WO2022115346A1

WO2022115346A1 - Catalyst heater with serpentine concentric segments

Info

Publication number: WO2022115346A1
Application number: PCT/US2021/060249
Authority: WO
Inventors: Gregory Albert Merkel
Original assignee: Corning Incorporated
Priority date: 2020-11-26
Filing date: 2021-11-22
Publication date: 2022-06-02

Abstract

A heater assembly including a continuous body. The continuous body includes a plurality of segments that extend between first and second ends. The segments are arranged with respect to a plurality of concentric rings that are concentric about a central axis. A plurality of returns is arranged with each return connecting two of the segments together. The two segments connected by each return are respectively aligned with two radially adjacent concentric rings and are also successive in series along a length of the continuous body. A plurality of circumferential gaps are located between opposing pairs of the returns. Each circumferential gap circumferentially separates two of the segments aligned with respect to a same one of concentric rings. A method of manufacturing a heater assembly and a fluid treatment system including the heater assembly are also disclosed.

Description

CATALYST HEATER WITH SERPENTINE CONCENTRIC SEGMENTS BACKGROUND [0001] This application claims the benefit of priority under 35 U.S.C. §119 of U.S. Provisional Application Serial No.63/118686 filed on November 26, 2020, the content of which is relied upon and incorporated herein by reference in its entirety. 1. Field [0002] This disclosure relates to fluid treatment systems, such as exhaust aftertreatment systems, and more particularly heater assemblies to aid in the treatment of fluids, such as electrically powered heaters useful for activating catalysts in exhaust aftertreatment systems. 2. Technical Background [0003] Some fluid treatment systems, such as engine exhaust aftertreatment systems, may benefit from additional heat supplied from a supplemental heater. Examples of such systems include electrically heated catalyst (EHC) systems that have an electrically powered heater useful to quickly achieve temperatures sufficient to initiate activation of a catalyst material in the aftertreatment of engine exhaust. SUMMARY [0004] In some embodiments, a heater assembly is disclosed herein comprising: a continuous body having a central axis, the continuous body comprising: first and second ends; a plurality of segments arranged in series extending along a length of the continuous body between the first and second ends, wherein the segments are arranged with respect to a plurality of concentric rings that are concentric about the central axis; a plurality of returns, each return connecting two of the segments together, wherein each return comprises a bend such that the two segments connected by each return are respectively aligned with two radially adjacent concentric rings and are also successive in series along a length of the continuous body; and a plurality of circumferential gaps located between opposing pairs of the returns, wherein each circumferential gap circumferentially separates two of the segments aligned with respect to a same one of concentric rings. [0005] In some embodiments, the heater assembly comprises a pair of electrodes and wherein the first and second ends of the continuous body are connected to respective ones of the electrodes. [0006] In some embodiments, the electrodes are integrally formed with the continuous body as a single monolithic component. [0007] In some embodiments, multiple of the circumferential gaps and corresponding pairs of returns are arranged together at different radial positions along one or more radii extending from the central axis. [0008] In some embodiments, the circumferential gaps and corresponding pairs of returns are arranged with respect to at least two radii. [0009] In some embodiments, the circumferential gaps and corresponding pairs of returns are arranged with respect to from two to eight radii. [0010] In some embodiments, the radii are evenly circumferentially spaced about the central axis. [0011] In some embodiments, each radially successive pair of returns, starting from a first pair of returns connecting the segments aligned with the two outermost concentric circles, are arranged at a different one of the radii until at least one pair of the returns is aligned with respect to each of the radii. [0012] In some embodiments, the segments of the continuous body are arranged with respect to at least ten concentric rings. [0013] In some embodiments, the concentric rings are circular. [0014] In some embodiments, the concentric rings are rectangular. [0015] In some embodiments, the heater assembly comprises at least two of the continuous bodies separate from each other arranged electrically in parallel. [0016] In some embodiments, the heater assembly comprises two of the continuous bodies and the two continuous bodies are symmetrical with respect to a line drawn through and perpendicular to the central axis. [0017] In some embodiments, the heater assembly has an outer peripheral shape defined by a shape of the concentric rings. [0018] In some embodiments, the continuous body comprises a conductive ceramic material. [0019] In some embodiments, the conductive ceramic material is a single-phase ceramic material. [0020] In some embodiments, the conductive ceramic material of the continuous body comprises at least one of a transition metal silicide or aluminide, or a solid solution thereof. [0021] In some embodiments, the transition metal silicide or aluminide comprises at least one of MoSi2, WSi2, TaSi2, TiSi2, ZrSi2, CrSi2, FeSi2, NiSi2, CoSi2, MoAl3, TiAl3, TaAl3, or ZrAl3. [0022] In some embodiments, the continuous body comprises the conductive ceramic material as a primary phase with one or more secondary phases. [0023] In some embodiments, a material of the continuous body has a conductivity of at least 0.2x104 ohm-1 cm-1. [0024] In some embodiments, the conductivity is from 0.2x104 ohm-1 cm-1 to 5x104 ohm-1 cm- 1. [0025] In some embodiments, a midline of the segments is aligned along respective concentric rings. [0026] In some embodiments, the segments are aligned along respective concentric rings in an oscillating manner. [0027] In some embodiments, the segments sinusoidally oscillate along the concentric rings. [0028] In some embodiments, a fluid treatment system is disclsoed comprising the heater assembly any of the preceding paragraphs. [0029] In some embodiments, the heater assembly is in fluid communication with a catalyst- loaded substrate. [0030] In some embodiments, a method of manufacturing the heater assembly of any of the preceding paragraphs is disclosed, the method comprising: shaping a mixture comprising a ceramic powder into a green body preform; and sintering the preform to convert materials of the preform into the continuous body. [0031] In some embodiments, sintering the preform converts materials of the green body preform into a monolithic component that comprises both the continuous body and a pair of electrodes connected to the first and second ends of the continuous body. [0032] In some embodiments, sintering the preform comprises one or more radially extending supporting elements connecting between radially adjacent ones of the segments, and the method comprises severing the supporting elements before or after the sintering. [0033] In some embodiments, a heater assembly is disclosed comprising: a pair of electrodes; a continuous body having an outer peripheral shape and a central axis, the continuous body comprising: a serpentine concentric pattern that comprises a plurality of concentric rings positioned about a central axis, wherein the continuous body comprises: a first segment and a second segment of the plurality of segments, wherein the first and second segments are circumferentially adjacent to each other and both aligned with respect to a first concentric ring of the concentric rings, a third segment of the plurality of segments that is radially adjacent to the first segment; a fourth segment of the plurality of segments that is radially adjacent to the second segment, wherein the third and fourth segments are both aligned with respect to a second concentric ring that is radially adjacent to the first concentric ring; a circumferential gap circumferentially separating the first segment from the second segment and circumferentially separating the third segment from the fourth segment; and a pair of returns at opposing sides of the circumferential gap, wherein a first return of the pair of returns connects the first segment to the third segment and a second return of the pair of returns connects the second segment to the fourth segment. [0034] It is to be understood that both the foregoing general description and the following detailed description are merely exemplary, and are intended to provide an overview or framework to understanding the nature and character of the claimed subject matter. The accompanying drawings are included to provide a further understanding and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiment(s), and together with the description, serve to explain principles and operation of the various embodiments. BRIEF DESCRIPTION OF THE DRAWINGS [0035] FIG. 1A shows an end face of a heater assembly comprising a heating element in the form of a continuous body arranged in a serpentine pattern of concentric segments according to one embodiment disclosed herein. [0036] FIG.1B is an enlarged view of the indicated area of FIG.1A showing two pairs of returns of the serpentine pattern of the continuous body. [0037] FIG. 1C is an enlarged view of the indicated area of FIG. 1A showing a centermost or innermost segment of the continuous body. [0038] FIG. 1D is a cross-sectional view taken generally along the line 1D-1D in FIG. 1B showing the thickness and axial height of the continuous body. [0039] FIGS. 2-14 show end faces of heater assemblies comprising a single continuous body according to various embodiments disclosed herein. [0040] FIGS. 15 and 16 show end faces of heater assemblies comprising a pair of continuous bodies arranged in parallel according to embodiments disclosed herein. [0041] FIGS. 17 and 18 show end faces of a heater assembly comprising temporary radial supports that respectively show the heater assembly before and after severing of the radial supports according to one embodiment herein. [0042] FIG. 19 shows two radially adjacent segments of a continuous body connected by a return, in which the segments are arranged sinusoidally along concentric rings according to one embodiment disclosed herein. [0043] FIGS.20 and 21 are graphs showing the heat up performance (temperature with respect to time) for various example heater assemblies disclosed herein. DETAILED DESCRIPTION [0044] Reference will now be made in detail to exemplary embodiments which are illustrated in the accompanying drawings. Whenever possible, the same reference numerals will be used throughout the drawings to refer to the same or like parts. The components in the drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the exemplary embodiments. [0045] Modifications of the disclosure will occur to those skilled in the art and to those who make or use the disclosure. Therefore, it is understood that the embodiments shown in the drawings and described herein are merely for illustrative purposes and not intended to limit the scope of the disclosure, which is defined by the following claims, as interpreted according to the principles of patent law, including the doctrine of equivalents. [0046] As used herein, the term “about” means that amounts, sizes, formulations, parameters, and other quantities and characteristics are not and need not be exact, but may be approximate and/or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding off, measurement error and the like, and other factors known to those of skill in the art. When the term “about” is used in describing a value or an end-point of a range, the disclosure should be understood to also include the specific value or end-point referred to. [0047] Directional terms as used herein—for example up, down, right, left, front, back, top, bottom—are made only with reference to the figures as drawn and are not intended to imply absolute orientation. [0048] In various embodiments, disclosed herein are gas flow-through heaters, such as can be used in an electrically heated catalyst (EHC) system. For example, an EHC system can be arranged to rapidly heat the exhaust gas from an internal combustion engine to a temperature at which catalytic conversion of the exhaust gas becomes effective. In comparison, existing EHC systems based upon spiral-wound sheets of corrugated metal have a high thermal mass resulting in a slow heating time. Slotted metal honeycomb heaters can be formed that have a lower thermal mass than the spiral-would corrugate sheets, and thereby a faster heat-up, but may exhibit deformation of the metal over the course of thermal cycling and require insulating elements to prevent the structure from short-circuiting. Non-slotted ceramic honeycomb heaters generally exhibit good dimensional stability, but may have undesirably low thermal stress resistance in some applications due to the rigidness of the ceramic structure and generally high coefficient of thermal expansion (CTE) of conductive ceramic materials. Such ceramic heaters may also require bonding of an electrode having a different composition (e.g., lower resistivity) over a large interfacial area, which may create additional thermal stresses due to CTE differences between the electrode and ceramic heater body. Advantageously, according to embodiments disclosed herein are designs for heating elements that are suitable for manufacture from ceramic materials and exhibit improved thermal stress resistance. Additionally, disclosed herein are heating elements that can be manufactured comprising an integrally-formed low-resistance electrode of the same material as the rest of the heating element. [0049] According to embodiments disclosed herein, the heating element comprises a continuous body, or ribbon, of electrically conductive material (e.g., conductive ceramic material) comprising a series of concentrically arranged segments interconnected in a serpentine pattern. The heating element can be formed such that the continuous body terminates at low-resistance electrodes that are integrally formed with the continuous body and/or made from the same material as the continuous body. Also disclosed herein are methods of manufacturing a heating element comprising multiple concentric segments arranged in a serpentine pattern from a raw material powder mixture and firing at high temperature to convert the powder compact into a sintered porous or non-porous body. The electrodes can be formed simultaneously as an integral part of the heater, in which the electrodes comprise the same raw material powder mixture as the heater body and the electrodes and heater body are fired together to create the heating element as an integral, single, or monolithic component by sintering of the powder during firing. [0050] The embodiments disclosed herein provide a highly strain-compliant geometry for a heater. Advantageously, the currently disclosed embodiments reduce stresses arising from thermal gradients across the heater and enable the use of materials having high coefficients of thermal expansion. The disclosed heater designs are suitable for manufacture by ceramic materials, which provides greater strength and dimensional stability at high temperatures in comparison to metals. [0051] In some embodiments, the continuous body is formed from an undoped single-phase ceramic material having an intrinsically high electrical conductivity, which may achieve more consistent conductivities than composites of high- and low-conductivity phases or doping of a single-phase material and enable manufacture of the heaters to be less sensitive to variability in raw materials, impurities, sintering conditions, and microstructure. [0052] In some embodiments, the electrodes are made from the same raw materials and therefore has the same composition as the heater body. Advantageously, this enables simultaneous green fabrication, drying/curing, and sintering of the both the heater body and the electrodes (e.g., integrally form the heater body and electrodes as a single monolithic heating element). Advantageously, this avoids the need to separately attach the electrodes to the heater and establishes a similar CTE for the electrodes and body, thereby reducing or even eliminating the thermal stresses between the electrode and heater body. [0053] Advantageously, the concentric pattern of the continuous body enables the opposite ends of the continuous body, and therefore the electrodes, to be positioned at any angular location relative to each other. Versatility of the positioning of the electrodes at any location around the perimeter of the heater advantageously enables the heater to accommodate the space requirements imposed by any given vehicle exhaust gas after-treatment system into which the heater is installed. [0054] The concentric serpentine design of the heaters described herein also advantageously exhibit a high fractional open frontal area, thereby contributing only a minimal increase in pressure drop (due to resistance to flow through the heater) to the aftertreatment system. [0055] Referring now to FIG. 1A and the detailed view of FIGS. 1B-1D, a heater assembly 10 is illustrated. The heater assembly 10 may be referred to herein interchangeably as a heater, flow- through heater, and/or disc heater. The heater assembly 10 comprises a continuous body 12 arranged in a serpentine pattern of concentric segments as described in more detail herein. The continuous body 12 may be referred to herein as being, or otherwise having the shape of, a ribbon. The continuous body 12 can also be considered as a heating element for the heater assembly 10, as the material of the continuous body 12 (and associated conductivity/resistivity) can be selected to provide resistance heating upon current flow through the continuous body 12. For example, the continuous body 12 can comprise a metal material, a conductive ceramic material, or a conductive composite material. [0056] The continuous body 12 extends in the serpentine pattern of segments arranged along concentric rings between opposite ends or termini 14, which in the embodiment of FIG. 1A comprise a pair of electrodes 16. The electrodes 16 can have the same dimensions as the continuous body 12, or different dimensions, e.g., widened relative to the continuous body as shown in FIG. 1A. The electrodes 16 can be connected to a suitable power source (e.g., battery) to apply a voltage across the electrodes, thereby creating a flow of current through the continuous body 12 between the electrodes 16. [0057] To assist in ascertaining orientation of the illustrated aspects of the heater assembly 10, x-, y-, and z- axes of a Cardinal coordinate system are provided in each of FIGS. 1A-1D. Accordingly, the illustrated z-direction (see FIG. 1D) corresponds to the axial direction of the heater 10, while the end faces span across the plane formed by the x- and y- axes. In this way, the z-direction, oriented orthogonal to the x- and y-directions, is parallel to the flow of gas through the heater assembly 10 when installed in a fluid treatment system, such as an exhaust aftertreatment system for an internal combustion engine. [0058] The “length” of the continuous body 12, as used herein, refers to the distance that the continuous body 12 travels (in the x-y plane, see FIG. 1A) between the opposite ends 14. The “thickness” of the continuous body 12 as used herein refers to the smallest dimension of the continuous body 12, and is denoted as t in FIGS. 1B and 1D (the thickness t spanning in the x- and/or y-directions). The “height” of the continuous body 12, as used herein, refers to the axial dimension of the continuous body 12 that extends in the z-direction, as shown in FIG. 1D. Since the dimensions of the disc heater 10 as whole are determined at least in part by the continuous body 12, the axial dimension of the disc heater 10 in the z-direction (e.g., the “thickness” of the disc heater 10 as a whole, in comparison to the thickness t of just the continuous body 12) is equivalent to the axial dimension or axial height, designated as axial height h, of the continuous body 12. The heater assembly 10 has an axis 18, which may be referred to as a central axis, that extends axially (in the z-direction) through the center of the pattern formed by the continuous body 12, as shown in FIG.1C. [0059] In some embodiments, the height h of the continuous body 12 is variable along its length between the opposite ends 14, while in other embodiments the height h is the same value along the entire length of the continuous body. For example, the axial height h of the continuous body 12 can widen at or near the ends 14, where the continuous body 12 transitions to the electrodes 16, which can also be of comparatively larger dimensions. In some embodiments, axial height h of the continuous body 12 has a relatively smaller value at or near the central axis 18 of the heater assembly 10 to concentrate more heat in the central region, for example, if this is where gas flow is highest when installed in a fluid treatment system. [0060] The concentric serpentine pattern of the continuous body 12 of the heater assembly 10 comprises a series of “segments” that repeatedly turn back and forth at rounded “bends” or “returns”. This series of segments are arranged along multiple concentric rings, which concentric rings are at various different radial distances from the central axis 18. For example, with respect to FIGS.1A and 1B, the continuous body 12 is arranged in a circular shape and thereby comprises a plurality of segments 20 that are arranged along a plurality of circle-shaped concentric rings. For example, in the embodiment of FIG.1A, the segments 20 are arranged in a pattern having nineteen concentric rings, with an outermost one of the concentric rings shown in a dash-dot pattern and identified as a concentric ring 22a The sixth concentric ring (counting radially inward from the outermost ring 22a) in the pattern of FIG. 1A is indicated as a sixth concentric ring 22f, while the other concentric rings are not illustrated for the sake of clarity of the other features shown in FIG. 1A. The concentric rings may be generally and/or collectively referred to herein (without an alphabetic suffix) as the concentric rings 22. Any number of the concentric rings 22 can be included. In some embodiments, the heater assembly 10 comprises segments aligned with respect to at least ten of the concentric rings. [0061] Since the peripheral shape of the heater assembly 10 in FIGS. 1A-1D is circular, the segments 20 are correspondingly curvilinear (arcuate) and the shape of the concentric rings is circular. However, the concentric shapes 22 do not need to be circular, the segments 20 do not need to be curvilinear, and any number of concentric rings can be included. For example, as described in more detail herein, the heater assembly 10 can have shapes other than circular, such as ellipsoidal, oval, oblong, tear drop, toroidal, triangular, rectangular, or other polygon, such that the segments 20 can be curved, straight, or include both curved and straight portions (e.g., in the rectangularly shaped heater shown in FIG.10). The overall peripheral shape of the heater assembly 10, as defined by the pattern of the continuous body 10, has a dimension, e.g., outer diameter, which is identified in FIG.1A as dimension D_H. In embodiments in which the peripheral shape is non-circular, the peripheral shape can be defined by multiple outer dimensions, such as the dimensions of the diagonal, and/or long and short sides of a rectangle. [0062] For the ease of discussion, the term “circumference” may be used herein to refer to the periphery of shapes other than circular (e.g., the “circumference” can be rectangular, triangular, or other polygonal shape), and “circumferential” may similarly be used herein to the direction along the outer peripheral shape of the heater, or along the shape of any of the concentric rings. Similarly, the term “radius” can refer to a line (or corresponding distance of such line) drawn from a central axis (the central axis 18) to the outer periphery, and thus “radial” refers to the direction of any such line, regardless of the shape of the heater or of the concentric rings. [0063] The outermost circumferential shape of the pattern (in the x-y plane), and correspondingly each of the concentric rings 22 in the pattern, that defines overall geometric shape of the heater assembly 10 can be set or selected depending on the application of the heater and/or the system into which is to be installed. For example, if the heater assembly 10 is to be positioned upstream of a catalytic converter or exhaust gas particulate filter (relative to a flow of exhaust gas), the heater assembly 10 can be arranged having the same or similar geometry (e.g., outermost size and shape) as the contour of the converter or filter. Additionally or alternatively, the continuous body 12 can be arranged in a pattern to provide the heater assembly 10 with the same or similar contour (peripheral shape) as the exhaust pipe, can, or other structure within which the heater assembly 10 is mounted. In some embodiments, the pattern of the continuous body 12 is arranged to give the heater assembly 10 a circular geometry. [0064] As also shown in FIGS. 1A and 1B, the continuous body 12 comprises a plurality of returns 24 that connect between the segments 20. For example, the returns 24 can be formed as turns or bends that transition between the segments 20 aligned with any given one of concentric rings 22 to the segments 20 of radially adjacent concentric rings 22. When formed as a U-shaped bend, the returns 24 have a radius ru, as shown in FIG. 1B. In this way, the returns 24 cause the continuous body 12 to “double-back” on itself, such that successive ones of the segments 20 along the length of the continuous body 12 are radially adjacent to each other. By radially adjacent, it is meant that a single radius can be drawn from the central axis 18 through both of the segments 20. Accordingly, radially adjacent segments are at different radial distances from the central axis 18 or otherwise aligned along different concentric rings that are radially adjacent. The radial distance between the concentric rings 22 (which also corresponds to the midline of the segments 20) is identified in FIG. 1B as equal to a radial distance d_c, with the corresponding radial distance between the closest portions of the radially adjacent segments 20 identified as a distance g_c. [0065] For example, in FIG. 1B a first radially adjacent pair of the segments 20, designated as a first segments 20a and a second segment 20b, are connected by a first return, designated as a first return 24a. In accordance with the preceding description, the first segment 20a is shown in FIG. 1B aligned with (extending along) the outermost concentric circle 22a, while the second segment 20b is shown aligned with (extending along) a second concentric circle 22b that is radially adjacent to the outermost concentric circle 22a. Similarly, FIG. 1C also shows a second radially adjacent pair of the segments 20, designated as a third segment 20c and a fourth segment 20d, which are connected by a second return 24b. As shown in FIG.1B, the third segment 20c is also aligned with the outermost concentric circle 22a, while the fourth segment 20d is aligned with the concentric circle 22b, which is radially adjacent to the concentric circle 22a. [0066] A small value of the separation between adjacent concentric segments of the heater, dc, is beneficial because it provides a smaller effective hydraulic diameter and better heat transfer to the flowing gas. However, a larger value of dc is beneficial because it implies a shorter total electrical path length and therefore a faster heating rate. Preferably the value of dc is between 0.04 and 0.20 inches. A small value of the ribbon thickness, t, is desirable because it provides greater strain relief to the structure during non-uniform heating and increases the fraction of open frontal area and reduces the pressure drop across the heater. A small value of t also allows for a greater thickness of the heater, h, to maintain a given cross sectional area of the ribbon, and a high ratio of h/t provides greater surface area for heat transfer to the gas. The thickness of the ribbon is preferably between 0.004 and 0.020 inches, and the height of the ribbon is preferably between 0.1 and 0.6 inches. The ratio of h/t is preferably at least 5 and more preferably at least 10, 20, 30, 40, and even 50. The ratio of t/dc is preferably at least 5, 7, 10, 12, 14, and even 16 to maximize strain relief under a temperature gradient. [0067] While the returns 24 connect radially adjacent pairs of the segments 20 together (e.g., the first and second segments 20a and 20b, and/or the third and fourth segments 20c and 20d), the returns 24 also result in the gaps 26 between circumferentially adjacent ones of the segments 20. For example, the first return 24a and the second return 24b, as shown in FIG. 1B, create, and are on opposite sides of, the gap 26. As shown in FIG. 1B, the gaps 26 are separated by a circumferential distance designated as a circumferential distance g_u, with the corresponding circumferential distance measured between the midlines of the material of the opposing pair of returns 24 designated as a circumferential distance d_u. As used herein, the term circumferentially adjacent means that the segments 20 are aligned with the same one of the concentric rings (e.g., at the same radial distance from the central axis if the shape is circular), but the segments are not successive along the length of the continuous body 12 (dashed lines in FIG. 1B showing the midline of the material of the continuous body 12, along which the length of the continuous body 12 extends). [0068] Referring again to FIG.1B, the segments 20a and 20c are referred to as circumferentially adjacent because both segments 20a and 20c are aligned with the circle 22a, but separated by the gap 26, and therefore not successively arranged along the length of the continuous body 12 (the segment 20a is successively arranged with respect to the segment 20b, not with the segment 20c). Similarly, the second and fourth segments 20b and 20d in FIG. 1B are circumferentially adjacent because they are both aligned with the circle 22b, but separated by the gap 26 and therefore not successively arranged along the length of the continuous body 12 (the segment 20b is successively arranged with the segment 20a, not with the segment 20d). [0069] The radially innermost (centermost) concentric ring, identified in FIG.1C as concentric ring 22s (the suffix ‘s’ denoting that the ring 22s is the 19^th concentric ring, counting radially inward from the outer periphery) can be suitably arranged to enable the continuous body 12 to be continuously formed in the concentric serpentine pattern. For example, in the embodiment of FIGS. 1A-1D at least two of the segments 20 are arranged for each of the concentric rings 22, except for the innermost concentric ring 22s, which only has a single one of the segments 20. Additionally, the centermost one of the segments 20 can have a radius r1, as shown in FIG. 1C, which can be the same as the radius ru of the returns 24, or a different value. Accordingly, the segments 20 of one or more of the innermost concentric rings 22 (at, or directly radially adjacent to, the central axis 18) can differ in general shape or orientation from the segments 20 at other locations in the continuous body 12. [0070] In order to arrange the continuous body 12 in the concentric serpentine shape, the returns 24 are arranged in pairs at each of the gaps 26, with a first return (e.g., the return 24a) in the pair mirroring the other return (e.g., the return 24b) in that pair on opposite sides of the gaps 26. The only exception is when one of the returns 24 is paired with one of the ends 14, such as shown in FIGS.7 and 9. Additionally, with the exception of the centermost segment (see FIG.1C) or when one of the returns 14 is paired with one of the ends 14 (see FIGS. 7 and 9), there is only one pair of the returns 24 between the segments 20 aligned with any given one of the concentric rings and the segments 20 aligned with the radially adjacent concentric rings. For example, the returns 24a and 24b form the only pair of returns 24 between the segments 20 aligned with the circle 22a (the segments 20a and 20c) and the segments 20 aligned with the circle 22b (the segments 20b and 20d). The location of each pair of the returns 24 between any two radially adjacent concentric rings is not otherwise limited. For example, as described further herein, in some embodiments multiple of the pairs of the returns 24 are aligned along the same radius, and/or along different radiuses. Furthermore, the returns 24 that join successive segments 20 are not restricted in shape or dimensions. However, the use of a semicircular U-shape for the returns 24 can advantageously minimize the stresses in the continuous body 12, particularly during non-uniform heating throughout the heater 10. [0071] In some embodiments, the conductivity of the material, such as a ceramic material, of the continuous bodies 12 is at least 0.2x10⁴ ohm^-1 cm^-1, or more preferably at least 0.5x10⁴ ohm^-1 cm^-1, at least 1x10⁴ ohm^-1 cm^-1, at least 2x10⁴ ohm^-1 cm^-1, or even at least 4x10⁴ ohm^-1 cm^-1, including ranges having one or more of these values as endpoints, such as from 0.2x10⁴ ohm^-1 cm- ¹ to 5x10⁴ ohm^-1 cm^-1. In some embodiments, a ceramic material of the continuous bodies 12 comprises at least one first or primary phases selected from the group comprising transition metal silicides and aluminides and their solid solutions with one another or with other elements and having a phase electrical conductivity of at least 0.2x10⁴ ohm^-1 cm^-1. In some embodiments, transition metal silicides and aluminides are selected in which the atomic fraction of transition metal in the compound is less than 0.5 and more preferably less than 0.35. In some embodiments, the transition metal silicide or aluminide comprises at least one of MoSi₂, WSi₂, TaSi₂, TiSi₂, ZrSi₂, CrSi2, FeSi2, NiSi2, CoSi2, MoAl3, TiAl3, TaAl3, or ZrAl3. The ceramic may optionally contain a secondary phase having a phase electrical conductivity less than 0.2x10⁴ ohm^-1 cm^-1. In some embodiments, the secondary phase comprises at least one of silicon metal, SiC, Si₃N₄, Si₂N₂O, sialons, AlN, Al₂O₃, mullite, ZrSiO₄, or cordierite. In some embodiments, the material of the continuous bodies comprises over 50 wt% of the first or primary ceramic phase, with the remaining portion being one or more secondary phases. The ceramic may also contain one or more metal oxide addition, e.g., to assist as a sintering aid, including for example Y2O3, lanthanide metal oxides, Al2O3, and SiO2. [0072] When a thermally induced stress arises, e.g., due to thermal expansion and/or non- uniform temperatures, the structure of the heater is able to advantageously accommodate those stresses by flexing at the returns 24. The strain experienced by the structure, ε_s, results in a strain in the continuous body 12 which strain reaches a maximum at the U-shaped return, designated as ε_u. Where the length of a given segment 20 between two returns 24 is designated herein as L_a and the radius of curvature at the U-shaped return 24 that joins two segments 20 is designated as ru, the strain at the returns (εu) is approximately related to the strain of the structure (εs) according to the flowing relation, in which E and G are respectively the Young’s elastic modulus and shear modulus of the ceramic, as follows:

[0073] According to Eq.1, the strain in the return relative to the strain in the structure (ε_u/ε_s) is minimized when the ribbon thickness (t) is much smaller than the radius of curvature (ru) of the return, and when the length (L_a) of the segments 20 of the continuous body 12 is much greater than the radius of curvature (r_u) of the return. For example, even in the case where r_u is only twice the value of t, and L_a is only twice the value of r_u, the ratio of ε_u/ε_s from Eq.1 is 0.13, an almost eight- fold reduction in strain. In some embodiments, the ratio of r_u/t is at least 2, or preferably at least 3, at least 4, at least 5, at least 6, at least 7, at least 8, at least 9, or even at least 10, including ranges including any of these values as endpoints, such as from 3 to 10 or more. In some embodiments, the ratio of La/ru is at least 20, at least 50, at least 100, at least 200, at least 300, at least 400, at least 500, at least 1000, at least 1500, or at least 2000, or even at least 2500, including ranges having any of these values as endpoints, such as from 50 to 2500, or more. Consequently, the geometry of the continuous body 12 can be selected such that the maximum strain in the material, located at the returns, is theoretically (in accordance with Eq.1) hundreds to even thousands times lower than the overall strain of the structure, such as at least 250 to more than 10,000 times lower. Accordingly, the embodiments disclosed herein are advantageously strain compliant. [0074] The thermal gradient across a heater in an exhaust gas environment may easily be as high as 500°C. For a conductive ceramic with a coefficient of thermal expansion even as low as 50x10- 7 K-1, this will produce an overall strain of 0.25%. Because ceramics typically fracture at a strain of about 0.10%, failure of a heater having a rigid structure is likely. However, in the present strain- tolerant serpentine heater structures, the strain in the ceramic when the structural strain is 0.25% may be orders of magnitude lower than 0.1%. Thus, the serpentine ribbon structure of the present flow-through heater is beneficial to its application as an EHC. [0075] The material properties and dimensions of the features of the heater assembly 10 can vary in order to achieve or provide one or more targeted performance characteristics. For example, the dimensions of the continuous body 12 can be selected with respect to the electrical properties of the material of the continuous body in order to provide an electrical resistivity that achieves a target power when a selected voltage is applied across the electrodes 16. [0076] In some embodiments, a relatively small value for the separation between adjacent concentric rings 22 (dimension d_c in FIG. 1B) relative to the other dimensions of the continuous body 12 is beneficial because it provides a smaller effective hydraulic diameter, and correspondingly better heat transfer, to the gas flowing through the heater assembly 10. However, in some embodiments a relatively larger value of dc can be beneficial because it results in a shorter total electrical path length and therefore a faster heating rate. Accordingly, the value of dc can be adjusted based on the intended application for the heater assembly 10. In some embodiments, the value of dc is between 0.04 and 0.20 inches. [0077] The positioning of the pairs of returns can differ from that shown in FIGS. 1A-1D, and the shape of the concentric rings (and corresponding the overall shape of the heater assembly 10 defined by the outer periphery of the continuous body 12) does not need to be circular. Various additional embodiments are shown in FIGS. 2-14. More particularly, the concentric rings are circular but with different positionings for the pairs of the returns in FIGS. 2-9 and 11-14, while FIG.10 depicts a heater assembly in which the shape of the concentric rings is rectangular (having rounded corners). [0078] Embodiments comprising concentric designs with segments aligned with concentric circles and semicircular U-shaped returns are illustrated by FIGS. 1A to 9, and 11 to 14. For convenience, locations of the segments 20 and the returns 24 within the heater assembly 10 may be referenced to a radial position and/or a circumferential position. The radial position will be denoted with respect to the corresponding concentric ring at which the segment 20 and/or return 24 is located, by sequentially counting the number of concentric rings, with the radially outermost concentric shape being counted as the “first” concentric ring. The circumferential position will be described in terms of the angular position with respect to the location of the midpoint of the outermost pair of returns (the circumferential center of the gap 26 between the pair of returns 24), with angles measured counterclockwise from that position. Therefore, the outermost pair of returns joins the segments of the outermost and next inner concentric shapes at the angular position of zero degrees (0°). [0079] Although any given pair of the returns 24 can be set to any location, the locations of the returns 24 can be arranged to follow any of various sequences or patterns. As examples, various embodiments are illustrated in the herein described FIGS.1A to 14. In these examples, the returns 24 (and corresponding gaps 26) are arranged so that multiple pairs of the returns lie upon multiple different radii that are separated from one another by an angular distance (thereby creating circumferential spacing between the radii). For convenience, the radii are designated in the illustrated Examples by dashed lines and sequential alphabetic letters (A, B, C, etc.), increasing counterclockwise from the outermost pair of returns. The outermost pair of returns is consistently identified at the radius A in each illustrated Example. [0080] In the embodiment of FIGS.1A-1D, the pairs of returns are arranged with respect to two radii (radius A and radius B) and the angular distance (in the circumferential direction) between the radii is 180°. Accordingly, in this embodiment the two radii lie along a common diameter, yielding a heater assembly with a bilateral symmetry. While this embodiment exhibits such symmetry, the pairs of returns do not need to be evenly spaced. For example, in some embodiments the radii A and B are separated by an angle less than 180° on one side and an angle greater than 180° on the other side. Similarly, equal angular spacing between the radii (and thus between the pairs of returns), is not required in any of the embodiments described herein. [0081] As the number of radii increases, the pairs of returns can be positioned more evenly at smaller angular spacings in the circumferential direction about the heater, which can be particularly useful for establishing the structural integrity of the heater and to minimize local stress concentrations. For example, FIG. 2 illustrates a configuration in which the pairs of returns are aligned with respect to three radii (A, B, C), in which case the pairs of returns are located at angular positions that are spaced 120° apart. In this embodiment, the pairs of returns are also equally spaced in the radial direction with a pair of returns for every three concentric rings. In other words, traveling in the radial direction along any of the radii (A, B, C), two out of every three rings have segments connected to a pair of returns. For example, as shown in FIG.2, there is a pair of returns at the radius A at the outer periphery, which pair of returns is connected to the segments of the two outermost concentric rings. At the third concentric ring (counting radially inwardly from the outer periphery), the segment 20 is unbroken and passes transversely though the radius A (i.e., the segment of the third concentric ring is not connected to a return at the radius A). This pattern repeats with a pair of returns connected to the segments aligned with the fourth and fifth concentric rings and then an unbroken segment at the radius A for the sixth concentric ring. Similar to the circumferential spacing between the radii, the pairs of returns do not need to be evenly spaced in the radial direction (i.e., there does not need to be a pair of returns every three concentric rings for all of the radii in the example of FIG. 2). [0082] FIG. 3 illustrates an embodiment in which the number of radii is four (A, B, C, D) and the pairs of returns are located at angular positions that are 90° apart. In this embodiment, successive returns are positioned in the repeating sequence A, C, B, D and with a pair of returns located at the angular position of the corresponding radii for every four concentric rings. As described above, other circumferential and radial spacings between the pairs of returns can be utilized, e.g., evenly spaced or variably spaced in one or both of the circumferential or radial directions. In particular, as the number of radii increases beyond four, greater numbers of combinations or permeations of radial and circumferential spacings between successive pairs of returns become possible. Some Examples having greater than four radii that provide a good distribution of the pairs of returns in both the radial and circumferential directions are described below, although other configurations are possible. [0083] FIG. 4 illustrates an embodiment in which the number of radii is five (A, B, C, D, E), and the positions of the returns are distributed by positioning successive returns in the order of radii A, C, E, B, D, and then starting over at A again, whereby the pairs of returns are located at angular positions that are 72° apart, with one of the pairs of returns located at each radii for every five concentric rings along a given radius. In FIG.5, the number of radii is six (A, B, C, D, E, F), the successive pairs of returns are positioned in the sequence A, C, E, B, F, D, A at angles that are 60° apart, with one pair of returns for every six concentric rings counted along a given radius. In FIG. 6, the heater comprises eight radii (A, B, C, D, E, F, G, H), the returns are spaced by positioning in the sequence A, D, G, B, E, H, C, F, A at angles that are 45° apart, with one pair of returns located for every eight concentric rings along each radius. It will be evident from the illustrated examples that the locations (circumferential and/or radial) of the pairs of returns can be extended in a similar manner to an increasing number of radii, corresponding to a greater number of angular positions, a smaller angular separation between radii, and/or greater number of concentric rings between successive pairs of returns along each given radius. Additionally, these patterns can be similarly applied to heaters having any number of concentric rings. [0084] FIGS.7 and 8 illustrate that the termini 14 of the continuous bodies 12 can be located at any desired angle of separation. That is, FIG. 7 and 8 show heaters having substantially similar patterns with the same number of concentric rings and positioning for each pair of the returns. However, in FIG. 7 the termini 14 of the continuous body 12 are on opposite sides, separated by 180° from each other, while in FIG. 8 the termini are on substantially the same side, separated by an angle of less than 90°. It is also noted with respect to FIG. 7 that one of the termini 14 (on the left hand side, with respect to the orientation of FIG. 7) is formed from the segment 20 at the outermost one of the concentric rings, while the other terminus 14 (on the right hand side, with respect to the orientation of FIG. 7) is formed from the segment 20 aligned with the second outermost concentric ring. Due to this arrangement, the return connecting between the segments of the outermost and second outermost concentric rings is not paired with another return but is instead paired with the terminus 14. [0085] FIG.9 illustrates a heater assembly having the same general configuration of FIG.7, but also comprising the electrodes 16 having dimensions larger than the continuous body 12. For example, as described herein, the electrodes 16 can be co-formed and co-sintered with the continuous body 12. The transition from the thickness of the electrode to the thickness of the continuous body 12 can be gradual or tapered, as illustrated, or abruptly occur at an edge. A gradual or tapered transition between a comparatively wider electrode and thinner continuous body can be particularly advantageous when the components are co-formed or co-sintered. [0086] FIG.10 illustrates a heater having a concentric serpentine pattern in which the segments comprise a series of rounded rectangles. Despite having a different shape, the heater assembly of FIG.10 is arranged with pairs of returns aligned with respect to four radii (A, B, C, D) in a manner akin to that described above with respect to FIGS.1A-9. In this way, it can be appreciated that the heater assembly 10 can be arranged with pairs of returns and radii with respect to which multiple of the pairs of returns are aligned in accordance with the above description of FIGS. 1A-9, while taking any suitable shape, such as ellipsoidal, oval, oblong, tear drop, toroidal, triangular, rectangular, or other polygon. Additionally, while the two termini 14 in FIG.10 are illustrated as being closely positioned next to each other, the termini can be separated by any other amount, such as 45°, 90°, or 180°. [0087] In some embodiments, each successive pair of returns is located at a position that is immediately counterclockwise from the preceding pair of returns by a designated angle. The angle can be the same between each successive return or it can be variable. For example, the case where the angle is 180° and 120° results in the patterns depicted in FIGS. 1A and 2, respectively. However, other sequences for setting the angular positions for the pairs of returns can be chosen that result in the positioning of the pairs of returns to follow a spiral pattern, such as illustrated in FIGS. 11-14. In FIG. 11, the locations of most of the pairs of returns follow a pattern in which each successive pair of returns (counting radially inward from the pair of returns connected to the outermost concentric ring) are positioned counterclockwise with an angular separation of 90°. In the embodiment of FIG. 12, the locations of most of the pairs of returns follow a spiral pattern in which each successive pair of returns is positioned counterclockwise with an angular separation of 72°, while in FIG. 13 the counterclockwise angular separation is 45°, and in FIG. 14 the counterclockwise angular separation is 135°. The angular separation between successive pairs of returns can be variable or change at various radial positions (i.e., at one or more of the concentric rings), such as near the central axis of the heater. For example, depending on the number of concentric rings in which the segments are arranged, the angular spacing for the pairs of returns for one or more of the concentric rings near the central axis 18 can differ from the angular spacings of the other pairs of returns in order to complete the formation of the continuous serpentine path for the continuous body 12 (e.g., as described with respect to FIG.1C). [0088] In some embodiments, the heater assembly 10 comprises multiple continuous bodies 12 that are arranged together in a parallel circuit, such as the embodiments illustrated in FIGS.15 and 16. Since each of the continuous bodies 12 are utilized as resistors for the heater assembly 10, these designs may be referred to a multi-resistor heaters. In the “two-resistor” heater assemblies 10 of FIGS.15 and 16, a first continuous body 12 is denoted with the suffix ‘a’, as first continuous body 12a, and a second continuous body 12 is denoted with the suffix ‘b’, as second continuous body 12b. The heater of FIG. 15 has four radii (A, B, C, D) with respect to which its pairs of returns 24 are arranged, in general accordance to the description above, while the pairs of the returns 24 in the embodiment of FIG. 16 are arranged with respect to six radii (A, B, C, D, E, F). Each of the first and second continuous bodies 12a and 12b are semi-circular in shape, with the first continuous body 12a as the “top” half of the heater assembly 10 and the second continuous body 12b as the “bottom” half of the heater assembly 10 with respect to the orientations of FIGS. 15 and 16. Thus, the line formed from radii A and C in FIG. 15 and from radii A and D in FIG. 16 mark the spatial division between the two continuous bodies 12a and 12b. [0089] Unlike the embodiments of FIGS. 1A-14, which had a differently shaped centermost or innermost segment 20 at the centermost or innermost concentric ring, there is no centermost or innermost segment in the embodiments of FIG.15 and 16, as the first and second continuous bodies 12a and 12b are instead arranged as parallel electrical pathways. That is, the first continuous body 12a defines a first continuous electrical pathway between its termini 14a, while the second continuous body 12b defines a second continuous electrical pathway between its termini 14b. Otherwise, the termini 14a and 14b generally resemble the termini 14 described above, and therefore can be connected to, such as being integrally formed with the electrodes 16 (not shown in FIGS. 15 and 16). The parallel circuit can be arranged with an electrical potential at each terminus 14a of the first continuous body 12a equal to, or approximately equal to, the potential at the respective terminus 14b of the second continuous body 12b. [0090] In FIG. 15, the returns 24 between successive circular concentric rings of continuous body 12a lie along the radius B, while the successive concentric rings of continuous body 12b lie along radius D, with the “left” sides connecting to the “right” sides only at an innermost semi- circular segment for each of the continuous bodies 12a and 12b. In FIG. 16, the positions of the returns 24 are alternately shifted to the left (along radius C for body 12a and along radius E for body 12b) and right (along radius B for body 12a and along radius F for body 12b) by 30° between to achieve a more even distribution of the returns 24, which increases structural stability and reduces stress concentration in the innermost segment. The geometric parameters defining the shape of the first continuous body 12a can be chosen to be the same or significantly or approximately the same as those of the second continuous body 12b (e.g., as mirror images) so that both continuous bodies have the same, or nearly the same, resistance and mass, and will therefore heat at a comparable rate, enabling uniform heating for the heater assembly 10. As in the case with a single continuous body, the positioning of the returns 24 does not change the electrical performance of the heater. [0091] In some embodiments, a relatively small value of the ribbon thickness (t) relative to the other dimensions of the continuous body 12 is desirable because it provides greater strain relief to the structure, particularly during non-uniform heating or other stress-creating event, and it also increases the fraction of open frontal area, which reduces the pressure drop across the heater. A small value of t also allows for a greater axial height (h) of the heater while maintaining the same thermal mass, and a high ratio of h/t provides greater surface area for heat transfer to the gas. In some embodiments, the thickness t of the continuous body 12 is between 0.004 and 0.020 inches, and the axial height h of the continuous body 12 is between 0.1 and 0.6 inches, although other dimensions are possible and may be advantageous depending on the intended application for the heater. In some embodiments, the ratio of h/t is preferably at least 5 and more preferably at least 10, at least 20, at least 30, at least 40, or even at least 50. In some embodiments, the ratio of t/d_c is preferably at least 5, at least 7, at least 10, at least 12, at least 14, or even at least 16, which increasingly improves strain relief under a temperature gradient or other stresses. [0092] In some embodiments, the continuous body 12 is fabricated by high-temperature sintering of a ceramic powder green body or preform in accordance with any suitable sintering process. When the ceramic material comprises at least one non-oxide phase, sintering can be performed in a vacuum or non-oxidizing atmosphere. The preform comprises particulate starting materials that can be mixed with organic binders, surfactants, lubricants, or other aids utilized in the ceramic sintering arts, and optionally with a liquid vehicle such as an aqueous or alcohol mixture. The preform can be shaped by a process such as extrusion, injection molding, gel casting, uniaxial die pressing, or additive manufacturing, among any other suitable shaping processes. [0093] The green body can optionally comprise additional temporary supporting elements as part of the structure to provide strength to the green body in the pre-sintered state. The use of such supports may be especially beneficial when the green body is formed by extrusion or other process in which the body is in a plasticized state before drying or curing. For example, FIG. 17 shows supporting elements 28 that extend radially between the segments 20 of radially adjacent concentric circles 22. The supporting elements 28 can be temporarily used to assist in one or more manufacturing steps, such as to increase strength during manufacturing processes while the continuous body 12 is in a green state. Correspondingly, the supporting elements 28 can be severed in later manufacturing steps, such as shown in FIG. 18, in which only severed portions 30 of the supporting elements 28 remain. The severing of the supporting elements 28 can occur either in the green state, e.g., after drying or curing, or in the sintered state after firing. Once severed, the supporting elements 28 no longer constitute an electrical pathway, and thus, electrical current will flow through the continuous body 12 as described herein. The severing of the temporary supporting elements 28 can be performed by any convenient means, such as by a blade, saw, laser, or abrasive water jet cutting. [0094] In some embodiments, the electrodes 16 required for lead attachment to a power source are fabricated as an integral part of the heater assembly 10 using the same raw material mixture, forming process, drying and/or curing step, and sintering conditions as the continuous body 12. Thus, the continuous body 12 can be formed together with the electrodes 16 as a single monolithic component. The electrodes 16 in these embodiments thereby comprise a physically continuous extension of the continuous body 12. The length of the electrodes can be determined by the structure into which the heater is to be mounted. For example, the electrodes can have a length that enable the electrodes to extend through and out of an outer housing or can in which the heater assembly 10 is mounted, which facilitates the connection of the electrodes 16 to a suitable power source, such as a battery. In some embodiments, the cross sectional area of each electrode 16 is preferably at least 10, at least 15, at least 20, at least 30, at least 40, or even at least 50 times the cross sectional area (h times t) of the continuous body 12, including ranges having these values as endpoints, which assists in reducing the electrical resistance of the electrodes, thereby minimizing the power loss through the electrodes 16. The transition in cross sectional area of the electrode 16 to the continuous body 12 is preferably gradual to reduce local stresses and smooth out thermal gradients, however the electrodes 16 can be arranged to abruptly change dimensions from those of the continuous body 12. The electrodes 16 can be of any convenient geometry, such being cylindrical, pyramidal, conical, cuboid, prismatic, or a combination including one or more of these shapes. In some embodiments, the use of a rectangular cross section for at least a portion of the electrode 16 can facilitate connection to a power source, such as a rectangular cross-section in which the cross-sectional dimensions of the electrodes 16 are the same as the axial height (h) of the continuous body 12. [0095] In some embodiments, the segments 20 extend along the concentric rings 22 in a manner other than being smoothly linear or arcuate with the midline of the segments 20 coincident along the corresponding concentric ring 22. For example, FIG. 19 illustrates an embodiment in which the segments 20 oscillate sinusoidally along the concentric rings 22. For example, a sinusoidal pattern to the segments can be useful to provide further strain relief. In other embodiments, the segments 20 can extend along the concentric rings 22 in other patterns, such as a zig-zag, a square- wave, or with protrusions or projections from one or both radial sides of the segments. These features can be useful for setting the geometric and corresponding electrical properties of the continuous body 12, such as utilizing sinusoidal, zig-zag, or other oscillating pattern to increase the electric path length (and thereby increase the resistance) and/or to increase the surface area of the continuous body 12 that interacts with the flow of gas through the heater assembly 10 (thereby increasing heat transfer with the gas flow). EXAMPLES [0096] The heating performance of various heater assemblies according to the embodiments disclosed herein were investigated. More particularly, combinations of different electrical resistivities for the material and geometric parameters of the continuous body 12 were tested for heaters with diameters (Dh in FIG.1A) of approximately 3.1 inches and approximately 5.66 inches, and having a power of 6 kW when the electrodes 16 are connected to a 48 volt battery. Various parameters of the tested examples are summarized in Table 1. [0097] In each example of Table 1, a single-phase molybdenum silicide (MoSi₂) based ceramic was chosen as the material of the continuous body 12, with the density, heat capacity, conductivity, and resistivity values as shown in Table 1. However, the embodiments herein are not restricted to MoSi2 for the material of the continuous body 12, as other conductive materials can be used, such as other conductive ceramics, metals, or composites thereof, including composites of conductive materials (e.g., metals or conductive ceramics) with non-conductive materials (e.g., non- conductive ceramics). [0098] In performing the calculations, a nominal value for the diameter of the innermost circular segment, designated in Table 1 as D_H', was initially chosen to determine the radius r₁ (see FIG. 1C) of this innermost circular segment. The total number of concentric rings, designated as m, is then found by m = 1 + [[(D_H'/2) – r₁)/d_c]] in which the double brackets, [[ ]], denotes the greatest integer less than or equal to the value in double brackets. The actual diameter of the heater, DH, was then determined as DH = 2(r1 + (m – 1)dc). The total path length of all circular segments of the continuous body 12, plus adjoining returns 24, is very closely approximated by the value of (2ʌr1 – 2ru – gu) + (m – 1)(2ʌr1 – 4ru – 2gu) + 2ʌdc(m – 1)(m)/2 + (m – 1)(2ʌru), ignoring the transition from the continuous body 12 to the electrodes 16. [0099] The calculated ratio of power (P=(V²/R_H)) to thermal mass (M=(m_HC_p)), given in Table 1 as (V²/R_H)/(m_HC_p), is equal to the initial Joule heating rate of the heater in the absence of heat transfer to the environment. This calculated ratio (P/M = (V²/R_H)/(m_HC_p)) multiplied by the surface area (S) of the heater, given in Table 1 as S(P/M), may also be of interest as, without wishing to be bound by theory, it is believed to relate to the effectiveness of the heater at transferring heat to the flowing gas. At a given power and level of porosity of the material of the continuous body 12 (taken in the examples of Table 1 to be 0% porosity), the initial heating rate can be shown to depend only on the value of d_c/p, where p is the resistivity of heater material at 20°C.

Table 1 – Selected and calculated parameters for heaters comprising a single continuous serpentine body of concentric segments

[0100] Example 1.1 shows that a 3.08 inch diameter heater with a concentric ring spacing (d_c) of 0.12 in, a ribbon thickness (t) of 0.0075 in, and an axial height (h) of 0.301, and comprised of MoSi₂ having a resistivity of 33.3 μohm cm, produces 6 kW power at 48 volts and has a predicted initial heating rate of 893 K s-1, ignoring heat transfer to the environment. [0101] Example 1.2 shows that increasing the concentric ring spacing (d_c) to 0.16 in, which reduces the length of the electrical pathway and therefore the thermal mass of the heater, while maintaining the same ribbon thickness of 0.0075 in, and reducing the height to 0.233 in produces 6 kW power at 48 volts and an increased predicted initial heating rate of 1489 K s-1. [0102] Example 1.3 demonstrates that maintaining the same concentric ring spacing (dc) of 0.16 in, as Ex. 1.2, and reducing the ribbon thickness (t) to 0.0055 in, and increasing the height (h) to 0.318 in to preserve the same resistance and power yields the same value for the initial heating rate because the ratio d_c/^ is unchanged. [0103] Example 1.4 illustrates a benefit of reducing the resistivity of the conductive material to 22.2 μohm cm while maintaining the same concentric ring spacing (d_c) and ribbon thickness (t) as Ex. 1.3 and reducing the axial height (h) of the heater to 0.212 in, to maintain a power of 6 kW, increases the initial heating rate further to 2234 K s-1. [0104] Example 1.5 shows that increasing the diameter (DH) of the heater to 5.66 in with a 0.010 in ribbon thickness (t) and 0.472 in ribbon height (h) results in a much slower initial heating rate of 204 K s-1 due to the substantially greater electrical path length, even though the spacing (dc) between segments is increased to 0.195 in. [0105] Example 1.6 shows that reducing the resistivity of the material to 22.2 μohm cm in a 5.66 in diameter (D_H) heater, while maintaining the same concentric ring spacing (d_c) and ribbon thickness (t) as Ex. 1.5 and reducing the height (h) to 0.315 in to maintain a power of 6 kW increases the predicted initial heating rate to 306 K s-1. [0106] The estimated ratio of material strain at the returns to the overall structural strain caused by thermal expansion, εu/εs, has been estimated from Eq. 1 for each example in Table 1 using the respective indicated values for t and ru. The strain ratio was computed for two different values of segment length, L_a. In the first calculation, L_a was taken as the average segment length between returns defined as L_a, avg = 0.5L_T/m, where L_T is the total path length of the continuous body 12 between its ends 14 and m is the total number of concentric rings 22. Since as described herein the structure of the centermost segment can differ from the other segments, the ratio εu/εs was also calculated with L_a taken to be equal to one-half of the length of the innermost segment (e.g., see FIG. 1C), excluding the radius of the returns at the innermost segment and one-half the gap distance between returns, L_a = ʌr₁ – r_u – 0.5g_u. Values of Young’s elastic modulus, E = 430 GPa, and shear modulus, G = 190 GPa, were taken as representative of a non-porous MoSi₂ ceramic. Relative to the global strain across the heater (e.g., due to thermal gradients), it is predicted that the local maximum strain in the heating element at the returns may be reduced by a factor of at least 2000 to 4000 based on the average segment length, and by as much as a factor of at least 40 to 70 in the innermost ring. [0107] It will be appreciated that Table 1 details only six possible examples, and that numerous other combinations of geometric parameters and material resistivity can be chosen to yield targeted or desired diameters and power outputs while further adjusting such attributes as surface area, thermal mass, heat transfer, and thermal stress distribution. [0108] To further compare the relative performance of the six examples of Table 1 with regard to heating rate, the Joule heating of each heater was calculated with the application of 48 volts for 10 seconds, ignoring any heat transfer to the environment. The temperature-dependent properties for these calculations were taken to be Cp (J g^-1 K^-1) = 0.4908 + 0.0000568(T) - 22.72(1/T) and ^ (μohm cm) = ^923K(T/293)^1.40 in which ^293K is the selected resistivity value at 20°C and T is the temperature in Kelvins. Voltages were held constant at 48 V. Calculations were performed at 0.01 s intervals in which the energy generated (power x time) in each interval was divided by the product of the mass and the heat capacity to derive the temperature increase during that time interval. Calculated heating curves for Examples 1.1 to 1.6 are compared in FIG. 20. Decrease in heating rate with increasing time and temperature is a consequence of the increasing resistivity of MoSi2 with temperature as typical for a pure phase exhibiting metallic conductivity. Also shown in FIG. 20 is the modeled heating curve for a representative slotted metallic honeycomb heater, such as taught generally in US Patent No. 5,254,840, which is identified in FIG. 20 as Ex. 1.7, assumed made from Inconel 625. Accordingly, the examples for heaters according to the current embodiments, even when made from ceramics, are seen to reach 1000°C as fast or faster than the representative slotted metal honeycomb heater. [0109] Examples in which the heater assembly 10 comprises two continuous bodies 12 arranged in parallel, as shown in and described with respect to FIGS. 15 and 16 are presented in Table 2. The examples of Table 2 are for a nominal 3.1 inch diameter heater powered by a 48 volt DC battery to yield a power of 6 kW. The electrical path length of each individual continuous body, denoted as length Li, is defined to a close approximation as (ʌr1 –2ru – gu) + (m – 1)( ʌr1 – 4ru – 2gu) + ʌdc(m – 1)(m)/2 + (m – 1)(2ʌru). Table 2 – Selected and calculated parameters for heaters comprising two continuous serpentine bodies of concentric segments arranged in parallel

[0110] Example 2.1 was calculated for a heater comprising non-porous MoSi2 having a resistivity of 33.3 μohm cm, a concentric ring circumferential separation (dc) of 0.045 in, a ribbon thickness (t) of 0.005 in, and an axial height (h) of 0.2812 in. The initial heating rate was calculated to be 572 K s^-1. [0111] Example 2.2 was calculated for a heater comprising a MoSi₂ ceramic with 40% porosity, a corresponding 40% reduction in density, and an assumed increase in resistivity to 100 μohm cm. The heater has a concentric ring separation (dc) of 0.090 in, a ribbon thickness (t) of 0.008 in, and an axial height (h) of 0.2849 in. The initial heating rate was calculated to increase to 1093 K s^-1. [0112] Example 2.3 comprises a zero-porosity MoSi2 having a resistivity of 33.3 μohm cm (the same as Example 2.1), but in which the concentric ring separation (dc) is increased to 0.065 in, the ribbon thickness (t) is increased to 0.007 in, and the axial height (h) is reduced to 0.1424 in. The wider spacing between the concentric rings compared to Ex. 2.1 resulted in the calculated initial heating rate increasing to 1172 K s^-1. [0113] Example 2.4 shows that a further increase in concentric ring separation (d_c) to 0.080 in with the same ribbon thickness (t) of 0.007 in and a reduction in axial height (h) to 0.1201 inches yields an additional increase in predicted initial heating rate to 1606 K s^-1. [0114] Example 2.5 illustrates that an additional increase in concentric ring separation (dc) to 0.111 in, a reduction in ribbon thickness (t) to 0.0045 in, and an increase in axial height (h) to 0.1421 in produced an increase in calculated initial heating rate to 2778 K s^-1. [0115] Example 2.6 was calculated for a Mo(Si,Al)₂ based ceramic having a higher room- temperature resistivity of 180 μohm cm, but a smaller rate of increase in resistivity with temperature relative to MoSi₂. Examples of similar materials include those commercially available from the Sandvik Group under the name Kanthal Super ER. When the concentric ring separation (dc) is 0.130 in, the ribbon thickness (t) is 0.010 in, and the axial height (h) is 0.2988 in, the calculated initial heating rate is 768 K s^-1. [0116] Calculated heating rates for a 10-second application of 48 V to the heaters of Examples 2.1 to 2.6 were computed similarly to Examples 1.1 to 1.6, and results from are shown in FIG.21. The performance of a representative slotted metal honeycomb is again shown in FIG. 21 and identified as Ex. 1.7. Examples 2.1 to 2.5 show that despite the decreasing heating rate with increasing temperature due to the positive temperature coefficient of resistance for pure MoSi₂, the very high initial heating rate allowed by the high room-temperature conductivity and the greater latitude of the two-resistor design yields a shorter time to reach 1000°C than for the representative slotted metal honeycomb heater of Ex. 1.7. Example 2.6 further shows the potentially beneficial heating behavior of an alternate conductive ceramic material. For example, although the higher resistivity at room temperature results in a slower initial heating rate for Ex.2.6, the more gradual increase in resistivity with temperature enables the heater to reach 1000°C more rapidly. [0117] In Tables 3 and 4, the power loss through a 1.5 inch long electrode comprised of the same material as the continuous body of the heater and having a square cross section in which the thickness of the electrode is the same as the axial height (h) of the heater has been calculated for the heaters of Examples 1.1 to 1.6 and 2.1 to 2.6. It is seen that the % power loss through the electrodes is between 0.046% and 0.36%. In some embodiments, the electrodes are configured to have less than 0.3%, less than 0.2%, or even less than 0.1% power loss relative to the combination of the electrode together with the ribbon (continuous body) of the heater. Table 3 - Calculated examples of the percent power loss for continuous electrodes of square cross section having the same material conductivity as the heaters in Examples 1.1 to 1.6.

Table 4 - Calculated examples of the percent power loss for continuous electrodes of square cross section having the same material conductivity as the parallel heaters in Examples 2.1 to 2.6.

[0118] It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the spirit or scope of the claimed subject matter. Accordingly, the claimed subject matter is not to be restricted except in light of the attached claims and their equivalents.

Claims

What is claimed is: 1. A heater assembly comprising: a continuous body having a central axis, the continuous body comprising: first and second ends; a plurality of segments arranged in series extending along a length of the continuous body between the first and second ends, wherein the segments are arranged with respect to a plurality of concentric rings that are concentric about the central axis; a plurality of returns, each return connecting two of the segments together, wherein the two segments connected by each return are respectively aligned with two radially adjacent concentric rings and are also successive in series along a length of the continuous body; and a plurality of circumferential gaps located between opposing pairs of the returns, wherein each circumferential gap circumferentially separates two of the segments aligned with respect to a same one of concentric rings.

2. The heater assembly of claim 1, wherein the heater assembly comprises a pair of electrodes and wherein the first and second ends of the continuous body are connected to respective ones of the electrodes.

3. The heater assembly of claim 2, wherein the electrodes are integrally formed with the continuous body as a single monolithic component.

4. The heater assembly of any one of claims 1-3, wherein multiple of the circumferential gaps and corresponding pairs of returns are arranged together at different radial positions along one or more radii extending from the central axis.

5. The heater assembly of claim 4, wherein the circumferential gaps and corresponding pairs of returns are arranged with respect to at least two radii.

6. The heater assembly of claim 5, wherein the circumferential gaps and corresponding pairs of returns are arranged with respect to from two to eight radii.

7. The heater assembly of claim 5, wherein the radii are evenly circumferentially spaced about the central axis.

8. The heater assembly of claim 5, wherein each radially successive pair of returns, starting from a first pair of returns connecting the segments aligned with the two outermost concentric circles, are arranged at a different one of the radii until at least one pair of the returns is aligned with respect to each of the radii.

9. The heater assembly of any one of claims 1-8, wherein the segments of the continuous body are arranged with respect to at least ten concentric rings.

10. The heater assembly of any one of claims 1-9, wherein the concentric rings are circular.

11. The heater assembly of any one of claims 1-10, wherein the concentric rings are rectangular.

12. The heater assembly of any one of claims 1-11, wherein the heater assembly comprises at least two of the continuous bodies separate from each other arranged electrically in parallel.

13. The heater assembly of claim 12, wherein the heater assembly comprises two of the continuous bodies and the two continuous bodies are symmetrical with respect to a line drawn through and perpendicular to the central axis.

14. The heater assembly of any one of claims 1-13, wherein the heater assembly has an outer peripheral shape defined by a shape of the concentric rings.

15. The heater assembly of any one of claims 1-14, wherein the continuous body comprises a conductive ceramic material.

16. The heater assembly of claim 15, wherein the conductive ceramic material is a single-phase ceramic material.

17. The heater assembly of claim 15, wherein the conductive ceramic material of the continuous body comprises at least one of a transition metal silicide or aluminide, or a solid solution thereof.

18. The heater assembly of claim 17, wherein the transition metal silicide or aluminide comprises at least one of MoSi₂, WSi₂, TaSi₂, TiSi₂, ZrSi₂, CrSi₂, FeSi₂, NiSi₂, CoSi₂, MoAl₃, TiAl₃, TaAl₃, or ZrAl₃.

19. The heater assembly of claim 15, wherein the continuous body comprises the conductive ceramic material as a primary phase with one or more secondary phases.

20. The heater assembly of any one of claims 1-19, wherein a material of the continuous body has a conductivity of at least 0.2x10⁴ ohm^-1 cm^-1.

21. The heater assembly of claim 20, wherein the conductivity is from 0.2x10⁴ ohm^-1 cm^-1 to 5x10⁴ ohm^-1 cm^-1.

22. The heater assembly of any one of claims 1-21, wherein a midline of the segments is aligned along respective concentric rings.

23. The heater assembly of any one of claims 1-22, wherein the segments are aligned along respective concentric rings in an oscillating manner.

24. The heater assembly of claim 23, wherein the segments sinusoidally oscillate along the concentric rings.

25. A fluid treatment system comprising the heater assembly of any one of claims 1-24.

26. The fluid treatment system of claim 25, wherein the heater assembly is in fluid communication with a catalyst-loaded substrate.

27. A method of manufacturing the heater assembly of claim 1, comprising: shaping a mixture comprising a ceramic powder into a green body preform; and sintering the preform to convert materials of the preform into the continuous body.

28. The method of claim 27, wherein sintering the preform converts materials of the green body preform into a monolithic component that comprises both the continuous body and a pair of electrodes connected to the first and second ends of the continuous body.

29. The method of claim 27, wherein sintering the preform comprises one or more radially extending supporting elements connecting between radially adjacent ones of the segments, and the method comprises severing the supporting elements before or after the sintering.

30. A heater assembly comprising: a pair of electrodes; a continuous body having an outer peripheral shape and a central axis, the continuous body comprising: a serpentine concentric pattern that comprises a plurality of concentric rings positioned about a central axis, wherein the continuous body comprises: a first segment and a second segment of the plurality of segments, wherein the first and second segments are circumferentially adjacent to each other and both aligned with respect to a first concentric ring of the concentric rings, a third segment of the plurality of segments that is radially adjacent to the first segment; a fourth segment of the plurality of segments that is radially adjacent to the second segment, wherein the third and fourth segments are both aligned with respect to a second concentric ring that is radially adjacent to the first concentric ring; a circumferential gap circumferentially separating the first segment from the second segment and circumferentially separating the third segment from the fourth segment; and a pair of returns at opposing sides of the circumferential gap, wherein a first return of the pair of returns connects the first segment to the third segment and a second return of the pair of returns connects the second segment to the fourth segment.