatic charge generator, further comprising inducing, with the electrostatic charge generator, a first static electrical charge on at least a portion of the heat exchange surface, sufficient to repel dust particles.

10. The method according to claim 1, wherein the base structure further comprises an anisotropic vibration transmissive mount to isolate vibrations from the heat source.

11. The method according to claim 10, wherein the anisotropic vibration transmissive mount comprises a displaceable piston in a cylinder.

12. The method according to claim 1, wherein the accumulation of particles on the heat exchange surface is reduced by: selectively generating vibrations with a vibrational transducer, and selectively cancelling the generated vibrations to isolate the base structure from the generated vibrations while permitting vibrations to oscillate the accumulation of particles.

13. The method according to claim 12, wherein the generated vibrations are isolated from the base structure by at least one of a plastic thermal transfer medium, a non-shear transmissive solid, and an active vibration suppression interface.

14. The method according to claim 13, wherein the non-shear transmissive solid is a heat transmissive metal wire bundle.

15. The method according to claim 1, wherein the heat exchange surface comprises a plurality of heat exchange elements having different resonance frequencies, further comprising generating vibrations at respective frequencies, to selectively resonate a portion of the plurality of heat exchange elements dependent on a frequency of the generated vibrations.

16. The method according to claim 1, wherein the heat exchange surface comprises at least one of a plurality of heat exchange elements having characteristic dimensions over at least two orders of size scales, and a set of elements having an approximately fractal geometry.

17. The method according to claim 1, wherein the heat exchange surface comprises a plurality of heat exchange elements, and the accumulation of particles on the heat exchange surface is reduced by altering at least one spatial relationship of a first of the plurality of heat exchange elements with respect to a second of the plurality of heat exchange elements with at least one of: a shape memory alloy configured to undergo a shape change as a result of transition through a predefined temperature range, an active actuator configured to alter at least one spatial relationship of a first of the plurality of heat exchange elements with respect to a second of the plurality of heat exchange elements in response to a control signal, and a passive actuator configured to alter at least one spatial relationship of a first of the plurality of heat exchange elements with respect to a second of the plurality of heat exchange elements in response to an environmental change, to thereby at least one of disrupt the accumulation of particles and alter a flow of a gas or fluid proximate to the accumulation of particles.

18. A heat transfer method, comprising: receiving heat from a heat source through a base structure; diffusion the received heat into a solid body having a resonant heat exchange surface; emitting the diffused heat into a surrounding flowing heat exchange medium, the surrounding flowing heat exchange medium having entrained particles which accumulate on the heat exchange surface; and dislodging the accumulated entrained particles from the heat exchange surface by selectively vibrating the heat exchange surface at a resonant frequency, wherein the resonant heat exchange surface comprises an actuator controlled by an automated electronic processor in dependence on a computational heat exchange model to alter a spatial relationship of a first portion of the resonant heat exchange surface respect to a second portion of the resonant heat exchange surface.

19. A method of reducing accumulation of particles on a heatsink, comprising: providing a heatsink having a thermal interface to a heat source, and a plurality of heat exchange surfaces; receiving heat from the heat source into the heatsink, and communicating the received heat to the plurality of heat exchange surfaces; flowing a heat exchange medium having entrained particles over the heat exchange surfaces to dissipate heat from the heatsink, wherein the heat exchange surfaces accumulate the entrained particles; disrupting the accumulation of entrained particles with at least one of a vibration induced by the flow of the heat exchange medium and an induced vibration in the heatsink; and isolating the vibration from the heat source, wherein the plurality of heat exchange surfaces are associated with an actuator controlled by an automated electronic processor in dependence on a computational heat exchange model to alter a spatial relationship of a first heat exchange surface respect to a second heat exchange surface.

20. The method according to claim 19, wherein the plurality of heat exchange surfaces comprises at least one heat exchange element having respective elements having approximately fractal geometry with characteristic dimensions over at least two orders of size scales.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 shows a set of governing equations for a parallel plate heatsink.

(2) FIG. 2 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is placed adjacent to the object to be cooled.

(3) FIG. 3 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is placed either adjacent to or surrounding the object to be cooled.

(4) FIG. 4 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a Quadratic Koch Island.

(5) FIG. 5A illustrates the basis for the Quadratic Koch Island.

(6) FIG. 5B illustrates a Quadratic Koch Island obtained after application of one iteration.

(7) FIG. 5C illustrates a Quadratic Koch Island obtained after application of several iterations.

(8) FIG. 6 illustrates the total length of all the fractal segments of a Quadratic Koch Island.

(9) FIG. 7A illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a modified Koch Snowflake.

(10) FIG. 7B illustrates the basis for generating the modified Snowflake.

(11) FIG. 8A illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a Sierpinski Carpet.

(12) FIG. 8B illustrates the basis for generating the Sierpinski Carpet.

(13) FIG. 9 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a Mandelbox.

(14) FIG. 10 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a Sierpinski tetrahedron.

(15) FIG. 11 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a Dodecaedron fractal.

(16) FIG. 12 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a Icosahedron flake.

(17) FIG. 13 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on an Octahedron flake.

(18) FIG. 14 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a 3D Quadtratic Koch.

(19) FIG. 15 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a Jerusalem cube.

(20) FIG. 16 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a von Koch surface.

(21) FIG. 17 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a Menger sponge.

(22) FIG. 18 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a 3D H fractal.

(23) FIG. 19 illustrates a fractal heatsink that is an exemplary embodiment of the invention. In this embodiment, the heatsink is based on a Mandelbulb.

(24) FIGS. 20-37 illustrate various heatsink designs and proposals, which may be used in conjunction with various embodiments of the technology.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(25) 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. There is a heat transfer surface 100 that allows the heatsink to rest comfortably on a surface, such as the solid to be cooled 190. In the illustrated embodiment, 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. The heat transfer surface may also comprise an anisotropic vibration transfer thermal interface material, such as a braided or straight fine copper wire bundle. Such a bundle advantageously has strands of different length, which, for example, could permit destructive interference of vibrations transmitted along each strand. A fractal-shaped heat exchange device begins at point 110. The base of the fractal-shaped heat exchange device at point 110 may also or alternately include a piston and cylinder, to provide vibrational isolation along the piston movement axis, while also transmitting heat from the heat source to the heatsink along the peripheral wall of the cylinder to the inner wall of the piston. The working fluid within the cylinder may be a heat transfer fluid, and a set of valves may be actuated based on the vibration to induce a flow. The heat transfer fluid may be a phase change fluid, and the gaseous phase may vent from the cylinder through a valve. Note that the heatsink has three branches leaving from point 110—branch 120, branch 140, and branch 160. Also note that 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. Thus, the fractal property of self-similarity is present. We call the structure that begins at point 110 the “first motif,” the structure from point 122 the “second motif,” and the structure that begins from point 142 the “third motif.” Note that, in the embodiment illustrated in FIG. 2, the replication from first to second motif and from second to third motif involves a linear displacement (upward) and a change of scale. In branches not going in the same direction as the prior branch, there is also a rotation. Under the limitations for ideal fractals, the second motif and third motif are a smaller, similar copy of the first motif. However, due to the limitations imposed by human-made structures and machines, 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-1 levels, if N is very large, the difference is insignificant. In other words, 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. In addition, 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. 2, there are no continuing branch divisions and iterations at point 162, even though an ideal fractal would have them. In an ideal fractal, there would be an infinite number of sub-branches from 110, 122, and 142. However, an imperfect fractal shape, as illustrated in FIG. 2, will serve the purposes of this invention.

(26) FIG. 2 shows various embodiments of the invention, which may be used individually, in combination, or in subcombination. When ambient air flows over a textured surface, such as a branching fractal or fractal-like shape, dust, fibers and/or debris may accumulate. In addition, in some cases, pollutants or oils may deposit. Such depositions tend to reduce the efficiency of heat transfer, and when sufficiently thick, should be removed or disrupted. According to one embodiment, a particle-dislodging device configured to mechanically disrupt an accumulation of particles on the plurality of heat exchange elements is provided, e.g., vibration transducer 126, fan 127, actuator 132, etc.

(27) Thus, for example, the particle-dislodging device may comprise a vibration transducer 126 configured to vibrate a plurality of heat exchange elements comprising the heat exchange surface. The vibration transducer 126 may be, for example, a piezoelectric transducer, an electromagnetic transducer, or a rotating motor. In the case of a vibration transducer, it is preferred that the vibrations be emitted at resonant frequencies of the heat exchange elements; which advantageously span a range due to the fractal or fractal-like disposition. Therefore, vibrational energy can be selectively targeted to certain elements, without resonant vibration of the entire structure. The vibrational energy may be controlled to scan a range of frequencies, or to target specific frequencies corresponding to targeted structures.

(28) The system may further comprise at least one vibrational transducer 130, controlled by a feedback-controlled vibration generator 128 to cancel vibrations at the base structure produced by the particle dislodging device 126, based on a signal from a vibration sensing transducer 131.

(29) A vibration damper may be provided to damp vibrations at the base structure, e.g., near the point 110. This may be an isotropic or anisotropic vibration isolator, and for example may comprise a bundle of wires (e.g., copper), a piston and cylinder, a particle-filled polymeric thermal interface material, copper nanotubes, or the like.

(30) A fan 126 or a heat transfer fluid (which may be gaseous or liquid) pump/compressor may be provided, which in turn may be controlled by e.g., motor speed control 128 to induce a time-varying flow of heat exchange media over the plurality of heat exchange elements. The fan 126 or pump/compressor may be configured to induce a flow of a gaseous heat transfer medium over the heat exchange surface along at least one vector, having at least one control input, wherein the at least one vector is altered in dependence on the at least one control input, by, for example a set of louvers 137. The flow rate may also be controlled over time, in dependence on thermal load, desired turbulence or other convective heat transfer phenomenon, acoustic emissions, or other criteria.

(31) The heat exchange media may comprises entrained particles 125, such as magnetic particles 125, which impinge on the surfaces of the heat exchange elements, and can dislodge surface debris. Advantageously, a magnetic collector can capture the particles for reuse, after mixed debris is separated. The entrained particles 125 may also be liquid droplets in a gas-liquid mixture.

(32) In an alternate embodiment, the particle-dislodging device comprises an electrostatic charge generator and an electrostatic discharge device 129. These cooperate to charge the surfaces of the heat exchanger, which in conjunction with a collection plate/discharge device, induce a force on the surface particles to move from the heat exchange surface to the collection plate.

(33) The particle-dislodging device may also comprise a shape memory alloy 132, which for example is passively controlled by a temperature, or actively controlled by control 133 to change the configuration of the heatsink. The control 133 may include an automated electronic processor in dependence on a computational heat exchange model of the heatsink system. Other types of actuator configured to alter at least one spatial relationship of a first portion of the heat exchange elements with respect to a second portion of the heat exchange elements are possible.

(34) In an alternate embodiment, the particle-degrading device is configured to chemically degrade an accumulation of particles on the plurality of heat exchange elements. For example, the particle-degrading device may be a pyrolizer 134, discharge plasma emitter 136, solvent wash (solvent as entrained particles 125), etc. These chemical degradation effects need not be constant, and can thus vary in intensity, duty cycle, etc. over time.

(35) A laser 135 may be provided to ablate or disrupt the accumulation. The laser may be, for example, controlled by electronically controlled mirrors. On some cases, a continuous scanning is desired, and the control may be a simple area scan of a pulsed laser beam.

(36) 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 fern-like fractal shape serve to increase the surface area. In addition, if a heat transfer fluid is induced to flow above the heat transfer surface 100, 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. Because 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.

(37) In a preferred embodiment, 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 W/(m*K) or diamond with a heat conductivity between 900 and 2320 W/(m*K). This would allow heat to quickly enter the heatsink from the solid and for heat to quickly exit the heatsink through the branches and leaves of the fern-like fractal 110. In another embodiment, 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 Apr. 15, 2010) incorporated herein by reference.

(38) Also note that this exemplary embodiment provides a plethora of openings, e.g. 124 and 126, between the branches or fractal sub-elements 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. In one embodiment of the invention, 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 fern-like fractal to the solid. However, the air or liquid outside of the solid are perfect for the fractal's exposure.

(39) Under the phonon model of heat exchange, applicable to carbon nanotubes, graphene materials, and perhaps others, 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.

(40) 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 pattern. Likewise, the presence of disruptions disturbs the surface layer and may enhance convective heat transfer.

(41) 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. In one embodiment, the heatsink 210 has an aperture 270 designed to hold the solid. Note that, as in FIG. 2, 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. In other words, 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. Also note that 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. Here, 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. In one embodiment, the fractal shape has some apertures in it (not illustrated) to allow the solid to be cooled to connect with other elements. Also, 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. Preferably, the point or bus wire connection is built using a strong heat conductor, such as carbon nanotubes or a diamond-like coating.

(42) Note that, as in FIG. 1, 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.

(43) In yet another embodiment of the invention, the heatsink 210 in FIG. 3 could be constructed without the connections at points 240, 250, and 260. In one embodiment, 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. Preferably, the liquid or gas surrounding the solid would conduct heat from the solid to the heatsink, which would then cause the heat to exit.

(44) In another embodiment of the invention, the heatsink comprises a heat exchange device which is structurally configured based on a Quadratic Koch Island as illustrated in FIG. 4.

(45) FIG. 5A illustrates a square with dimension x.sub.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 l 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.

(46) FIG. 6 illustrates the length of the fractal l.sub.f which is the total length of all the fractal segments. The length of each fractal section, l(n), decreases with each iteration of the fractal. The fractal section length is described by eq. 7.
l(n)=(¼).sup.nx.sub.0  (7)

(47) where,

(48) x.sub.0 is the length of the side of the original square,

(49) n is the number of iterations

(50) As can be seen from eq. 7, the fractal section length decreases after each iteration. When the number of iterations becomes increasingly large, the section length tends towards being negligible.

(51) Further, it may be mathematically shown that the overall length L of the fractal may be obtained from eq. 8.

(52) $\begin{array}{cc}L\left(n\right)=x_0\left(1+\frac{2}{3}\left(1-\frac{1}{4^n}\right)\right)& \left(8\right)\end{array}$

(53) where,

(54) x.sub.0 is the length of the side of the original square,

(55) n is the number of iterations

(56) Similarly, it may be shown that the circumference C of the Quadratic Koch Island can be obtained from eq. 9.
C=4(2.sup.nx.sub.0)  (9)

(57) where,

(58) x.sub.0 is the length of the side of the original square,

(59) n is the number of iterations

(60) It is evident that with each iteration, the circumference C increases. However, the cross-sectional area remains constant at x.sub.0.sup.2 since when a fractal area is added the same area is subtracted elsewhere.

(61) In one embodiment, 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.

(62) It may be shown with heat transfer analysis that 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.sup.n. 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.

(63) In yet another embodiment of the invention, 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. In the first iteration, two smaller equilateral triangles of width ⅓ of the base width w are added onto two sides of the base triangle. Similarly, by applying a second and a third iteration, the modified Koch Snowflakes as illustrated in FIG. 7A may be obtained.

(64) The surface area, A.sub.s(n), of the modified Koch Snowflake may be obtained from eq. 10.

(65) $\begin{array}{cc}{A}_s\left(n\right)=2\left(wt+\frac{\sqrt{3}}{4}{w}^2\right)+{.Math.}_1^n\left[{\left(\frac{w}{3^n}\right)}^2\left(\frac{\sqrt{3}}{2}\right)+\left(\frac{w}{3^n}\right)t\right]2^{2n-1}& \left(10\right)\end{array}$

(66) where,

(67) w is the width of the base triangle

(68) n is the number of iterations

(69) t is the thickness of the modified Koch Snowflake

(70) It is evident that the surface area of the modified Koch Snowflake increases with each iteration. More specifically, it may be observed that after 5 iterations there is an increase in surface area of about 58%.

(71) Further, the mass of the modified Koch Snowflake may be obtained using eq. 11.

(72) $\begin{array}{cc}m\left(n\right)=\left\{\frac{\sqrt{3}}{4}{w}^2+{.Math.}_1^n\left[{\left(\frac{w}{3^n}\right)}^2\left(\frac{\sqrt{3}}{4}\right)\right]2^{2n01}\right\}\rho t& \left(11\right)\end{array}$

(73) where, w, n, and t are as above, and ρ is the density of the material making up the modified Koch Snowflake.

(74) It may be observed that the change in surface area with respect to the baseline case (i.e., n=0) is a function of width (w) and thickness (t). However, the change in mass with respect to the baseline is dependent on the fractal geometry chosen. The mass of the modified Koch Snowflake increases with each iteration. However, it converges to a maximum value of mass increase of approximately 40%.

(75) A heat transfer effectiveness (ε) 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. ε may be calculated from eq. 13.

(76) 0$\begin{array}{cc}\mathrm{.Math.}=\frac{Q_c}{h{A}_b\left(T_b-T_{\infty }\right)}& \left(13\right)\end{array}$

(77) where,

(78) Q is the heat rate

(79) h is the heat transfer co-efficient

(80) A is the area

(81) T is the temperature

(82) Further, a heat transfer efficiency (η) 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. η may be calculated from eq. 12.

(83) $\begin{array}{cc}\eta =\frac{Q_c}{h{A}_S\left(T_b-T_{\infty }\right)}& \left(12\right)\end{array}$

(84) where, Q, h, A, and T are as above.

(85) The heat transfer effectiveness (ε) increases with each iteration. In an embodiment, 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 (ε) may increase by up to 44.8%. Further, the increase in heat transfer effectiveness (ε) per mass may be up to 6%. In one embodiment, the material used to make the modified Koch Snowflake may be aluminum. Consequently, heat transfer effectiveness (ε) per mass of approximately two times larger than that obtained using copper may be achieved.

(86) Further, the heat transfer effectiveness (ε) per mass depends on the thickness of the modified Koch Snowflake. In an embodiment, the ratio of width (w) to thickness (t) corresponding to the modified Koch Snowflake may be 8. Accordingly, an increase in heat transfer effectiveness (ε) per mass of up to 303% may be achieved at the fourth iteration.

(87) In yet another embodiment of the invention, 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 ⅓ 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.

(88) The surface area, A.sub.s(n), of the Sierpinski Carpet may be obtained from eq. 13.

(89) $\begin{array}{cc}{A}_s\left(n\right)=2w^2+3wt-{.Math.}_1^n{8}^{n-1}\left[2{\left(\frac{w}{3^n}\right)}^2-4\left(\frac{w}{3^n}\right)t\right]& \left(13\right)\end{array}$

(90) where,

(91) w is the width of the base square

(92) n is the number of iterations

(93) t is the thickness of the Sierpinski Carpet

(94) Starting from n=0, with each subsequent iteration, 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.

(95) Further, the mass of the Sierpinski Carpet may be obtained using eq. 14.

(96) $\begin{array}{cc}m\left(n\right)=\left\{w^2-{.Math.}_1^n\left[8^{n-1}{\left(\frac{w}{3^n}\right)}^2\right]\right\}\rho t& \left(14\right)\end{array}$

(97) where w, n, and t are as above, and ρ is the density of the material making up the Sierpinski carpet

(98) It may be seen from eq. 11 that with each iteration, the mass of the Sierpinski carpet decreases. For example, after five iterations, there is a reduction of 45% of mass of the Sierpinski carpet.

(99) The heat transfer effectiveness (ε) corresponding to the Sierpinski carpet increases with each iteration. In an embodiment, the Sierpinski carpet corresponding to three iterations may be used to form the heat exchange device. Accordingly, in this case, the heat transfer effectiveness (ε) may increase by up to 11.4%. Further, the increase in heat transfer effectiveness (ε) per mass corresponding to the Sierpinski carpet may be up to 59%. In one embodiment, the material used to make the the Sierpinski carpet may be aluminum. Consequently, heat transfer effectiveness (ε) per mass of approximately two times larger than that obtained using copper may be achieved.

(100) Further, the heat transfer effectiveness (ε) per mass corresponding to the Sierpinski carpet depends on the thickness of the corresponding to the Sierpinski carpet. In an embodiment, 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 (ε) per mass of up to 303% may be achieved at the fourth iteration.

(101) In other embodiments, 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: A “scale 2” and “scale 3” Mandelbox; Sierpinski tetrahedron; Fractal pyramid; Dodecahedron fractal; 3D quadratic Koch surface (type 1); 3D quadratic Koch surface (type 2); Jerusalem cube; Icosahedron fractal; Octahedron fractal; Von Koch surface; Menger sponge; 3D H-fractal; and Mandelbulb.

(102) In accordance with an embodiment, 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)

(103) where boxFold(v) means for each axis a:

(104) $\begin{array}{cc}\mathrm{if}v\left[a\right]>1& v\left[a\right]=2-v\left[a\right]\\ \mathrm{else}\mathrm{if}v\left[a\right]<-1& v\left[a\right]=-2-v\left[a\right]\end{array}$

(105) and ballFold(r, v) means for v's magnitude m:

(106) $\begin{array}{cc}\mathrm{if}m<r& m=m/r^2\\ \mathrm{else}\mathrm{if}m<1& m=1/m\end{array}$

(107) In an instance, using the values of s=2, r=0.5 and f=1 in eq. 12, the standard Mandelbox may be obtained.

(108) In accordance, with another embodiment, 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.

(109) The initial surface area of the (iteration-0) tetrahedron of side-length L is L.sup.2√3. At the next iteration, the side-length is halved and there are 4 such smaller tetrahedra. Therefore, the total surface area after the first iteration may be calculated by eq. 16.

(110) $\begin{array}{cc}4\left({\left(\frac{L}{2}\right)}^2\sqrt{3}\right)=4\frac{L^2}{4}\sqrt{3}=L^2\sqrt{3}& \left(16\right)\end{array}$

(111) This remains the case after each iteration. Though the surface area of each subsequent tetrahedron is ¼ that of the tetrahedron in the previous iteration, there are 4 times as many—thus maintaining a constant total surface area. However, the total enclosed volume of the Sierpinski tetrahedron decreases geometrically, with a factor of 0.5, with each iteration and asymptotically approaches 0 as the number of iterations increases.

(112) In accordance with another embodiment, the heatsink may comprise a heat exchange device which is structurally configured based on a dodecaedron fractal. The dodecahedron fractal, also called as dodecahedron flake, may be formed by successive flakes of twenty regular dodecahedrons, as exemplarily illustrated in FIG. 11 for second iteration. Each flake is formed by placing a dodecahedron scaled by 1/(2+φ) in each corner, wherein φ=(1+√5)/2.

(113) In accordance with another embodiment, 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. Each flake may be formed by placing an icosahedron scaled by 1/(2+φ) in each corner, wherein φ=(1+√5)/2.

(114) In accordance with another embodiment, 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 ½ in each corner.

(115) In accordance with another embodiment, 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.

(116) In accordance with another embodiment, 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:

(117) 1. Start with a cube.

(118) 2. Cut a cross through each side of the cube, leaving eight cubes (of rank +1) at the corners of the original cube, as well as twelve smaller cubes (of rank +2) centered on the edges of the original cube between cubes of rank +1.

(119) 3. Repeat the process on the cubes of rank 1 and 2.

(120) Each iteration adds eight cubes of rank one and twelve cubes of rank two, a twenty-fold increase.

(121) In accordance with another embodiment, 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.

(122) In accordance with another embodiment, the heatsink may comprise a heat exchange device which is structurally configured based on a Menger sponge, as exemplarily illustrated in FIG. 17. The Menger sponge may be constructed as follows:

(123) 1. Begin with a cube (first image).

(124) 2. Divide every face of the cube into 9 squares, like a Rubik's Cube. This will sub-divide the cube into 27 smaller cubes.

(125) 3. Remove the smaller cube in the middle of each face, and remove the smaller cube in the very center of the larger cube, leaving 20 smaller cubes (second image). This is a level-1 Menger sponge (resembling a Void Cube).

(126) 4. Repeat steps 2 and 3 for each of the remaining smaller cubes, and continue to iterate ad infinitum.

(127) In accordance with another embodiment, 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 √2. Further, by adding line segments on the direction perpendicular to the H tree plane, the 3D H fractal may be obtained.

(128) In accordance with another embodiment, 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 Mandelbulb may be defined as the set of those C in .sup.3 for which the orbit of <0, 0, 0> under the iteration vv.sup.n+c is bounded, where the “nth power” of the vector v=x, y, z in .sup.3 is given by eq. 17.
v.sup.n:=r.sup.n sin(nθ)cos(nϕ), sin(nθ)sin(nϕ), cos(nθ)  (17)

(129) Where

(130) r=√{square root over (x.sup.2+y.sup.2+z.sup.2)},

(131) ϕ=arc tan(y/x)=arg(x+yi), and

(132) θ=arc tan(√{square root over (x.sup.2+y.sup.2/z)})=arc cos(z/r).

(133) In accordance with another embodiment of the invention disclosed herein, the heatsink comprises a heat exchange device having a plurality of heat exchange elements which are perforated. As a result, an enhanced heat transfer may be achieved. Additionally, use of perforations may increase heat transfer by up to a factor of two per pumping power. Further, in a specific embodiment, 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. Furthermore, 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.

(134) In an embodiment, 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. As a non-limiting example, the minimum value may be ten.

(135) In another embodiment, a spacing between the plurality of heat exchange elements is determined based on a height of the plurality of heat exchange elements. In a specific embodiment, for a given heat rate, an optimal spacing between the plurality of heat exchange elements may decrease with an increase in height of the plurality of heat exchange elements.

(136) In yet another embodiment, a shape corresponding to the plurality of heat exchange elements may be configured to provide enhanced heat transfer. For instance, the plurality of heat exchange elements may be fluted. As a result, an increase in heat transfer by up to 9% may be achieved. In another instance, the plurality of heat exchange elements may be wavy providing an increase in heat transfer by up to 6%. In one embodiment, the shape corresponding to the plurality of heat exchange elements may be triangular, circular, elliptical, rectangular and trapezoidal. For instance, the plurality of heat exchange elements may be elliptically annular. Further, an elliptical aspect ratio corresponding to the plurality of heat exchange elements may be varied in order to obtain greater heat transfer efficiency. As a non-limiting example, the elliptical aspect ratio may be increased in order to obtain higher heat transfer efficiency. In another instance, the plurality of heat exchange elements may be trapezoidal with an optimal aspect number of 1.5. In yet another instance, the plurality of heat exchange elements may be diamond shaped pin fins. Further, the pitch corresponding to the plurality of heat exchange elements may be varied to obtain enhanced heat transfer. For example, 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.

(137) In other embodiments of the invention, the surface geometry of the plurality of heat exchange elements may be varied in order to provide enhanced heat transfer. For instance, square ribs along the plurality of heat exchange elements may be used. As a result, thermal performance may increase by up to 30%. In another instance, 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. In yet another instance, grooves may be created on the surfaces of the plurality of heat exchange elements. As a result, heat transfer could increase by up to 25%. In a further instance, 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%. Further, in an instance, convex shaped dimples may be used to obtain greater heat transfer.

(138) In some other embodiments, 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.

(139) In other embodiments, the plurality of heat exchange elements may be configured in order to control an amount of heat transfer by radiation. For example, 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. On the other hand, the height of the plurality of heat exchange elements may be increased in order to reduce the amount of heat transfer by radiation. As another example, the plurality of heat exchange elements may be circular around an annular heat pipe. Further, 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.

(140) In an embodiment, 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.

(141) In another embodiment, 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. In general, the heat transfer is directly proportional to the fractal dimension. However, this relationship is valid only till a limited number of iterations.

(142) In yet another embodiment, 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.

(143) In another embodiment, heat transfer may be controlled based on the velocity of fluidic heat exchange medium flowing over the plurality of heat exchange elements. In general, the heat transfer is directly proportional to the velocity of fluidic heat exchange medium under forced convection. Additionally, 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. In another embodiment, 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.

(144) In accordance with embodiments disclosed herein, the heat sink may be manufactured using manufacturing techniques such as, but not limited to, injection 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.

(145) In a particular embodiment, 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.

(146) In another embodiment, 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.

(147) In yet another embodiment, 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.

(148) In a further embodiment, the heatsink may be manufactured using die casting. In this technique, 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.

(149) Those skilled in the art will recognize many ways to fabricate the heatsinks described herein. For example, 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 16 μm. Also, it is possible to grow a crystal structure using a recursive growth algorithm or through crystal growth techniques. For example, 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. For larger heatsinks, such as those intended to be used in car radiators, traditional manufacturing methods for large equipment can be adapted to create the fractal structures described herein.

(150) FIGS. 20-37 illustrate various heatsink designs and proposals, which may be used in conjunction with various embodiments of the technology. In general, these provide heat transfer surfaces with large surface area, and in many cases, small terminal features, which can accumulate or trap dust or particles. According to the present technology, the accumulation or dust and/or particles may be reduced by the various means disclosed herein.

(151) This document describes in detail illustrative examples of the inventive apparatus, methods, and articles of manufacture for making and using fractal heatsinks, along with systems and methods for removing dust and particles from their surfaces. Neither the specific embodiments of the invention as a whole, nor those of its features necessarily limit the general principles underlying the invention. The specific features described herein may be used in some embodiments, but not in others, in the various combinations and permutations, without departure from the spirit and scope of the invention as set forth herein. Various physical arrangements of components and various step sequences also fall within the intended scope of the invention. Many additional modifications are intended in the foregoing disclosure, and it will be appreciated by those of ordinary skill in the art that in some instances some features of the invention will be employed in the absence of a corresponding use of other features. The illustrative examples therefore do not limit the metes and bounds of the invention and the legal protection afforded the invention, which function is carried out by current and future claims and their equivalents.