Spot Heater

Abstract

A device is described in which the shape of a resistive heater material is configured to provide rapid and strong heating of a small area. The resistive heating material is heated unevenly while efficiently using power.

Claims

1. A spot heater, comprising: a sheet of a resistive heating material that comprises an area or areas of reduced cross-sectional area which are adapted to constrict current flow through the sheet of resistive heating material; and an actuator for providing electrical current through the sheet.

2. The spot heater of claim 1 comprising at least one electrical connection of the sheet to an anode and at least one electrical connection of the sheet to a cathode.

3. The spot heater of claim 1 wherein the resistive sheet is a triangle with an anode connected at one edge of the triangle through a busbar and a cathode connected to an opposite point of the triangle.

4. The spot heater of claim 1 wherein the resistive sheet comprises a “bow-tie” configuration with the resistive sheet having two sides where each side is larger (in volume and preferably in area) toward the outer edges (in the direction of current flow during operation) and smaller in between wherein the hottest spot occurs where the smaller regions meet.

5. The spot heater of claim 1 wherein a notch is present in the resistive heating material.

6. The spot heater of claim 1 wherein the areas of reduced cross sections have cross-sectional areas that are at least 40%, 50%, 70%, 80%, or at least 90% (or 50 to 97%) smaller than areas toward the outer edges.

7. The spot heater of claim 6 wherein temperature in a hot spot is at least 10, 20, 50, 100, 200, or at least 300 K hotter than other areas of the sheet of heating material.

8. The spot heater of claim 1 wherein the sheet of resistive heating material has a plurality of cut-outs or openings and wherein, during operation, hot spots occur at constrictions between the cut-outs or openings in material.

9. The spot heater of claim 8 wherein the cut-outs or openings are voids.

10. The spot heater of claim 8 wherein the cut-outs or openings are filled with an insulating material.

11. The spot heater of claim 1 wherein the sheet material comprises at least 2, at least 5, at least 10, at least 50, or 2 to 1000 hot spots created by areas (spots) of constrained current flow (during operation).

12. The spot heater of claim 1 wherein the sheet has a surface area of at least 10, 20, 50, or 100 cm.sup.2 and optionally were each hot spot has an area of at least 0.1, 0.2, 0.5, 1 or between 0.1, 0.2, 0.5, 1 to 1, 2, or 5 cm.sup.2; wherein a single sheet of the resistive heating material comprises at least 10, 20, 50, 100 or 10 to 10,000 cut-outs or openings and 10, 20, 50, 100 or 10 to 10,000 hot spots; or any combination of these features.

13. A method of resistive heating, comprising: providing a sheet of a resistive heating material that comprises an area or areas of reduced cross-sectional area which are adapted to constrict current flow through the sheet of heating material; passing an electric current through the sheet such that the area or areas adapted to constrict current flow become a hot spot or hot spots that increase in temperature to a temperature that is at least 5 K greater than the average temperature of the sheet.

14. The method of claim 13 wherein a notch in the resistive heating material creates the hot spot.

15. The method of claim 13 wherein the temperature in a hot spot is at least 10, 20, 50, 100, 200, or at least 300 K hotter than other areas of the sheet of heating material.

16. The method of claim 13 wherein the hottest contiguous 10% of the sheet is at least 10, 20, 50, 100, 200, or at least 300 K hotter than the 50% of the sheet where the resistive sheet is coldest (as measured at the sheet surface).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

[0016] FIG. 1 illustrates a shaped resistive heater with aligned conductive fibers.

[0017] FIG. 2 shows some parameter definitions for a resistive heater.

[0018] FIG. 3 shows that increasing the gap angle increases the power density in an approximately linear fashion.

[0019] FIG. 4 illustrates the effect of two different gap angles on power density and current density.

[0020] FIG. 5 shows power density as a function of gap height (in inches) for gap angles of 10° (top) and 25° (bottom).

[0021] FIG. 6 illustrates how the extent of constriction controls the power density of a hot spot.

[0022] FIG. 7 shows the use of a notch to constrict flow and create a hot spot that is distanced from the heat sink created by the electrode.

[0023] FIG. 8 illustrates the effect of constriction angle.

[0024] FIG. 9 illustrates the effect of material height downstream of the hot spot.

[0025] FIG. 10 shows the effect of gap length in a notched spot heater.

[0026] FIG. 11 shows how a wider gap length will decrease the peak current density values substantially.

[0027] FIG. 12 illustrates a calculated heat profile of a spot heater in which the CNT sheet is surrounded by a layer of Kapton tape on either side.

[0028] FIG. 13 illustrates an embodiment in which the resistive material is shaped to replace a busbar with the resistive heater material.

[0029] FIG. 14 is a photograph of a triangular spot heater in use.

[0030] FIG. 15 is a diagram of the construction of the triangular spot heater.

[0031] FIG. 16 shows 3 spot heaters that were tested as explained in the examples.

[0032] FIG. 17 shows a thermal image of a bow-tie shaped heater.

[0033] FIG. 18 shows the time needed for three different shapes to reach 700° F. for the same applied current.

[0034] FIG. 19 shows a thermal image of a heater with diamond cutouts that are located to create hot spots at specific points.

DESCRIPTION OF THE INVENTION

Resistive Heating Materials

[0035] The preferred materials for the heater are those that can withstand high power densities in the range of 50,000 to 200,000 W/in.sup.2 or 100,000 to 150,000 W/in.sup.2, or about 120,000 W/in.sup.2 and have low thermal mass to allow for rapid heat-up. Suitable materials include metallic foils and carbon-based materials such as graphite foils, carbon nanotube bucky papers, graphene sheets, and similar materials. However, to avoid excessive heat spreading, which would eliminate the effectiveness of the spot heat, it is preferred that conductive materials have thermal conductivity less than about 50 W/mK and/or sufficiently low mass (e.g. a thin film) and on a thermally insulating substrate. Inks and dispersions of these materials can also be used to print or spray-apply patterns of heaters onto substrates. For reusable heaters, any binding material in the ink must be selected to withstand the temperatures that will be generated or must be removed in a second processing step before use.

[0036] Because low thermal mass is a highly desirable property of the resistive heating material, carbon nanotubes are especially desirable materials for the present invention. The term “carbon nanotube” or “CNT” includes single, double and multiwall carbon nanotubes and, unless further specified, also includes bundles and other morphologies. The invention is not limited to specific types of CNTs. The CNTs can be any combination of these materials, for example, a CNT composition may include a mixture of single and multiwall CNTs, or it may consist essentially of DWNT and/or MWNT, or it may consist essentially of SWNT, etc. CNTs have an aspect ratio (length to diameter) of at least 50, preferably at least 100, and typically more than 1000.

[0037] The sheets of resistive heating elements can be sheets of commercially-available bucky-paper. The sheets can be stamped or cut to provide the features desired. (2) Alternatively, the heaters can be constructed using processes similar to those in printed circuit board (PCB) processes. The precursor ink is applied to a thermally stable substrate into the desired geometry. The system is cured, washed, and/or baked to eliminate thermally labile components.

[0038] Other materials of construction, such as to create laminates, can be used. For any substrate that is in contact with the heater, the material should be selected for the service temperature that will be achieved and any dielectric resistance needed to isolate the heater electrically from other conductive components. For high temperature applications, where the heater operates at 500 to 700° F., suitable plastic materials include polyimides (Kapton HN, Meldin® 7001), polyamide imide (Torlon), polybenzimidazoles, and polytetrafluoroethylene.

[0039] The heaters can also be applied to glass, ceramics, and other hybrid organic-inorganic systems. Bonding for composites and other laminates can, likewise, utilize adhesives that are appropriate for the target temperatures. Arrays of these designs can be used in applications where fast heat up time is desired such as ovens for food preparation, clothes dryers, dishwashers or on components for evaporative heaters for refrigerators.

[0040] For resistive heaters formed with conductive fibers, it is preferred that the fibers are non-aligned. If the fibers are aligned, and the film is then cut into the shapes of this invention, there will be pathways that are terminated (see FIG. 1). Because in an aligned film, there is minimal interaction between adjacent pathways, focusing geometries do not provide current density amplification. In a randomly oriented sample, the number of connections between adjacent films is maximized. In practice aligned samples do not normally have such perfect alignment. Nonetheless, it is desirable to maximize the connection between parallel pathways, whether through random alignment or other methods.

[0041] Since the preferred resistive elements are carbon nanotube (CNT) sheets or other shapes; the following discussion incorporates known descriptions of CNT resistive heater features that can be incorporated into preferred embodiments of the invention.

[0042] A CNT network can be prepared, for example, as a dispersion of CNTs applied directly to a substrate where the solvents used in the dispersion process are evaporated off leaving a layer of CNTs that coagulate together into a continuous network. The CNT network may be prepared from dispersions and applied by coating methods known in the art, such as, but not limited to, spraying (air assisted airless, airless or air), roll-coating, gravure printing, flexography, brush applied and spin-coating. The thickness of the CNT layer is preferably in the range from 0.005 μm to 100 μm, or in the range of 0.05 μm to 100 μm, or in the range of 0.3 μm to 100 μm.

[0043] The CNT layer may include other optional additives such as p-dopants. P-dopants could include, but are not limited to, perfluorosulfonic acids, thionyl chloride, organic pi-acids, nitrobenzene, organometallic Lewis acids, organic Lewis acids, or Bronsted acids. Materials that function as both dispersing agents and dopants such as Nafion and hyaluronic acid may be present. These materials contain p-doping moieties, i.e. electron accepting groups, within their structure, often as pendant groups on a backbone. Generally, these additives will be present as less than 70% by weight of the CNT film, and in some embodiments as less than 50% by weight of the CNT film. CNT network layers of the present invention preferably contain at least 25 weight % CNT, in some embodiments at least 50 wt %, and in some embodiments 25 to 100 wt % CNT. The volume fraction in the network layer is preferably at least 2% CNTs, more preferably at least 5%, and in some embodiments 2 to about 90%. The remainder of the composite may comprise air (by volume) and/or other materials such as residual surfactant, carbonaceous materials, or dispersing agent (by weight and/or volume). Polymers and carbohydrates that function as both dispersing agents and dopants can be distinguished from other polymer materials, i.e. those functioning as only a dispersing agent or those functioning as a structural component. Because of the presence of electron accepting moieties, these materials can form a charge transfer complex with semiconducting CNTs, which p-dopes the semiconducting CNTs and raises the electrical conductivity. Thus, these dual dispersing agent/dopants can be tolerated at a higher mass percentage within the CNT layer than other types of polymer materials or surfactants.

[0044] If present, the thickness of a coating composition over the CNT material is preferably 2 mm or less, more preferably 150 μm or less, preferably 50 μm or less, in some embodiments, a thickness of 250 nm to 50 μm; thicker layers can experience foaming or bubbling during application that leads to pathways for a subsequent topcoat to penetrate and disrupt the conductivity of the CNT layer. Since it is important to reduce heat loss, any adjacent layer should not form a substantial heat sink. In some embodiments, the spot heater is applied to a substrate into which the heat is to be directed, the other major surface of the heater can be a thermally insulating material or a thermally reflective material.

[0045] A coating composition can be applied to the CNT network by known methods; for example, bar coating or spraying. Techniques, such as troweling, that disrupt the CNT network should be avoided. After application of a protective coating to the CNT network, the coated substrate can be cured (in some embodiments, curing is conducted at ambient temperature). In the curing operation, the film forming materials crosslink to leave a mechanically durable and chemically resistant film.

[0046] A multilayered laminate resistive heater could be manufactured with conventional roll coat equipment. The electronic leads could be printed on a base substrate, such as 3M's Aerospace quality protective film. The carbon nanotube dispersion can then be applied to the film printed with circuitry with conventional roll coating methods. The protective coating could also be applied in this manner in-line.

[0047] In some embodiments, the CNT is substantially polymer-free such that polymer (if present) does not significantly affect the electrical properties of the layer; in some embodiments, the interior of the CNT layer contains 10 weight % polymer or less, more preferably 5 wt % or less, and still more preferably 2 wt % or less. In some embodiments, a pressure sensitive adhesive (PSA) is present on the major side of the substrate opposite the side over which the CNT layer is disposed. The PSA can be used to adhere the resistive heater to a surface in need of heating. A resistive heater laminate can be applied in the field since the substrate can be backed with a pressure sensitive adhesive (an adhesive that bonds to a substrate by the application of pressure) and a release layer. The release layer would be removed and the laminated heater applied to a substrate like a sticker. A more permanent installation of a laminate heater can be applied with a structural adhesive such as epoxy instead of a pressure sensitive adhesive. If an adhesive is used to bond to a surface in need of heating, the adhesive is preferably thermally conductive.

[0048] The aqueous or non-aqueous solvent present in common top coats, when applied to a CNT material, may disrupt the electrical properties of the CNT material by several mechanisms. One mechanism is by increasing the electrical resistance between adjacent CNTs. Topcoats dissolved in solvents can infiltrate the CNTs, permitting the topcoat resin system to permeate and cure between the individual CNT fibers. The CNTs require intimate contact to transport electrical charge from one CNT to another; charge transport takes place though either tunneling or hopping. If a non-conductive polymer resin remains between the CNTs, it prevents close contact of CNTs, which increases the energy associated with electron hopping or tunneling, and behaves as a high resistance resistor in series. The effect is that the bulk conductivity of the CNT material is reduced significantly. Treatment of CNTs with surfactants or dispersing agents is often used to improve their interaction with water or solvents. After film formation; these surfactants and dispersing agents often remain in the film, continuing to modify the surface properties of the CNTs. This renders the CNT layer more susceptible to penetration by aqueous or non-aqueous solvents. To avoid this problem, in some preferred embodiments, a solvent-free protective layer can be used to prevent the change in resistance that accompanies the application of either organic-solvent-based or water-based coatings to CNT materials. In some embodiments, a polyurethane coating is in direct contact with the CNT layer.

[0049] The polymer protective coating provides sufficient chemical resistance so as to prevent solvents (including water), or other environmental hazards from subsequently applied coatings or solvents from penetrating the polymer and disrupting the CNT network or changing its conductivity significantly.

[0050] CNT layers have many contacts between CNTs and good conductivity that is, a resistivity less than 0.05 Ω.Math.cm, preferably less than 0.002 Ω.Math.cm. The sheet resistance of this layer should be less than 500 Ω/square, preferably less than 200 Ω/square, more preferably less than 50 Ω/square. A CNT layer may be planar, cylindrical, or other contiguous geometry; in some preferred embodiments, the CNT layer is substantially planar (similar to a sheet of paper or a nonwoven textile sheet, a few fibers may project from a planar layer). These are preferred characteristics of the CNT layer both before and after an optional coating is applied over the CNT layer.

[0051] Application of a coating should result in less than 80% change in resistance, preferably less than 10% change in resistance, and still more preferably less than 5% change in resistance, after curing the coating. Likewise, application of subsequent layers on top of this stack preferably do not increase the resistance by more than 5%, preferably by 3% or less.

[0052] The resistive heating film may have an essentially constant film thickness and a varied shape (in two dimensions) to provide one or more constrictions. The thickness of the resistive element preferably varies by 25%, 10%, or 5% or less. In some embodiments, a resistive heating film has a maximum thickness of 5 mm or less, in some embodiments in the range of 0.001 to 3 mm, or 0.01 to 2 mm, or 1 mm or less, or at least 0.1 mm and/or at least 0.001 mm.

[0053] Alternatively, the constriction can be formed in three dimensions such as by a (truncated) cone or (truncated) pyramid or a sheet of truncated cones or pyramids, or a curved hourglass shape. These are the three dimensional equivalent of the bow tie configuration. Likewise, other versions of the two dimensional sheets can be reconfigured in the equivalent in three dimensions.

Variables

[0054] To evaluate concepts and trends discussed in this patent application, computational electrodynamics modeling was used. The code calculates electric current density from the electric potential between the two electrical leads. Since the geometries are complex and potentially 3-dimensional, the geometry is discretized into small elements, referred to as control volumes, in which the governing equations can be more readily solved.

[0055] The solver is an iterative solver, solving the governing equation for electric potential on the control volumes, balanced with the applied boundary conditions. The result is a electric potential field that an be used to calculate current density and ultimately power density. The code works by iteratively solving the governing equations on the cells, moving closer to a solution that satisfies the boundary condition, while maintaining stability and accuracy. The code typically converges onto the solution within 200 iterations. The solver computes the electric potential using the following equation, which is integrated on the faces and volume of the control volumes, respectively, depending on their integral format

[00001]$-{\oint }_A.Math.\sigma .Math.{\nabla }_{\varnothing }.Math..Math.\mathrm{da}-{\oint }_A.Math.\sigma .Math.\frac{\partial A}{\partial t}.Math.\mathrm{da}=-{\oint }_A.Math.{\mathrm{\sigma \rho }}_{ϵ}.Math.\mathrm{da}+{\int }_V.Math.s_{\varnothing }.Math.\mathrm{dV}$

Once calculated, the electric potential is calculated, the current density can be calculated according to the following relation, where J is the current density and E is the electric field vector J=GE

[00002]$\mathrm{Symbols}.Math.\text{:}$$\mathrm{.Math.}.Math.\text{-}.Math.\mathrm{electrical}.Math..Math.\mathrm{permittivity}$$\sigma .Math.\text{-}.Math.\mathrm{electrical}.Math..Math.\mathrm{conductivity}$$A.Math.\text{-}.Math.\mathrm{magnetic}.Math..Math.\mathrm{potential}.Math..Math.\mathrm{vector}$$\varnothing .Math.\text{-}.Math.\mathrm{electric}.Math..Math.\mathrm{potential}$${\oint }_A.Math.\mathrm{da}.Math.\text{-}.Math.\mathrm{Integral}.Math..Math.\mathrm{over}.Math..Math.\mathrm{control}.Math..Math.\mathrm{volume}.Math..Math.\mathrm{face}$$\frac{\partial A}{\partial t}.Math.\text{-}.Math.\mathrm{Time}.Math..Math.\mathrm{variation}.Math..Math.\mathrm{in}.Math..Math.\mathrm{magnetic}.Math..Math.\mathrm{field}$$\rho .Math.\text{-}.Math.\mathrm{electric}.Math..Math.\mathrm{charge}.Math..Math.\mathrm{density}.Math.$${\int }_V.Math.\mathrm{dV}.Math.\text{-}.Math.\mathrm{Integral}.Math..Math.\mathrm{over}.Math..Math.\mathrm{control}.Math..Math.\mathrm{volume}$$s_{\varnothing }.Math.\text{-}.Math..Math.\mathrm{Source}.Math..Math.\mathrm{term}.Math..Math.\mathrm{representing}.Math..Math.\mathrm{electric}.Math..Math.\mathrm{currents}.Math..Math.\mathrm{flow}.Math..Math.\mathrm{through}.Math..Math.\mathrm{the}.Math..Math.\mathrm{control}.Math..Math.\mathrm{surface}.Math..Math.\mathrm{face}$

Several parametrics were run to determine the sensitivity of maximum power density on these variables. The maximum values were taken from an infinitesimally small location and therefore will not likely be as high as calculated.

[0056] Some factors that can be varied to control properties of the spot heater include: 1) the height ratio from the incoming lead to the constriction, 2) the angle that the constriction forms, and 3) height of the section after the constriction.

[0057] The distance to the start of the feature is preferably large enough to ensure that the heat created does not disrupt the bond of the electrode to the resistive element. Preferably at least 0.2 cm or at least 0.5 cm, or at least 0.8 cm from the attachment to the anode and/or cathode. Preferably, there is no heat sink such as a high thermal conductor (especially one that has a mass of 50% or greater of the mass of the resistive heater material (typically a CNT sheet)) thermally connected to the heater and within 0.2 cm or at least 0.5 cm, or at least 0.8 cm from the nearest edge of a gap where the hot spot is formed.

[0058] FIG. 2 shows some parameter definitions. FIG. 3 shows that increasing the gap angle increases the power density in an approximately linear fashion. FIG. 4 compares the effect of two different gap angles on power density and current density.

[0059] Gap height affects the power density achieved in a significant way; the smaller the gap height, the higher the power density. This is shown in FIG. 5 for gap angles of 10 and 25 degrees.

[0060] The size of the leads also makes a difference.

[0061] The focusing factor effectively relates to the volume cross section at the constriction vs the volume for electrons to flow at the lead. This is because you have the same amount of electrons flowing at both points, so continuity requires there to be a higher current (or flux of electrons) at the smaller point, thus higher power density. Therefore, the focusing factor should be

[00003]$\frac{A_{\mathrm{Lead}}}{A_{\mathrm{Constriction}}}.$

That is a generic sense, for a resistive heater with constant thickness, this can be written as effectively

[00004]$\frac{H_{\mathrm{Lead}}}{H_{\mathrm{Constriction}}}$

where H is the height or length of the lead/constriction.

[0062] In some embodiments of the invention, the resistive heating sheet or spot heater can be characterized by any of the configurations or values shown in the figures. These characterizations include ±30%, or ±20%, or ±10% of any of these configurations or values including, but not limited to, power density, relative area, height, width, angle, and/or relative length ratios (for example, a constriction width to non-constricted width of at least one side) as shown in the figures.

[0063] The constriction (percentage reduction in cross-sectional area perpendicular to net current flow) is the most important parameter as demonstrated by the images in FIG. 6. In this image, the only dimension changed in the minimum thickness. The scale is limited to 4000 W/in.sup.2, however this clips the maximum value. Therefore, the max value is listed in the text box associated with each image. The reason the constriction is so significant is because it funnels all electrons in the circuit to a central location, increasing the current density locally. This is especially pronounced at the edges of the constriction.

[0064] In another preferred orientation, a notch is located in the center of the heater instead of at one end, and keep the heat away from the leads which act as a heat sink. See FIG. 7. A notch is preferably created by an angle of at least 70 degrees, or at least 80 degrees, on both sides of the gap; and preferably where the gap is located at least 0.4 cm from any electrode connected to the resistive heater.

[0065] The angle at which the constriction is made also plays an important role, as is shown in FIG. 8. The angle on the right side of the constriction is varied from 75° (left) to 35° (right) while all other dimensions are maintained. It is observed that the peak value decreased by approximately 20%. Constriction angle is the angle of inclination of the resistive material as the material increases in height (or cross-sectional area) in direction of net current flow away from the gap. For direct current, there is an incoming constriction angle and an outgoing constriction angle. Constriction angle (either or both of incoming and outgoing) is preferably at least 35°, or at least 45°, or at least 60°.

[0066] Downstream of the constriction, the amount to which the heater expands is an important parameter. FIG. 9 compares two heater designs that have identical geometry except the downstream expansion. In this scenario a 50% decrease in peak power density is observed. Thus, a downstream height of at least 50% or at least 75% that of the upstream resistive material is desirable.

[0067] Extending these concepts to the extreme, if a vertical slit is created that is very fine, the maximum power density at these edges can be increased further. FIG. 10 shows this concept compared to the previous one with a 2.6× increase in peak power density, locally. There may be considerations, such as electrical or thermal shorts, that limit how thin a gap can be if the constriction angle approaches 90 degrees.

[0068] In a variation, the width of the vertical slit is observed to be very critical. FIG. 11 shows how a wider gap length will decrease the peak values substantially.

[0069] A thermal model has been developed to assess how rapidly one of the optimized heaters would be expected to heat up. For this model, it was assumed that the heater was surrounded by a layer of Kapton tape on either side. This is depicted in FIG. 12. When run at 4.5V, the heater is observed to achieve a temperature of approximately 1200° F. in one second. When run at 9.0V, the heater is observed to achieve a temperature of 2000° F. in only 0.25 seconds.

[0070] In some embodiments, the spot heater heats to more moderate temperatures, for example, 250 F to 350° F., allowing the use of resistive heating materials that are more thermally labile, such as metal or carbon-filled polymers. Such systems can be injection molded or 3D-printed into three-dimensional geometries.

Other Designs

[0071] Another possible design is schematically illustrated in FIG. 13. The resistive heating element can be cut so that no busbars are required and heater connects directly to the power source via strips.

[0072] This can be laser cut from a single material and avoid the copper wire or other electrical connection. In the figure above, the connections to the resistor may not be shown to scale and may be wider to provide less temperature rise in the strips. The strip carrying electricity to the triangle may also be shaped to provide a plurality of connections to the side of the triangle furthest from the constriction in order to more evenly distribute current flow as current enters or exits the triangle.

EXAMPLES

[0073] Several polyimide tape heater geometries can achieve up to ±1600° F. (870° C.) with a voltage between 6 and 9 in <1 second. The heating is so rapid that it can create a small combustion of the tape. This is useful for single-use applications or multiuse with lower voltage and compatible materials. Additionally, 800° F. (426° C.) can be achieved with the polyimide heaters in approximately 30 seconds with very low power (1.5v). These characteristics can be used to define some preferred embodiments of the invention.

[0074] As shown in FIG. 14, a triangular piece of buckypaper was connected to two electrical leads and current from a 9V battery was passed through the device. As can be seen in the photo, a red hot spot was generated near the apex of the triangle in less than 0.5 seconds. The illustrated device was sandwiched between two sheets of Kapton tape; however, these are not required for the invention.

[0075] As shown in FIG. 16, three geometries were cut from 1″×1″ squares of bucky paper-square, triangle, bowtie.

[0076] Materials: MWNT bucky paper, 60 gsm from Buckeye Composites approx 0.5 ohms/square surface, copper braid hex wik WC54 for leads, EJ2189 silver epoxy to attach leads to heaters, Tempilaq 700° F. temperature indicating paint over entire heater surface, Kapton tape Procedure: Voltage was applied to leads and recorded time required to visually observe Tempilaq paint turn from pale orange to black at any location on the heater.

[0077] The results of the heating tests showed that the triangle and bowtie geometries reach at least 700° F. faster than a square geometry even though the current path length between busbars is equivalent for each heater at 1″. This type of heater can be made from other materials such as etched foil. It is the geometry that is the key feature to create areas of high watt density.

[0078] The square heater showed uniform heating across the heater. The triangle heater showed a low temp of 68.8° C. (155° F.) on cold side of heater and the hot end was at least 700° F. The bowtie configuration showed low temp of 98.9° C. (209° F.) on the outside and at least 700° F. in center (see FIG. 17). The results of time for each shape to reach 700° F. are shown in FIG. 18

[0079] Another device that was tested was a CNT resistive heating sheet in which diamond-shaped holes were cut in the material. FIG. 19 is a thermal image of a heater with diamond cutouts that are located to create hot spots at specific points. The thermal gradients can be understood by reference to the temperature scale shown on the right. As can be seen, thermal hotspots are observed at constrictions in the direction of current flow but not at constrictions in other directions (note that relatively cool spots are observed at constrictions orthogonal to current flow.

Calculated Example

[0080] The calculated example below illustrates some advantages of the invention.

TABLE-US-00001 4000.0 Power generated, W/in2 620.0 W/cm2 0.250 Area of 5 mm rectangular spot (cm2) 155.0 Power needed in 5 mm spot (W) 17.2 Power = V*I, I needed for 9 V (A) 0.5 Resistance needed V = IR, V/l (ohms) 0.5 Sheet Resistance needed for 5 mm square (ohm/sq) 4000.0 Power generated, W/in2 620.0 W/cm2 0.003 Area of 0.5 mm rec. spot (cm2) 1.6 Power needed in 5 mm spot (W) 0.2 Power = V*I, I needed for 9 V (A) 52.3 Resistance needed V = IR, V/l (ohms) 52.3 Sheet Resistance needed for 5 mm square (ohm/sq)