TWI679921B - Variable pitch resistance coil heater - Google Patents

Abstract

A heater includes a resistance coil, a first conductive pin and a second conductive pin. The resistance coil includes a first end connected to the first conductive pin, and a second end connected to the second conductive pin. The resistance coil defines a first portion adjacent to the first end, a second portion adjacent to the second end, and a third portion disposed between the first portion and the second portion. At least one of the first part, the second part, and the third part has a continuously variable pitch along its length.

Description

Variable pitch resistance coil heater

The present disclosure relates to electric heaters, and more specifically to electric heaters that use resistance coils to generate heat.

The narratives in this section only provide background information about the disclosures in this case and may not constitute conventional technology.

The tubular heater generally includes a resistance coil, an insulating material surrounding the resistance coil, and a tubular sheath surrounding the insulating material. The resistance coil is connected to a pair of conductive pins protruding from the tubular sheath for connection to a power source. The resistance coil generates heat, which is transferred to a tubular sheath, heating a surrounding environment or part.

Tubular heaters are often used in heat exchangers. The heat capacity of a heat exchanger depends on the heat generating capacity of a tubular heater, in particular a resistance coil. In order to increase the heat capacity of the heat exchanger, more tubular heaters can be provided in the heat exchanger, resulting in a large structure. Also, heat exchangers using conventional tubular heaters may have performance issues, such as increased hydrocarbons and severe fouling due to overheating at an outlet, which can eventually lead to failure.

In one aspect, the present disclosure provides a resistive element for use in a heater. The resistance element includes a resistance coil having a first end and a second end. The resistance coil includes a first portion adjacent to the first end, a second portion adjacent to the second end, and a third portion disposed between the first portion and the second portion. At least one of the first part, the second part, and the third part has a continuously variable pitch along its length.

In another aspect, a resistance element used in a heater includes a resistance coil having a first end and a second end opposite the first end. The resistance coil includes a plurality of first portions defining a first fixed outer diameter, and a plurality of second portions defining a second fixed outer diameter, wherein the second fixed outer diameter is smaller than the first fixed outer diameter. At least one of the first part and the second part has a continuously variable pitch.

In a further aspect, a heater includes a first conductive pin, a second conductive pin, and a plurality of resistance coils. Each of these resistance coils includes a first end connected to the first conductive pin and a second end connected to the second conductive pin. At least one of the first, second and third resistance coils has a continuously variable pitch.

Further areas of applicability will be apparent from the description provided herein. It should be understood that the narrative and specific examples are intended for illustrative purposes only and are not intended to limit the scope of the disclosure in this case.

The content of the following description is merely exemplary in nature and is not intended to limit the content, application, or use of the disclosure in this case.

Referring to FIG. 1, a typical tubular heater 10 generally includes a tubular outer sheath 12, a pair of conductive pins 14 protruding from opposite ends of the tubular outer sheath 12, and a pair of conductive pins 14 disposed between the conductive pins 14. The resistance coil 16 and an insulating material 18. The resistance coil 16 usually includes a resistance type metal alloy and is formed in a spiral coil shape. The resistance coil 16 generally has a fixed pitch P ₀ along the length of the resistance coil 16 to provide uniform heating along the length of the tubular outer sheath 12. An insulating material 18, such as magnesium oxide, is disposed inside the tubular outer sheath 12 to surround and electrically insulate the resistance coil 16.

Referring to FIG. 2, a tubular heater 20 constructed according to the teaching content disclosed in the present case includes a tubular outer sheath 22, first and second conductive pins 24 and 26, and first conductive pins 24 and A resistance coil 28 between the second conductive pins 26. The resistance coil 28 includes a spiral coil having a fixed outer diameter. The resistance coil 28 has a first end 30 connected to the first conductive pin 24 and a second end 32 connected to the second conductive pin 26. The resistance coil 28 and the first and second conductive pins 24 and 26 form a resistance coil assembly. The resistance coil 28 defines a plurality of locations having different pitches. Although three locations A, B, and C are shown in the figure, it can be understood that the resistance coil 28 may have any number of locations without departing from the scope of the disclosure of the present case.

As shown, the resistance coils 28 have pitches P ₁ , P _2, and P ₃ in the locations A, B, and C, respectively. P _{3 is} greater than P ₁ , and P _{1 is} greater than P ₂ . The resistance coil 28 has a fixed pitch along the length of each location. The first location A having a pitch P ₁ is disposed near the first end portion 30. The second location B with a pitch P ₂ is disposed in a middle portion and is adjacent to the first location A. The third location C having a pitch P ₃ is disposed adjacent to the second location B and the second end portion 32. A plurality of different pitches plurality of location A, B and C of P _1, P ₂ and P ₃ to provide a variable watt density, such that a predetermined temperature profile along the length 22 of the outer tubular sheath provided. The pitches P ₁ , P _2, and P ₃ in the locations A, B, and C are determined based on a desired temperature profile along the length of the outer tubular sheath 22. This predetermined temperature profile may be fixed to provide uniform heating along the length of the outer tubular sheath 22. Alternatively, considering the temperature gradient of the heat sink or fluid proximate the outer tubular sheath 22 along the outer tubular sheath 22, the predetermined temperature profile may be varied to provide varying heating along the length of the outer tubular sheath 22. These multiple different pitches can range, for example, from approximately 1.5 inches (38.1 mm) to approximately 4.5 inches (114.3 mm). An insulating material 34 surrounds the resistance coil 28 and is filled in the tubular outer sheath 22. The insulating material 34 is a compact magnesium oxide (MgO) in one form disclosed in this case. In other forms, an insulating material such as MgO may be mixed with other materials such as boron nitride (BN) to improve thermal transfer characteristics. It should be understood that these insulating materials 34 are only examples and should not be construed as limiting the scope of the disclosure in this case.

Referring to FIG. 3, a tubular heater 40 constructed according to the teaching content disclosed in this case has a structure similar to that of FIG. 2 except for the resistance coil 42. The resistance coil 42 in this embodiment has a continuously variable pitch, accompanied by the ability to accommodate an increase or decrease of the pitch P ₄ to P ₈ on the next 360 ° coil. The continuously variable pitch of the resistance coil 42 allows the resistance coil 42 to provide a gradual change in the flux density of a heater surface (ie, the surface of the outer tubular sheath 22).

An electric group coil 28 having different pitches (P ₁ , P ₂ , P ₃ ) and a resistance coil 42 having a continuously variable pitch (P ₄ to P ₈ ) in different locations A, B and C can use a fixed node From the coil. A knife-edge device is used to hold the opposite standing end of a section / zone of a coil, and stretch or compress the coil to the desired length in the same section / zone to adjust the nodes in the section / zone. distance. The resistance coil 28 may include a material such as a nickel-chromium alloy, and is formed by using a nickel-chromium alloy resistance wire in a fully annealed state or a "fully hard" condition. The hardness of a metal is proportional to the uniaxial undulating stress. Harder metals are more resistant to plastic deformation, and thus facilitate the process of making coils with a desired localized pitch or continuously variable pitch. In addition to 80/20 nickel-chromium alloy, other resistance alloys can be used to form resistance coils with regional pitch or continuously variable pitch. When a nickel-chromium alloy is used, the pitch of the coil may be in a range of about 0.5 to about 2.5 times the diameter of the resistance coil 28. When other materials are used for the resistance coil 28, the coil may have a larger or smaller pitch range, and therefore the values mentioned herein are merely examples, and should not be interpreted as limiting the scope of the disclosure in this case.

The resistance wire used to form the resistance coil 28 or 42 may have a cross-section of any shape, such as a circle, a rectangle, or a square, without departing from the scope of the disclosure of this case. A non-circular cross section appears to exhibit better resistance to plastic deformation.

Referring to FIGS. 4 to 6, the resistance coil 28 may have a different configuration. As shown in FIG. 4, the resistance coil 50 may have a conical shape with a variable outer diameter. For example, the resistance coil 50 may have a minimum outer diameter D ₁ near a first end 52 of a first conductive pin 56 and a maximum outer diameter D1 near a second end 54 of a second conductive pin 58. Outside diameter D ₂ . The resistance coil 50 may have a localized pitch or a continuously variable pitch (P ₁₀ ~ P ₁₂ ) along its length.

The resistance coil may alternatively have a double spiral or a triple spiral as shown in Figs. 5 and 6, respectively. In FIG. 5, the resistance coil 60 has a double spiral and includes a first spiral element 62 and a second spiral element 64. The first and second spiral elements 62 and 64 are formed around the same axis, and are connected to the first and second conductive pins 66 and 68 to form a parallel circuit. The first and second spiral elements 62 and 64 may have a regional pitch (P ₁₃ , P ₁₄ , P ₁₅ ) or a continuously variable pitch. In FIG. 6, the resistance coil 70 is shown as having a triple spiral, and includes a first spiral element 72, a second spiral element 74, and a third spiral element 76 connected to a first conductive pin 78. And a second conductive pin 80 to form a parallel circuit.

Referring to FIG. 7, another form of the tubular heater 200 constructed according to the teaching content of the disclosure of the present case includes an outer sheath 202, which is tubular in one form of the disclosure of the present case; the first and second conductive pins 204 and 206; a resistance coil 208 disposed between the first and second conductive pins 204 and 206; and an insulating material 210 filled in the tubular outer sheath 202 to electrically insulate the resistance coil 208. In this form, the resistance coil 208 includes a spiral coil having a fixed outer diameter. The resistance coil 208 includes a first end 212 connected to the first conductive pin 204 and a second end 214 opposite to the first end 212 and connected to one of the second conductive pins 206. The resistance coil 208 has a first portion 216 adjacent to the first end 212, a second portion 218 adjacent to the second end 214, and a third portion 220 disposed between the first portion 216 and the second portion 218. The first, second, and third portions 216, 218, and 220 may have different pitches to provide different watt density / heat output density. Therefore, the first, second, and third portions 216, 218, and 220 define a plurality of heating zones A, B, and C. Although only three locations A, B, and C are shown in the figure, it is understood that the resistance coil 208 may have any number of heating locations without departing from the scope of the present disclosure.

At least one of the first, second, and third portions 216, 218, and 220 may have a continuously variable pitch. In one form, the first and second portions 216 and 218 have a fixed pitch, and the third portion 220 has a continuously variable pitch. The pitch of the first portion 216 may be equal to or different from the pitch of the second portion 218. The pitch of the first portion 216 and the second portion 218 may be larger or smaller than the pitch of the third portion 220. Therefore, the first and second portions 216 and 218 of the resistance coil 208 generate a fixed watt density in heating zone A and heating zone B, and the third portion 220 of the resistance coil 208 generates a variable watt density in heating zone C / Heat output density.

Alternatively, the first, second, and third portions 216, 218, and 220 each have a continuously variable pitch. Thus, the heating zones A, B, and C each produce a variable watt density.

Referring to FIG. 8, a tubular heater 250 constructed according to the teaching content disclosed in the present case includes first and second conductive pins 252 and 254, and a tube disposed between the first and second conductive pins 252 and 254. Resistance coil 256. This resistance coil 256 has a first end connected to one of the first conductive pins 252 and a second end connected to one of the second conductive pins 252. The resistance coil 256 includes a first portion 260 connected to the first conductive pin 252, a second portion 262 connected to the second conductive pin 254, and a first portion disposed between the first and second portions 260, 262. Third part 264. The first, second and third sections 260, 262 and 264 have different pitches and / or diameters, thus defining three heating zones A, B and C.

The first portion 260 of the resistance coil 256 has a fixed pitch P ₁ and a variable diameter. The diameter gradually increases from the first conductive pin 252 to the third portion 264 to define a push portion. The second portion 262 of the resistance coil 256 has a fixed pitch P ₂ and a variable diameter. The diameter gradually increases from the second conductive pin 254 to the third portion 264 to define a push portion. Therefore, despite the fixed pitch of the first and second sections 260 and 262, the heating zones A and B can still provide a variable watt density.

The third portion 264 of the resistance coil 256 may be configured to have a continuously variable pitch and a fixed diameter. Therefore, the heating zone C also provides a variable watt density and thus a variable heat output density to provide a desired heating profile for a heating target.

Referring to FIG. 9, a tubular heater 300 constructed according to the teaching content disclosed in the present case includes a first conductive pin 302, a second conductive pin 304, and one of the first and second conductive pins 302 and 304. A resistor coil 306 is connected to the pins at intervals. The resistance coil 306 includes a plurality of first portions 308 having a first diameter, a plurality of second portions 310 having a second diameter smaller than one of the first diameters, and a third portion 312. The first and second portions 308 and 310 may be placed alternately or "alternately" along the length of the resistance coil 306. The third portion 312 is provided with opposite first and second ends 311 and 313 of adjacent resistance coils 306 and forms a push-out portion. The third portions 312 each have a variable diameter, which gradually increases from the first conductive pin 302 or the second conductive pin 304 to an adjacent first portion 308. The first and second portions 308 and 310 each have a variable pitch to provide a variable watt density / heat output density.

FIG. 9 shows three first portions 308 having a fixed diameter. The first portion 308 closest to the first conductive pin 302 may have a continuously variable pitch, which gradually increases closer to the center of the resistance coil 306. The first portion 308 closest to the second conductive pin 304 may have a continuously variable pitch, which gradually increases closer to the center of the resistance coil 306. The first portion 308 adjacent to the center of the resistance coil 306 may have a fixed pitch or a variable pitch, which may be different from the variable pitch of the first portion 308 at the opposite standing ends 311, 313.

Referring to FIG. 10, a tubular heater 350 constructed according to the teaching content disclosed in the present case includes a first conductive pin 352, a second conductive pin 354, and a plurality of resistance coils 356, 358, and 360. The first and second conductive pins 352 and 354 extend in a first direction X and are parallel to each other. The plurality of resistance coils 356, 358, 360 are disposed between the first and second conductive pins 352, 354, and are aligned along the first direction X to define a plurality of heating zones A, B, and C. The resistance coils 356, 358, and 360 each have a first end 362 connected to one of the first conductive pins 352 and a second end 364 connected to one of the second conductive pins 354. Therefore, a plurality of resistance coils 356, 358, and 360 are connected to the first and second conductive pins 352, 354 to form a parallel circuit. The resistance coils 356, 358, 360 may have the same / different pitch or the same / different outer diameter, or any combination thereof to provide a desired heating profile. For example, the resistance coils 356, 358, 360 may have a configuration similar to any of the resistance coils described herein with reference to the drawings.

The resistance coils described in any of the forms disclosed in this case may be assembled to include a plurality of portions having a fixed pitch, a variable pitch, a fixed diameter, a variable diameter, or any combination thereof. Therefore, the resistance coil can be configured to provide a desired heating profile, considering factors that affect the heating profile, such as proximity to the heat sink, temperature distribution of the fluid to be heated, and the like. With the proper combination of resistance coils, only one heater and one resistance coil can be used to provide the desired heating profile, whether uniform or non-uniform. Alternatively, a heater may include multiple resistance coils with fixed / variable pitch and fixed / variable diameter to provide a desired heating profile.

Referring to FIG. 11, a modified tubular heater 90 constructed according to the teaching content disclosed in the present case is shown to define a U-shape and includes a hairpin bend 92. (It should also be understood that any curved configuration such as 45º or 90º can be used as a variation of the tubular heater 90, and therefore the 180º hairpin configuration should not be interpreted as limiting the scope of the disclosure in this case.) The variable pitch configuration can be used in the 92 part of the hairpin bend to reduce current crowding. The tubular heater 90 may be used in an electric heat exchanger of a direct type (shown in FIGS. 8 and 9) or an electric heat exchanger of an indirect type.

As shown, the tubular heater 90 includes a tubular outer sheath 91 defining a hairpin bend 92 and a pair of conductive pins 94 protruding from opposite ends of the tubular outer sheath 91. The pair of conductive pins 94 are arranged in parallel and separated by a distance H. The hairpin bend 92 has a curvature defining a radius R. The tubular outer sheath 91 has an outer diameter D ₃ . The tubular heater 90 includes a resistance coil (not shown in FIG. 7) that may have a localized pitch as shown in FIG. 2 or a continuously variable pitch as shown in FIG. 3.

Referring to FIG. 12, a heat exchanger system including a plurality of tubular heaters 90 is shown and is generally designated by reference number 100. The heat exchanger 100 is a direct electric heat exchanger including an outer tube 102 surrounding a plurality of tubular heaters 90. In addition, the tube 102 includes an inlet 106 and an outlet 108. The fluid to be heated flows into and out of the outer tube 102 through the inlet 106 and the outlet 108.

Referring to FIG. 13, the tubular heater 90 extends from the inlet 106 to the outlet 108 and has a hairpin bend 92 disposed near the outlet 108. When the fluid enters the inlet 102, the fluid is gradually heated by the tubular heater 90 until the fluid leaves the outer tube 102 through the outlet 108. The fluid near the inlet 106 is colder than the fluid near the outlet 108.

In a conventional direct heat exchanger, the tubular heater has a fixed pitch resistance coil to provide a fixed heat flux density (ie, watt density) along the length of the tubular sheath outside the tubular heater. To avoid degradation of the heat medium, and / or achieve a desired heater durability, and / or for other safety reasons, this watt density is usually specified or calculated to limit the maximum jacket temperature. Because the watt density along the length of the tubular heater is fixed, the jacket temperature varies according to several thermodynamic factors, including the temperature gradient of the fluid along the tubular heater and the fluid flow rate.

Heat exchangers using traditional tubular heaters generally have performance issues such as increased hydrocarbons at the outlet and "coking". Fluid near the inlet is colder than fluid near the outlet. When a conventional tubular heater provides uniform heating along its length, fluids near the inlet may not heat quickly enough, while fluids near the outlet may overheat, causing increased hydrocarbons and "coke" at the outlet. By using a resistance coil with a variable pitch, the tubular heater can be designed to generate more heat near the inlet and less heat near the outlet. Therefore, the heat exchanger including the resistance coil disclosed in this case can rapidly increase the temperature of the fluid without overheating the fluid at the outlet.

Furthermore, a tubular heater constructed in accordance with the teachings disclosed in this case can be installed in an existing heat exchanger, and the heating profile can be changed if desired. Engineering errors may occur during the design of the heat exchanger, such as errors in under-rated kW. The tubular heater disclosed in this case can replace the existing heater to provide a higher kilowatt bundle in the same heat exchanger package / size / occupied area by changing the pitch of the resistance coil. In addition, a conventional heater can be redesigned to provide a lower average watt density and / or jacket temperature for longer durability.

A tubular heater with a continuously variable pitch resistance coil is used to produce a continuously variable watt density along the length of the outer tubular sheath. Therefore, the tubular heater disclosed in this case has the advantage of reducing the size of the tubular heater, and thus adding a heat exchanger to reduce the manufacturing cost and the occupied area.

The narrative of the disclosure in this case is merely an example in nature, and therefore there can be variations within the scope of the disclosure in this case without departing from the substance of the disclosure in this case. These variations are not deemed to depart from the spirit and scope of the disclosure in this case.

10, 20, 90, 200, 250, 300, 350‧‧‧ tubular heaters

12, 91‧‧‧ tubular outer sheath

14‧‧‧conducting pin

16, 28, 40, 42, 50, 60, 70, 208, 256, 306, 356, 358, 360‧‧‧ resistance coils

18, 34, 210‧‧‧ insulating materials

22‧‧‧ Tubular outer sheath; outer tubular sheath

24, 56, 66, 204, 252, 302, 352‧‧‧ first conductive pin

26, 58, 68, 206, 254, 304, 354‧‧‧ second conductive pin

30‧‧‧ first end (partial)

32‧‧‧ second end (partial)

52, 212, 362‧‧‧ first end

54, 214, 364‧‧‧ second end

62, 72‧‧‧ first spiral element

64, 74‧‧‧Second spiral element

76‧‧‧ third spiral element

92‧‧‧hairpin bend

94‧‧‧conducting pin

100‧‧‧ heat exchanger

102‧‧‧External tube

106‧‧‧ Entrance

108‧‧‧ exit

202‧‧‧ Outer Sheath

216, 308‧‧‧ Part I

218, 310‧‧‧ Part II

220, 312‧‧‧ Part III

260‧‧‧ Part I; Section I

262‧‧‧ Part Two; Part Two

264‧‧‧ Part III; Section III

311‧‧‧ (first)

313‧‧‧ (second)

A‧‧‧first location; (heating) location

B‧‧‧Second Location; (Heating) Location

C‧‧‧ third location; (heated) location

D ₁ ‧‧‧ minimum outer diameter

D ₂ ‧‧‧ Maximum outer diameter

D ₃ ‧‧‧ outer diameter

H‧‧‧distance

P ₁ ~ P ₈ , P ₁₀ ~ P ₁₅ ‧‧‧ pitch

R‧‧‧ radius

X‧‧‧ first direction

The drawings described herein are for illustration purposes only and are not intended to limit the scope of the disclosure in this case in any way.

In order that the present invention may be better understood, an embodiment provided by way of example will now be described, with reference to the accompanying drawings, in which:

Figure 1 is a cross-sectional view of one of the conventional tubular heaters;

2 is a cross-sectional view of a tubular heater constructed according to the teaching content disclosed in the present case;

FIG. 3 is a cross-sectional view of a tubular heater in another form constructed according to the teaching content disclosed in the present case;

4 is a schematic diagram of a resistance coil in a tubular heater constructed according to the teaching content disclosed in this case;

5 is a schematic diagram of a resistance coil having another form with a continuously variable pitch, and the resistance coil can be used in a tubular heater constructed according to the teaching content disclosed in the present case;

6 is a schematic diagram of a resistance coil in another form of a tubular heater constructed according to the teaching content disclosed in this case;

7 is a cross-sectional view of a tubular heater in another form constructed according to the teaching content disclosed in the present case;

8 is a schematic diagram of a tubular heater in another form constructed according to the teaching content disclosed in the present case, in which an outer sheath and an insulating material are removed for illustration;

FIG. 9 is a schematic diagram of a tubular heater according to yet another form constructed according to the teaching content disclosed in the present case, in which an outer sheath and an insulating material are removed for illustration;

FIG. 10 is a schematic diagram of a tubular heater according to another form of the teaching content disclosed in the present case, in which an outer sheath and an insulating material are removed for illustration;

11 is a plan view and a side view of a modified tubular heater constructed according to the teaching content disclosed in this case;

FIG. 12 is a side view of an electric heat exchanger of a tubular heater constructed using the teaching content disclosed in this case; and

FIG. 13 is a cross-sectional view of a part of the electric heat exchanger of FIG. 12.

Corresponding reference numbers in the several views of the drawings indicate corresponding parts.

Claims (14)

A resistance element used in a heater includes a resistance coil having a first end and a second end opposite to the first end. The resistance coil defines a first adjacent to the first end. A portion; a second portion adjacent to the second end; and a third portion interposed between the first portion and the second portion; wherein the third portion has a fixed diameter and a continuously variable pitch and the first portion Each of the first and second portions has a variable diameter and a fixed pitch such that each of the first, second, and third portions provides a variable watt density along its length. The resistance element of claim 1, wherein the first part and the second part have the same fixed pitch. The resistive element of claim 1, wherein the first part and the second part have different pitches. The resistive element of claim 1, wherein at least one of the first part and the second part defines a push having an increasing outer diameter along a length from the first end or the second end to the third part. Pull out As in the resistive element of claim 1, wherein the first portion defines a push-out portion having an increasing outer diameter along a length from the first end to the third portion, and the second portion defines a distance from the second end to the The length of the third part has a push-out portion with an increasing outer diameter. A resistive element comprising: a resistive coil having a first end and a second end opposite to the first end, the resistive coil defining: a plurality of first portions defining a first fixed diameter; and A plurality of second portions, which define a second fixed diameter smaller than one of the first fixed diameter; wherein the first portion and the second portion are staggered, and at least one of the first portion and the second portion One has a continuously variable pitch. As in the resistance element of claim 6, each of the first part and the second part has a variable pitch. As in the resistive element of claim 6, some of the first part and the second part have a fixed pitch, and other of the first part and the second part have a continuously variable pitch. The resistance element of claim 6, further comprising at least a third portion, which defines a push portion adjacent to one of the first end and the second end. The resistive element according to claim 9, wherein the at least one third part is connected between the first end and the first part, and is pushed from the first end to the first part. The resistance element of claim 10, wherein the at least one third portion has a variable pitch. A heater includes: a first conductive pin; a second conductive pin; and a plurality of resistance coils, each resistance coil including a first end directly connected to the first conductive pin, and directly connected to A second end of the second conductive pin; wherein the first conductive pin and the second conductive pin extend in a first direction and are parallel to each other, and the plurality of resistance coils are arranged on the first A conductive pin and the second conductive pin are aligned in a direction parallel to the first direction, and at least one of the plurality of resistance coils has a continuously variable pitch. The heater of claim 12, wherein the plurality of resistance coils have at least one of different pitches and different diameters. The heater of claim 12, wherein the plurality of resistance coils each have a variable pitch from the first end to the second end.