Patent ID: 12193594

DETAILED DESCRIPTION

FIG.1depicts a perspective view of an example of a kettle100for transferring thermal energy to a contained fluid such as water, a liquid, a substance, or a mixture of liquid and a solid (e.g., soup). While the kettle100is provided as one example, in other embodiments any container (e.g., a vessel) may be utilized such as, but not limited to, a pot, pan, or any other container which may hold a substance. In some embodiments, various embodiments described herein may be utilized with a cooking implement.

The kettle100includes a base portion102and a wall portion104. The base portion102and the wall portion104may be formed from a single piece of material or, alternately, by multiple pieces of material. The kettle may be formed in any number of ways such as, for example, welding or crimping the base portion102to the wall portion104. The base portion102and the wall portion104may be comprised of one or a plurality of applicable materials that may assist in containing the substance and/or transferring thermal energy from the outside of the kettle100to the inside of the kettle100.

The kettle100may comprise any kind of material. For example, the base portion102and/or the wall portion104may comprise material such as, but not limited to, stainless steel, copper, ceramic(s), and/or the like. The base portion102and/or the wall portion104may comprise an alloy or any combination of materials. In some embodiments, the base portion102and the wall portion104may include a sandwich structure of various layers of materials. For example, the base portion102and/or the wall portion104may be clad and include a layer of copper, aluminum, or other metal(s) sandwiched between layers of steel (e.g., between layers of stainless steel).

The base portion102and the wall portion104may combine to create a vessel106that functions to contain a volume of a substance. In various embodiments, the kettle100may be referred to as a vessel or, in some embodiments, the kettle may comprise a vessel. The vessel106is a portion of the kettle100that may contain or hold the substance. In various embodiments, the kettle100receives heat from an external heat source and transfers heat through the base102to the contained substance.

In various embodiments, the base portion102, and potentially, the wall portion104are in thermal contact with the substance (e.g., fluid) contained within the kettle100. In some embodiments, the thermal contact enables thermal energy to transfer from or through the base portion102and/or the wall portion104to the contained substance (e.g., held by the vessel106). For example, the substance is in thermal contact with the base portion102because the substance within the kettle100is in physical contact with the base portion102and/or wall portion104. In transferring thermal energy to the contained substance, the base portion102and/or the wall portion104may, in some embodiments, absorb thermal energy from a thermal energy source (e.g., fire, heating element, or the like such as, but not limited to, electric, ceramic, halogen, gas, hydrocarbon(s), or induction heating elements). Further in transferring thermal energy to a contained substance, the base portion102and/or the wall portion104can transfer energy absorbed from the thermal energy source to the contained substance. It will be appreciated that the thermal energy source may be external to the kettle100(e.g., a stove or fire). In another example, the thermal energy source may be internal to the kettle100(e.g., an electric kettle or any other electrically heated vessel).

In an example of operation, the base portion102and/or the wall portion104may absorb thermal energy from many different types of thermal energy sources. In various embodiments, the base portion102and/or wall portion104may receive thermal energy from, but not limited to, conduction, convection, induction, or radiation heating. Additionally, the base portion102and/or the wall portion104can transfer absorbed thermal energy to the contained substance and/or facilitate convection in the contained substance.

The kettle100includes a receiving aperture108. The receiving aperture108is an opening through which the substance (e.g., fluid such as a liquid, or mixture of a liquid and a solid) may be passed out of and/or into the vessel106. In some embodiments, once the substance is contained within the vessel106, thermal energy can be transferred from the external heating source through the base portion102and/or the wall portion104.

The kettle100includes a dispensing aperture110. The dispensing aperture110is an opening through which the substance may be passed out from the vessel106. The dispensing aperture110may be shaped to allow for the pouring of the substance. In some embodiments, the dispensing aperture110passes heated fluid after a desired amount of thermal energy is transferred to the fluid. For example, the dispensing aperture110may be used to pass a contained liquid out of the vessel106after enough thermal energy is transferred to the liquid contained within the vessel106to cause the liquid to boil, or to cause the liquid to reach a desired temperature.

FIG.2Ais a planar view of an example kettle bottom surface with a cavity defined between an edge208of the base of the kettle and a thick metal encapsulated base202in the prior art. In the prior art, some kettles include a thick aluminum encapsulated base (or other encapsulated metal) for uniform or even heating. In this example, the thick metal encapsulated base202is flat and is a major portion (e.g., a predominant portion) of the bottom of the kettle. An encapsulated base edge204and edge208of the kettle may define a cavity206along the rim of the base of the kettle. A diameter210is a diameter of the base of the kettle.

The edge208may allow for the thick metal encapsulated base202to be coupled to the bottom of the kettle. The edge208and cavity206may also help capture the edge of stove flames to entrap heat. Although there is an increase in surface area, the increase in heat transfer is nominal because the increase in the surface area is nominal.

FIG.2Bis a cross section view of an example kettle bottom surface with a cavity206defined between an edge208of the kettle and a thick metal encapsulated base202in the prior art. In this cross-sectional view, the cavity206is shown between the edge208of the kettle and the encapsulated base202. As can be seen, there is not a substantial or significant increase in surface area of the bottom when compared to a kettle with a flat bottom.

FIG.2Cincludes dimensions for the cross section view ofFIG.2B. Here, dimension “d1” represents the diameter of the thick metal encapsulated base202. Dimension “d2” represents the diameter of the base of the kettle (e.g., diameter210). Dimension “h” represents the distance that the thick metal encapsulated base202extends perpendicularly from the base of the periphery of the kettle. Given these dimensions, the increase in surface area for the kettle bottom surface inFIG.2Crelative to a kettle with a flat bottom surface is:

Δ⁢area=(area⁢of⁢this⁢example⁢kettle⁢bottom⁢surface)-(area⁢if⁢the⁢kettle⁢bottom⁢surface⁢was⁢flat)
With the dimensions shown inFIG.2C:

Δ⁢area=(π)⁢(h)⁢(d⁢2+((22)-1)⁢(d⁢1)+(2-1)⁢(h))
The percentage increase in the surface area for this example kettle bottom surface relative to the surface area if the kettle bottom surface was flat equals:
(100%)(Δarea)/(area if the kettle bottom surface was flat)
For example, using the dimensions as labeled inFIG.2C, a kettle with approximate dimensions of d1=7 inch, d2=9 inch, and h=¼ inch, will have a percentage increase in the surface area of approximately ten percent (e.g., 10%) relative to a kettle with a flat bottom. This percentage increase in the surface area (of this kettle in the prior art) is nominal, and it does not significantly or appreciably increase the surface area (relative to a flat bottom surface) such that the thermal transfer would also significantly or appreciably increase.

FIG.3is a cross sectional view of a vessel106(e.g., a portion of the kettle100) in some embodiments. The vessel106is formed by a base portion102and a wall portion104. The base portion102includes a base outer surface302and a base inner surface304. The base outer surface302is the surface opposite of the base inner surface304.

In various embodiments, the base outer surface302is the surface of the base portion102through which thermal energy is received from the thermal energy source. The base outer surface302may include a heating surface portion that receives and absorbs heat from the thermal energy source. The base inner surface304is the surface of the base portion102through which absorbed thermal energy may be transferred to the contained substance (e.g., a fluid contained or held within the vessel106). Thus, the base portion102may be thermally coupled to the substance contained within the vessel106through the base inner surface304. In various embodiments, the base inner surface304may physically contact at least some of the substance contained within the vessel106, and thereby be thermally coupled to the substance contained within the vessel106.

In some embodiments, at least one of the base outer surface302and/or the base inner surface304includes a shaped portion. A shaped portion of the base outer surface302or the base inner surface304is shaped such that there is substantially more surface area when compared to a flat surface. A shaped portion of the base outer surface302may include, for example, raised rectangular ridges, raised sinusoidal ridges, raised rectangular ridges, posts, raised portions, protrusions, indentations, or the like of any size or shape. A shaped portion may include raised portions of a surface, depressed portions in the surface, or a combination of raised portions and depressed portions (e.g., a combination of protrusions and indentations) of the surface. Substantially more surface area may, for example, include 1.2 or more times (e.g., 1.5 times or more, 2 times or more, 3 times or more, or the like) of a surface area when compared to the surface area of a flat surface. Examples of shaped portions with substantially increased surface area (in comparison with a flat surface), are described herein. In various embodiments, only a portion of the base outer surface302and/or the base inner surface304includes shaped portions.

The wall portion104includes a wall outer surface306and a wall inner surface308. The wall outer surface306is opposite the wall inner surface308. In some embodiments, all or a portion of the wall outer surface306may receive thermal energy from the thermal energy source. A portion of the wall inner surface308may transfer thermal energy from the wall outer surface306to the contained fluid. Thus, a portion of the wall portion104may be thermally coupled to the contained fluid. In various embodiments, the wall inner surface308may physically contact at least some of the fluid contained within the vessel106, and thereby be thermally coupled to the substance contained within the vessel106.

In some embodiments, at least a portion of the wall outer surface306and/or at least a portion of the wall inner surface308include a shaped portion. A shaped portion of the wall outer surface306or the wall inner surface308is shaped such that the shaped portion has substantially more surface area than if the shaped portion of the corresponding wall outer surface306or wall inner surface308was flat.

A shaped portion of the wall outer surface306and/or the shaped portion of the wall inner surface308may include, for example, raised sinusoidal ridges, raised rectangular ridges, indented sinusoidal furrows, indented rectangular ridges, posts raised portions, depressed portions, protrusions, indentations, or the like of any size or shape. A shaped portion may include raised portions of a surface, depressions in the surface, or a combination of raised portions and depressed portions (e.g., a combination of protrusions and indentations) of the surface. Examples of shaped portions with substantially increased surface area (in comparison with a flat surface), are described herein. In various embodiments, only a portion or the entire wall outer surface306and/or only a portion of the wall inner surface308includes a shaped portion.

A base inner surface304and/or a wall inner surface308with substantially more surface area than a flat corresponding portion will increase the rate at which thermal energy is transferred to a substance contained within the vessel106(e.g., substantially increased). For example, the rate that thermal energy is transferred to the volume of substance may be directly proportional to the surface area of the volume of fluid in thermal contact with the heated surface(s) (e.g., wall inner surface308and/or base inner surface304). Increasing the surface area of the base inner surface304of the base portion102, and/or the wall inner surface308(e.g., with protrusions, ridges, fins, furrows, indentations, and/or the like) increases the surface area of contact between a contained substance in the vessel106and at least a portion of the base inner surface304and/or at least a portion of the wall inner surface308. Due to the (e.g., substantially) increased surface area between the substance and the base inner surface304and/or the wall inner surface308, the rate of heat transfer from the thermal energy source (e.g., from a heat source via the base outer surface302) to the substance contained in the vessel106may be (e.g., substantially) increased.

Similarly, increasing the surface area of the base outer surface302of the base portion102, and/or the wall outer surface306(e.g., with protrusions, ridges, fins, indentations, and/or the like of any size or shape) may increase the surface area of contact between the thermal energy provided by the heat source and at least a portion of the base outer surface302of the base portion102, and/or the wall outer surface306. Due to the (e.g., substantially) increased surface area between the thermal energy of the heat source and the base outer surface302and/or the wall outer surface306, the rate of heat transfer from the thermal energy source (e.g., from a heat source via the base outer surface302and/or the wall outer surface306) to the substance contained in the vessel106may be (e.g., substantially) increased.

Increasing the amount of thermal energy that is absorbed by, or increasing the amount of thermal energy which transfers through, or increasing the flux of thermal energy which transfers through, or increasing the rate at which thermal energy transfers through at least a portion of the base portion102and/or at least a portion of the wall portion104may increase the temperature difference between the base portion102and/or the wall portion104and a substance contained within the vessel106. Increasing the temperature difference between at least a portion of the base portion102and/or at least a portion of the wall portion104relative to a substance contained within the vessel106may lead to an increased rate at which thermal energy is transferred from the base portion102and/or the wall portion104to the substance. As a result of increasing the rate at which thermal energy is transferred from the base portion102and/or the wall portion104to the substance contained within the vessel106, more thermal energy is transferred to the substance during a specific (e.g., limited) amount of time. In one example, a fluid may boil faster as a result of the (e.g., substantially) increased surface area(s) of the base portion102and wall portion104.

In some embodiments, in configuring a portion of a base inner surface304and/or a wall inner surface308to be shaped to have more surface area than a corresponding portion of the surface that is flat, a greater amount of thermal energy is transferred from a heat source to a substance contained within the vessel106. Increasing the surface area of the base inner surface304and/or the wall inner surface308may increase the amount of surface area that is in thermal contact with a substance contained within the vessel106. As a result of increasing the amount of surface area that is in thermal contact with a substance contained within the vessel106and/or in thermal contact with a heat source, an increased amount of thermal energy may be absorbed by, or otherwise transferred to, the substance during a specific (e.g., limited) amount of time.

It will be appreciated that the thermal energy source may be external (i.e., separate) to the vessel106. For example, the thermal energy source may be a fire or heating element on a stove. In this example, the thermal energy source (or a component of the thermal energy source) may not be integral to, fixed to, or permanently attached to the vessel106. In some embodiments, the thermal energy source may be configured or arrayed within a horizontal zone below the vessel106.

In some embodiments, the thermal energy source may be internal to the vessel106(e.g., contained within the base of the vessel106). For example the thermal energy source may be between the base outer surface306and the base inner surface304. In this example, the thermal energy source may be internal to the vessel106and receive power from an electrical source coupled to the vessel106(e.g., through a cable, stand, or plate).

The vessel106may be any shape. In some embodiments, the sides of the vessel106form a polygon with any number of sides. For example, the sides of the vessel106may form a hexagon. All or some of the sides of the vessel106may be rounded or angular.

AlthoughFIGS.4-14depict patterns of protrusions and indentations (e.g., ridges and furrows), the pattern of protrusions and indentations may not, or need not, be uniform. For example, a shaped surface may comprise a random assortment of any shapes (e.g., a random assortment of protrusions and/or indentations) to increase surface area. In one example, the random assortment increases the surface area by at least 1.2 times (or more) relative to the surface area of a flat surface. In other examples, the random assortment increases the surface area by at least 1.5 times or more, 2 times or more, 3 times or more, or the like relative to the surface area of a flat surface. All or a part of a surface (e.g., base outer surface302, base inner surface304, wall outer surface306, or wall inner surface308) may comprise patterns, random assortments, or a combination of patterns and random assortments of shapes.

Further, althoughFIGS.4-14depict patterns of protrusions and indentations, the protrusions and/or indentations (e.g., ridges, furrows, corrugations, or the like) may include any number of geometric shapes or forms of any size or shape. Width, depth, and/or other defining measurement(s) of protrusions and/or indentations may vary over any trajectory and/or may vary with respect to other protrusions and/or indentations that are formed on the inner or outer surfaces of the kettle106.

FIG.4is a planar view of an example shaped surface400that is corrugated according to an example pattern. In various embodiments, all or a portion of the base inner surface304, the base outer surface302, the wall inner surface308, an/or the wall outer surface306, may be shaped according to at least a portion of the shaped surface400shown inFIG.4.

The shaped surface400includes a plurality of ridges402-1. . .402-n(hereinafter referred to as “ridges402”) and furrows404-1. . .404-n(hereinafter referred to as “furrows404”). By including ridges402and furrows404, the surface area of the shaped surface400is increased over the surface area of a flat surface having the same diameter406that the shaped surface400has.

One or more of the ridges402may include portions that extend from the surface and one or more of the furrows404may be the lowest portion (e.g., at the bottom or in the surface such as an indentation) of the shaped surface400. In some embodiments, the shaped surface400has a surface area that is at least 1.2 times greater or more than if the bottom of the kettle was flat. In various embodiments, the shaped surface400has a surface area that is at least two times greater than if the shaped surface400was flat. In some embodiments, the shaped surface400has a surface area that is at least three times greater than if the bottom of the kettle100was flat. In some embodiments, the ridges402and the furrows404, in the example pattern shown inFIG.4, are parallel to each other. In various embodiments, all or some of the ridges402and the furrows404may, or may not, be parallel to each other.

In some embodiments, adjacent ridges402and furrows404are shaped as a sinusoidal wave. In being shaped as a sinusoidal wave, ridge sides of the ridges402are curved towards ridge top planes at the top of the ridges402. The ridge top plane is a hypothetical flat surface which contains the top of each ridge402. For example, the ridge top plane may be a tangential plane containing the peak (e.g., highest amplitude value) point of one, all, some, or most ridges402. In some embodiments, the period, amplitude, phase angle, and/or symmetry of different portions of any number of the sinusoidal waves may vary.

Additionally, in being shaped as a sinusoidal wave, furrow sides of the furrows404are curved towards furrow bottom planes at the bottom of the furrows404. The furrow bottom plane is a hypothetical flat surface which contains the bottom of each furrow404. For example, the furrow bottom plane may be a tangential plane containing the trough (e.g., lowest amplitude value) point of all, some, or most furrows404.

In some embodiments, adjacent ridges402and furrows404are shaped as a square wave. In being shaped as a square wave, the top portion of each of the ridges402(e.g., highest amplitude value) may be in a tangential plane (e.g., a ridge top plane). Similarly, bottom portions of each of the furrows404(e.g., lowest amplitude value) may be in a tangential plane (e.g., a furrow bottom plane). In various embodiments, the period, amplitude, phase angle, and/or symmetry of any portion of any or all of the square waves may vary.

In various embodiments, regardless if the shaped portion is sinusoidal, is rectangular wave shaped, includes posts, includes protrusions, includes indentations, and/or the like, one, some, or all of the shaped portions (e.g., ridges402) may have different heights (e.g., may have different highest amplitude values) whereby not all of the peaks (e.g., top portions) of the shaped portions may be in a plane. Similarly, one, some, or all of the shaped portions (e.g., furrows404) may have different troughs (e.g., may have different lowest amplitude values) whereby not all of the lowest point of the shaped portions may be in a plane. In various embodiments, symmetry of any or all of the shaped surface (e.g., any or all of the posts, waves, protrusions, and/or indentations) may vary.

AlthoughFIG.4depicts eighteen (18) parallel shaped portions400, there may be any number of shaped portions that may be parallel, partially parallel, or not parallel. It will be appreciated that there may be any number of shaped portions400(including high portions and low portions of any shape or combination of shapes), and the shaped portions400may vary in their size(s).

FIG.5is a planar view of an example shaped surface500that is corrugated according to another example pattern. In various embodiments, an applicable combination of all or a portion of a base inner surface, and all or a portion of a base outer surface may be shaped according to the shaped surface500shown inFIG.5.

The shaped surface500includes a plurality of ridges502-1. . .502-n(hereinafter referred to as “ridges502”) and furrows504-1. . .504-n(hereinafter referred to as “furrows504”). In including ridges502and furrows504, the surface area of the shaped surface500is increased over a surface area of a flat surface of the same size as the shaped surface500. In some embodiments, the shaped surface500has a surface area that can be at least 1.2 times or greater than if the shaped surface500was flat. In various embodiments, the shaped surface500has a surface area that can be at least two times or greater than if the shaped surface500was flat. In another embodiment, the shaped surface500has a surface area that can be at least three times or greater than if the shaped surface500was flat.

The ridges502and the furrows504are arranged adjacent to each other concentrically about a pattern center506of the shaped surface500. The pattern center506can be the center of the base outer surface302or the center of a base inner surface304depending on which surface of the base is patterned according to the shaped surface500shown inFIG.5. In some embodiments, one or more pattern center(s)506may originate anywhere on the base outer surface302, the base inner surface304, wall outer surface306, and/or wall inner surface308.

In some embodiments, the ridges502and the furrows504can be shaped as a sinusoidal wave, as discussed with respect toFIG.4. In another embodiment, the ridges502and the furrows504can be shaped as a square wave, as discussed above with respect toFIG.4.

AlthoughFIG.5depicts ten (10) concentric circles, there may be any number of concentric circles or partially concentric circles. It will be appreciated that there may be any number of shaped portions (including high portions and low portions of any shape or combination of shapes), and the shaped portions may vary in their size(s).

FIG.6is a planar view of an example shaped surface600that is corrugated according to another example pattern. In various embodiments, an applicable combination of all or a portion of a base inner surface and/or all or a portion of a base outer surface may be shaped according to the shaped surface600shown inFIG.6.

The shaped surface600includes a plurality of ridges602-1. . .602-n(hereinafter referred to as “ridges602”) and furrows604-1. . .604-n(hereinafter referred to as “furrows604”). In including ridges602and furrows604, the surface area of the shaped surface600is increased over a surface area of a flat surface of the same size as the shaped surface600. In some embodiments, the shaped surface600has a surface area that can be at least 1.2 times or greater than if the shaped surface600was flat. In another embodiment, the shaped surface600has a surface area that can be at least two times or greater than if the shaped surface600was flat. In another embodiment, the shaped surface600has a surface area that can be at least three times or greater than if the shaped surface600was flat. The ridges602and the furrows604radiate out from a pattern center606. The pattern center606can be the center, or originate at one or more points distant from the center, of the base outer surface302or the base inner surface304depending on which surface of the base is patterned according to the shaped surface600shown inFIG.6. In the pattern shown inFIG.6, the furrows604increase in furrow width608as the furrow extends out from the pattern center606. In other embodiments, a ridge width of a ridge can increase as the ridge extends out from the pattern center606.

In various embodiments, different patterns may include different pattern centers any of which may be different than the center of a bottom outer surface302and/or the center of a bottom inner surface304(e.g., pattern center606inFIG.6). For example, a bottom outer surface302may include any number of pattern centers located next to each other, each pattern center including its own center. Any number of shaped surfaces may be oriented in any manner. As a result, each pattern and/or combination of patterns of shaped surfaces may be oriented around any number of pattern centers.

In some embodiments, the ridges602and furrows604can be shaped as a sinusoidal wave, as discussed with respect toFIG.4. In various embodiments, the ridges602and furrows604may be shaped as half circles. In another embodiment, the ridges602and the furrows604can be shaped as a square wave, as discussed with respect toFIG.4.

AlthoughFIG.6depicts twenty four (24) shaped portions radiating from a center, there may be any number of shaped portions radiating form the center. It will be appreciated that there may be any number of shaped portions (including high portions and low portions of any shape or combination of shapes), and the shaped portions may vary in their size(s).

FIG.7Ais a cross-sectional view of a shaped surface700that includes ridges702and furrows704shaped according to a sinusoidal wave. The shaped surface700shown inFIG.7Acan be formed in accordance with the example patterns shown inFIGS.4-6. The shaped surface700can be formed on any combination of a base inner surface304, a base outer surface302, a wall inner surface308, and a wall outer surface306. In some embodiments, the shaped surface700shown inFIG.7Ahas at least 2 times greater surface area (e.g., at least 2.3 times greater surface area) than the surface area of a flat surface.

The ridges702include ridge sides706that are curved towards a ridge top plane708(e.g., a plane tangent to the peaks of the sinusoidal waves). In an embodiment, the ridges702can be shaped such that a cross section of a ridge of the ridges702exhibits reflection symmetry about a ridge axis of symmetry710that is normal to the ridge top plane708.

The furrows704include furrow sides712that are curved towards a furrow bottom plane714(e.g., a plane tangent to the troughs of the sinusoidal waves). In an embodiment, the furrows704can be shaped such that a cross section of a furrow of the furrows704exhibits reflection symmetry about a furrow axis of symmetry716that is normal to the furrow bottom plane714.

An example function of heat transfer is as follows, where “U” is the heat transfer coefficient, “Area” is the area for which the heat is transferred to the substance, and “ΔT” is the difference in temperature (e.g., between a solid surface such as a portion of the kettle100and a contained liquid):
Q=(U)(Area)(ΔT)
Here, “Q” has units of energy per time (e.g., Joules per second).

In various embodiments, an arc length for a sinusoidal wave is defined as follows. Assuming the sinusoidal wave includes component a, where a=peak amplitude (measured from the zero crossings) and 2π/b=period of the sinusoidal wave:

y=a⁢sin⁢bxdydx=ab⁢cos⁢bxArc⁢Length=S=2⁢∫0πb1+(dydx)2⁢dx=S=2⁢∫0πb1+a2⁢b2⁢cos2(bx)⁢dxAssuming a=π and b=1 then:
S=2∫0π√{square root over (1+π2cos2(x))}dx
S=2(7.21403)=14.482
Assuming unit width, the area equals (S)(1) or S.

FIG.7Bis a cross-sectional view of a shaped surface750that is corrugated with ridges702and furrows704shaped according to a square wave. The shaped surface750shown inFIG.7Bcan be formed in accordance with the example patterns shown inFIGS.4-6. The shaped surface750can be formed on any combination of a base inner surface304, a base outer surface302, a wall inner surface308, and a wall outer surface306. In some embodiments the shaped surface750shown inFIG.7Bhas at least 3 times greater surface area than a surface area of a flat surface.

The ridges702include planar tops that form the tops of the ridges702. The ridges702include ridge sides706that extend linearly upwards towards a ridge top plane708. The ridge top plane708is formed along a planar top of a ridge with a corresponding ridge side706that extends linearly upwards towards the ridge top plane708.

The furrows704include planar bottom that form the bottoms of the furrows704. The furrows704include furrow sides712that extend linearly downwards towards a furrow bottom plane714. The furrow bottom plane714is formed along a planar bottom of a furrow with a corresponding furrow side712that extends linearly downward towards the furrow bottom plane714.

In various embodiments, a rectangular wave pattern is as follows. Assuming the rectangular wave includes component a where a is the peak amplitude (e.g., the height measured from the zero crossings) and b is the width of a rectangular wave (e.g., as measured along the zero crossings):
S=4a+2bIf a=b=π, S=4π+2π=6π=18.85Relative to a flat surface with length
2b=2π=6.2832
Assuming unit width, the area equals (S)(1) or S.
For example:

AreaArea Relative(Assumingto aSurfaceUnit Width)Flat SurfaceFlat6.28321.000Sinusoidal in one dimension14.4822.305with amplitude defined aboveequal to half of the periodRectangular in one dimension18.853.000with amplitude defined aboveequal to half of the period

FIG.8is a planar view of a shaped surface800that is corrugated according to another example pattern. In various embodiments, an applicable combination of a portion of a base inner surface304, a base outer surface302, a wall inner surface308, and a wall outer surface306may be shaped according to the shaped surface800shown inFIG.8.

The shaped surface800includes a plurality of ridges802-1. . .802-n(hereinafter referred to as “ridges802”) and furrows804-1. . .804-n(hereinafter referred to as “furrows804”). By including ridges802and furrows804, the surface area of the shaped surface800is increased relative to the surface area of a flat surface of a same size as the shaped surface800. In some embodiments, the shaped surface800has a surface area that is at least 1.2 times greater than if the shaped surface800was flat. In another embodiment, the shaped surface800has a surface area that is at least two times greater than if the shaped surface800was flat. In another embodiment, the shaped surface500has a surface area that can be at least three times or greater than if the shaped surface500was flat. The ridges802are shaped along the longitudinal length of the ridges802according to a planar square wave pattern. Similarly, the furrows804are shaped along the longitudinal length of the furrows according to an inverse of a planar square wave pattern of which the ridges802adjacent to the furrows804are shaped.

FIG.9is a planar view of a shaped surface900that is corrugated according to another example pattern. In various embodiments, an applicable combination of a portion of a base inner surface304, a base outer surface302, a wall inner surface308, and a wall outer surface306may be shaped according to the shaped surface900shown inFIG.9.

The shaped surface900includes a plurality of ridges902-1. . .902-n(hereinafter referred to as “ridges902”) and furrows904-1. . .904-n(hereinafter referred to as “furrows904”). In including ridges902and furrows904, the surface area of the shaped surface900is increased over a surface area of a flat surface of a same size as the shaped surface900. In some embodiments, the shaped surface900has a surface area that is at least 1.2 times greater than if the shaped surface900was flat. In some embodiments, the shaped surface900has a surface area that is at least two times greater than if the shaped surface900was flat. In another embodiment, the shaped surface900has a surface area that is at least three times greater than if the shaped surface900was flat. The ridges902are shaped along the longitudinal length of the ridges902according to a planar sinusoidal pattern. Similarly, the furrows904are shaped along the longitudinal length of the furrows according to an inverse of a planar sinusoidal wave pattern of which the ridges902adjacent to the furrows904are shaped.

FIG.10is a planar view of a shaped surface1000with a plurality of protrusions according to a protrusion pattern. In various embodiments, protrusions included in the protrusion pattern of the shaped surface shown inFIG.10can include any combination of square shaped protrusions, trapezoid shaped protrusions, triangular shaped protrusions, sinusoidal shaped protrusions, and/or protrusions of any shape or pattern.

The protrusion pattern shown inFIG.10includes protrusion lines1002-1. . .1002-n(hereinafter referred to as “protrusion lines1002”), in which protrusions are formed to increase the surface area of the shaped surface1000. In the shaped surface shown inFIG.10, the protrusion lines1002are parallel to each other.

FIG.11is a planar view of a shaped surface1100with a plurality or protrusions according to another protrusion pattern. In various embodiments, protrusions included in the protrusion pattern of the shaped surface shown inFIG.11can include any combination of square shaped protrusions, trapezoid shaped protrusions, sinusoidal shaped protrusions, and/or protrusions of any shape or pattern.

The protrusion pattern shown inFIG.11includes protrusion columns1102-1. . .1102-n(hereinafter referred to as “protrusion columns1102”) and protrusion rows1104-1. . .1104-n(hereinafter referred to as “protrusion rows1104”). Protrusions are formed within the protrusion columns1102and the protrusion rows1104to increase the surface area of the shaped surface1100. The protrusion columns1102and the protrusion rows1104intersect to form an array of protrusions on the shaped surface1100.

FIG.12is a planar view of a shaped surface1200with a plurality or protrusions according to another protrusion pattern. In various embodiments, protrusions included in the protrusion pattern of the shaped surface shown inFIG.12can include any combination of square shaped protrusions, trapezoid shaped protrusions, sinusoidal shaped protrusions, and/or protrusions of any shape or pattern.

The protrusion pattern shown inFIG.12includes protrusion rings1202-1. . .1202-n(hereinafter referred to as “protrusion rings1202”) concentrically formed about a pattern center1204of the shaped surface1200. The pattern center1204can be a center of the base outer surface302or the center of a base inner surface304depending on which surface of the base is patterned according to the shaped surface1200shown inFIG.12. Protrusions are formed within the protrusion rings1202to increase the surface area of the shaped surface1200.

In various embodiments, different protrusion patterns (including, for example, the protrusion pattern shown inFIG.12) may include one or more different pattern centers, any of which may be different than the center of a bottom outer surface302and/or the center of a bottom inner surface304. For example, a bottom outer surface302may include any number of pattern centers located next to each other, each pattern center including its own center. Any number of shaped surfaces may be oriented in any manner. As a result, each pattern and/or combination of patterns of a shaped surface may be oriented around any number of pattern centers.

FIG.13is a planar view of a shaped surface1300with a plurality or protrusions according to another protrusion pattern. In various embodiments, protrusions included in the protrusion pattern of the shaped surface shown inFIG.13can include any combination of square shaped protrusions, trapezoid shaped protrusions, sinusoidal shaped protrusions, and/or protrusions of any shape or pattern.

The protrusion pattern shown inFIG.13includes protrusion radials1302-1. . .1302-n(hereinafter referred to as “protrusion radials1302”) formed to radiate out from a pattern center1304, center area, or other focal points or areas, of the shaped surface1300. The pattern center1304can be a center of the base outer surface302or the center of a base inner surface304depending on which surface of the base is patterned according to the shaped surface1300shown inFIG.13. Protrusions are formed within the protrusion radials1302to increase the surface area of the shaped surface1300. The protrusion radials1302have protrusion radial widths1306that can be constant along the length of the protrusion radials1302, or they can change along the length of the protrusion radials1302. For example, protrusion radial widths1306of the protrusion radials1302can increase along the length of the protrusion radials1302as the protrusion radials1302extend out from the pattern center1304.

In various embodiments, different protrusion patterns (including, for example, the protrusion pattern shown inFIG.13) may include different pattern centers any of which may be different than the center of a bottom outer surface302and/or the center of a bottom inner surface304. For example, a bottom outer surface302may include any number of pattern centers located next to each other, each pattern center including its own center.

FIG.14Ais a cross-sectional view of a shaped surface1400with protrusions1402shaped as a sinusoidal wave. In various embodiments, the protrusions1402shown inFIG.14Acan be arranged in the protrusion patterns shown inFIGS.10-13.

In being shaped as a sinusoidal wave, the protrusions1402have protrusion sides1404that curve upwards towards a protrusion plane1406. The protrusion plane1406is a plane formed across the tops (e.g., peaks) of the protrusions1402at a protrusion height1408of the protrusions1402. In the shaped surface1400shown inFIG.14A, the protrusions1402all have the same protrusion height1408. The protrusion cross-section of the protrusions1402exhibit reflection symmetry about a protrusion axis of symmetry1410normal to the protrusion plane1406.

FIG.14Bis a cross-sectional view of a shaped surface1450with protrusions1452shaped as a square wave. In various embodiments, the protrusions1452shown inFIG.14Bcan be arranged in the protrusion patterns shown inFIGS.10-13.

In being shaped as a square wave, the protrusions1452have protrusion sides1454that extend upwards towards a protrusion plane1456. The protrusion plane1456is a plane formed across the top portions (e.g., peaks) of the protrusions1452at a protrusion height1458of the protrusions1452. In the shaped surface1450shown inFIG.14B, the protrusions1452all have the same protrusion height1458.

The shaped portions (e.g., protrusions and/or indentations) may comprise any materials including, but not limited to, an alloy, a ceramic, a metal, or any combination of any materials. In some embodiments, shaped portions may include a sandwich structure of various layers of materials.

In various embodiments, any or all of the shaped portions may include the same material as all or a part of the base of a vessel. In some embodiments, any or all of the shaped portions are of a different material as all or a part of the base of a vessel.

FIGS.15A-Gdepict a variety of different protrusions and/or indentations that may be on the outer base of a vessel, inside the vessel, or on both the outer base and inside the vessel (e.g., base inner surface304and base outer surface302). In some embodiments, there may be any combination of one or more different shapes (e.g., one or more in any combination of protrusions and/or indentations). For example, a bottom of a vessel may include conical protrusions as well as conical or triangular indentations on the bottom of the vessel.

FIG.15Adepicts interlocking elbow shaped surfaces in some embodiments. In various embodiments, the interlocking elbow shaped surfaces may project outward forming at least one protrusion from the base of the kettle (i.e., toward the outside of the kettle). In various embodiments, the elbow shaped surfaces may project inward (forming at least one indentation) from the base of the kettle (i.e., toward the inside of the kettle). A kettle may include any combination of projections and indentations. It will be appreciated that any shape, form, size, or any combination of shapes, forms, and sizes may be used for protrusions and/or indentations.

FIG.15Bdepicts conical shaped protrusions in some embodiments.FIG.15Cdepicts conical shaped indentations in some embodiments.FIG.15Ddepicts triangular shaped protrusions in some embodiments.FIG.15Edepicts triangular shaped indentations in some embodiments.FIG.15Fdepicts dimple shaped indentations in some embodiments.FIG.15Gdepicts dimple shaped protrusions in some embodiments. InFIG.15B-G, the protrusions extend toward, and the indentations extend away from, the top of the page on which they are depicted.

Although the shaped protrusions and indentations inFIG.15B-Gappear to be the same shape, size, height, symmetry, or the like, they may be different for any number of the shaped protrusions and/or shaped indentations. Further, there may be any amount of space between the shaped protrusions and/or indentations. Moreover, although the protrusions and/or indentations appear to be right next to each other, the protrusions and/or indentations may be spaced in any way or in any pattern.

In various embodiments, fluid inside the vessel (e.g., the kettle100ofFIG.1) may undergo movement caused by convection. Convection may be characterized by movement within the fluid caused at least in part by the tendency of hotter and therefore less dense portions of the fluid (and/or material in the fluid) to rise while colder, denser portions of the fluid (and/or material in the fluid) move downward. Convection may be caused by non-uniform heating. Convection in a plane horizontal to a layer of fluid heated from one side (e.g., below) may be termed Rayleigh-Bénard convection.

In the prior art, kettles and other cooking vessels celebrate the feature of uniform heating. While uniform heating may keep a solid in a pan (e.g., a steak) from cooking unevenly, convection in a fluid may enhance heat transfer to a fluid contained in the vessel, thereby allowing fluids (e.g., water, liquid, substance, or liquid/solid mixtures) to heat more quickly. Further, the fluid motion due to convection may facilitate mixing of the fluid.

Convection may be caused (e.g., induced) in any number of ways. In some embodiments, there may be variations in the thickness of the base or walls of the vessel which may cause convection. For example, with regard toFIG.3, one section of a base portion may be thicker than another section of the base portion. Similarly, one section of a wall portion may be thicker than another section of the wall portion. In one example, a vessel may have a thicker base at the periphery and a thinner base at the center. In another example, the base portion may include a plurality of portions (e.g., a pattern) that are thicker than other portions of the base (e.g., a pattern of thicker portions in all or a section of the base portion). Similarly and/or in addition, the wall portion may include a plurality of portions (e.g., a pattern) that are thicker than other portions of the wall (e.g., a pattern of thicker portions in all or a section of the wall portion). The variations in thickness may create uneven heating such that may cause convection.

In various embodiments, the base portion may be thicker in some areas and thinner in others. For example, a vessel may have a thicker base at the periphery and a thinner base at the center (e.g., an inverted cone on the base outer surface302or the base inner surface304). It will be appreciated that, in some embodiments, the base portion may be thinner in some areas and thicker in others (e.g., a cone shape). Base portions in these configurations may contribute to convection.

In some embodiments, the thickness of the base portion may be consistent, but convection may be caused by including different materials within the base102and/or walls104of the vessel106. As discussed herein, the vessel106may, for example, include a core of one metal (e.g., aluminum) clad in stainless steel or other non-reactive metal(s) or alloy(s), and the base of the vessel may have sections of a core that are thicker than other portions (e.g., some portions of the core may be thicker aluminum or copper than other portions of the core). The variations in thickness of the core and variations in the amount of material with different thermal properties (discussed further herein) may create uneven heating such that convection may be induced.

There may be any number of different materials in the base and/or walls of the vessel that may cause convection. For example, different materials may be utilized that have different thermal properties. The different material can be included in some portions (i.e., not all) of the base (e.g., the base may include stripes, squares, chunks, bits or other portions of different materials with different thermal properties than the material which is included in the rest of the base) so as to induce convection. It will be appreciated that highly heat conductive materials may be included (e.g., copper or aluminum) and/or heat insulating materials can be included in the base or walls of the vessel.

For example, the sides and/or base of a vessel may include materials of different thermal characteristics (e.g., with different thermal diffusivities). In some embodiments, the sides and/or base of the vessel may include either exposed (e.g., on the base inner surface304of the vessel) or clad (e.g., within a core) strips of material that are different (e.g., the strips may be of aluminum and the rest of the base may be stainless steel). There may be any pattern of strips or materials of any shapes within (or on) the base inner surface304, base outer surface302, wall inner surface308, and/or wall outer surface306of the vessel. In another example, any or all of the shaped surfaces (seeFIGS.4,10, and11) may comprise different materials than all or parts of the base and/or walls of the vessel.

It will be appreciated that a vessel may include variations in thickness and/or different materials.

Differences in surface area at the base102and/or walls104of a vessel106between a thermal energy source and fluid (e.g., the base outer surface302of a vessel or a base inner surface304of the vessel106) may cause convection of fluid within the vessel106. As discussed herein the shaped portion of the wall outer surface306and/or the shaped portion of the wall inner surface308may include, for example, raised sinusoidal ridges, raised rectangular ridges, indented sinusoidal furrows, indented rectangular ridges, posts, raised portions, depressed portions, protrusions, indentations, or the like of any size or shape. The shaped portion may include raised portions of a surface, depressions in the surface, or a combination of raised portions and depressed portions (e.g., a combination of protrusions and indentations) of the surface. Examples include, but are not limited to, shaped portions with (e.g., substantially) increased surface area (in comparison with a flat surface). In various embodiments, only a portion or the entire wall outer surface306and/or at least a portion of the wall inner surface308includes a shaped portion.

As previously discussed, differences in surface area across the base102or walls104of a vessel106between a thermal energy source and fluid (e.g., the base outer surface302of a vessel106or a base inner surface304of the vessel106) may cause (e.g., induce) convection of fluid within the vessel106. For example, differences in surface area of ridges and/or furrows (e.g., changes in surface area of the protrusions and/or indentations) of the base outer surface302of a vessel106may cause heat transfer to be non-uniform, thereby causing convection (e.g., motion) of the fluid inside the vessel106as well as increases in heat transfer.

In various embodiments, differences in surface area of all or some of the base or walls of the vessel106may increase, by convection, the rate at which thermal energy is transferred to a substance (e.g., fluid) contained within the vessel106. The increased rate of thermal energy transfer may be substantially increased when compared to vessels in the prior art (e.g., with less surface area and/or uniform construction which do not induce convection). Further, the convection induced by the differences in surface area may further cause mixing of the substance within the vessel106.

FIG.16Ais a cross-sectional view of a shaped surface1600with rounded protrusions1602. In various embodiments, the protrusions1602shown inFIG.16Acan be arranged in the protrusion patterns shown inFIGS.10-13.

The rounded protrusions1602may be shaped as waves. The protrusions1602may have different amplitudes (e.g., heights) as depicted inFIG.16Aor may have heights in any pattern. In some embodiments, the protrusions1602have protrusion sides1604that are directed upwards towards protrusion planes1606-1616. The protrusion planes1606-1616are planes that are formed across the tops (e.g., peaks) of the protrusions1602.

In the shaped surface1600shown inFIG.16A, the protrusions1602have a pattern of protrusion heights that are higher at the periphery and shorter at the center. It will be appreciated that the protrusion heights may be random or may be of any pattern. For example, protrusion heights may be shorter at the periphery and higher at the center. In another example, each protrusion may be higher or shorter than an adjacent protrusion (e.g., taller protrusions may be next to shorter protrusions).

It will also be appreciated that there may be any number of patterned shapes on each vessel (e.g., on the outer surface302or the base inner surface304). For example, there may be any number of circular patterns of protrusions on the base of a vessel. For example, each circular pattern may include protrusions like those depicted inFIG.16A(e.g., shorter at the center and higher at the periphery of each circular pattern). As similarly discussed, the circular pattern of protrusions may be higher in the center and lower at the periphery of each circular pattern. A circular pattern may be asymmetric. In some embodiments, circular patterns across the base of a vessel may have different protrusions, different patterns, different size, and/or different shape. Similarly, there may be a combination of circular, rectangular, and/or square patterns (or patterns of any shape) on the base outer surface302or the base inner surface304.

FIG.16Bis a cross-sectional view of a shaped surface1650with protrusions1652shaped as a square wave. In various embodiments, the protrusions1652shown inFIG.16Bcan be arranged in the protrusion patterns shown inFIGS.10-13.

In being shaped as a square wave, the protrusions1652have protrusion sides1654that extend upwards towards one of protrusion planes1656,1658,1660,1662,1664, and1666. The protrusion planes1656-1666are planes that are formed across the top portions (e.g., peaks) of the protrusions1652.

As similarly discussed regarding the shaped surface1600shown inFIG.16A, the protrusions1652have a pattern of protrusion heights that are higher at the periphery and shorter at the center. It will be appreciated that the protrusion heights may be random or may be of any pattern. For example, protrusion heights may be shorter at the periphery and higher at the center. In another example, each protrusion may be higher or shorter than an adjacent protrusion (e.g., taller protrusions may be next to shorter protrusions).

It will be appreciated that the variety of different protrusions and/or indentations depicted inFIGS.15A-Gmay have sections of protrusions and/or indentations with different surface area than other sections of protrusions and/or indentations. Differences in surface area and/or materials (e.g., with different thermal diffusion properties) may promote non-uniform heating and induce convection. The variety of different protrusions and/or indentations depicted inFIGS.15A-Gmay be on the outer base of a vessel, on the inner base of a vessel, on the inner wall of a vessel, and/or on the outer wall of a vessel. In various embodiments, the variety of different protrusions and/or indentations depicted inFIGS.15A-Gmay be on the base inner surface304and the base outer surface302). In some embodiments, there may be any combination of one or more different shapes (e.g., one or more in any combination of protrusions and/or indentations). For example, a bottom of a vessel may include conical protrusions as well as conical or triangular indentations in the bottom of the vessel.

It will also be appreciated that there may be multiple patterned shapes on the inside and/or the outside of the vessel. For example, there may be any number of square or circular patterns of protrusions on the base outer surface302or the base inner surface304. For example, each circular pattern may include protrusions like those depicted inFIG.16B(e.g., shorter at the center and higher at the periphery of each circular pattern). As similarly discussed, the circular pattern of protrusions may be higher in the center and lower at the periphery of each circular pattern. A circular pattern may be asymmetric. In some embodiments, circular patterns across the base of a vessel may have different protrusions, different patterns, and/or be of any size and/or shape. Similarly, there may be a combination of circular, rectangular, and/or square patterns (or patterns, sizes, or any shape) on the base of the outer surface302or the base inner surface304.

In various embodiments, the shaped portion of the base outer surface302, base inner surface304, wall outer surface306, and/or wall inner surface308is shaped to have 1.2 or more times (e.g., 1.5 times or more, 2 times or more, 3 times or more, or the like) the surface area than its corresponding flat surface. Further, sections of the base portion(s) may have different surface area(s) than other sections of the base portion(s), thereby further inducing convection.

In various embodiments, the shaped portions may comprise different materials that induce and/or further contribute to non-uniform heating and convection. The shaped portions (e.g., protrusions and/or indentations) may comprise any material or the like including, but not limited to an alloy, a ceramic, a metal, or any combination of any materials. In some embodiments, shaped portions may include a sandwich structure of various layers of materials. In various embodiments, any or all of the shaped portions are of the same material as all or a part of the base of a vessel. In some embodiments, any or all of the shaped portions are of a different material as all or a part of the base of a vessel.

In various embodiments, the vessel may include a mechanical mixer which may mix fluids in the vessel and force convection. For example, there may be one or more mixers (e.g., a blade or a propeller driven by a motor with a power source such as a battery) attached to the base, top, receiving aperture, or walls inside the vessel.

FIG.17is a planar view of a shaped surface1700with a plurality of protrusions according to another protrusion pattern. The protrusions included in the protrusion pattern of the shaped surface shown inFIG.17may include different protrusions with different surface areas. Further, the protrusions may comprise different material(s) from each other and/or the base of the vessel.

In various embodiments, protrusions included in the protrusion pattern of the shaped surface shown inFIG.17can include any combination of square shaped protrusions, trapezoid shaped protrusions, and sinusoidal shaped protrusions. Each square shaped protrusion, trapezoid shape protrusion, and sinusoidal shaped protrusion included in the shaped surface shown inFIG.17can be formed around a central protrusion axis for each protrusion.

The protrusion pattern shown inFIG.17includes protrusion radials1702-1. . .1702-n(hereinafter referred to as “protrusion radials1702”) formed to radiate out from a pattern center1704along central spines to create a star pattern of the shaped surface1700. The pattern center1704can be a center of the base outer surface, or the center of a base inner surface, depending on which surface of the base is patterned according to the shaped surface1700shown inFIG.1700. Protrusions are formed within the protrusion radials1702to increase the surface area and/or provide differences in surface area of the shaped surface1700. The protrusion radials1702have protrusion radial widths1706that can be constant across the length of the protrusion radials1702or can change along the length of the protrusion radials1702. For example, protrusion radial widths1706of the protrusion radials1702can increase along the length of the protrusion radials1702as the protrusion radials1702extend out from the pattern center1704.

It will be appreciated that the bottom outer surface302of the kettle and/or an inside surface (e.g., bottom inner surface304) may include any shape of ridges, furrows, protrusions, indentations, and/or the like in any pattern that increases (e.g., substantially) surface area. If there is a substantial increase in surface area between the outside bottom surface of the kettle and a thermal source, the kettle may absorb heat at a substantially higher rate. If there is a substantial increase in surface area between the inside bottom surface of the kettle and a liquid in the kettle, then the kettle may transfer heat from the kettle to an enclosed substance or liquid at a substantially higher rate.

Changes in surface area may also induce convection. As a result, the transfer of, or the rate of transfer of, heat from the vessel to an enclosed substance or liquid may occur at a substantially higher rate. Further, the induced convection may mix the substance or liquid, and may lead to more rapid heating of a substance or liquid contained in the vessel.

As a fluid within the vessel heats, convection currents can form, and temperature-dependent physical properties (e.g., density, surface tension, and kinematic viscosity) can induce convection currents having characteristic patterns (e.g., 2-dimensional rolls or hexagonal cells). These convection currents induce mixing, and lead to more rapid heating of a fluid contained in the vessel.

It will be appreciated that a horizontal layer of convecting fluid may exhibit self-organizing (e.g. pattern-forming) properties. For example, depending on the fluid and non-uniform heating, toroidal vortices may result (e.g., because of the instability of differentially rotating fluid and convection rolls).

In various embodiments, convection of fluid within the vessel may generate convective flow structures within the fluid. A flow structure may depend, for example, upon surface tension of the fluid, nature of heat transfer, variations in non-uniform heating, protrusions and/or indentations or indentations on the base and or walls of the vessel, and shape of the vessel. In one example, flow patterns may include polygonal (e.g., hexagonal) cells with upflow at the center of each cell and downflow at the periphery. The pattern, for example, may resemble a honeycomb pattern of individual cells. In some embodiments, convection can lead to a variety of flow patterns, all of which lead to higher overall heat transfer, or a higher rate of heat transfer, to the fluid as a result of fluid motion and possible mixing.

It will be appreciated that convection patterns of quasi-two-dimensional rolls or three-dimensional cells may appear in the fluid. The structure of thermogravitational (buoyancy-driven) convection may differ from thermocapillary (surface tension-driven) convection.

The configuration of a cell in projection onto a plane (e.g., x and y coordinate plane) is called the cell planform.FIG.18Ais a planform schematic diagram of two-dimensional rolls of convection cells. Since the wavevector is oriented in the x-direction, such rolls (parallel to the y-axis) may be identified as “x-rolls.” In the vicinity of the interface between two such rolls, the fluid may circulate in the x,y plane in opposite directions.

FIG.18Bis a planform schematic diagram of hexagonal L- and G-cells. This system may be a superposition of three roll sets with wavevectors having the same modulus and directed at an angel of 2π/3 to each other. A hexagonal cell may be identified as an L- or G-cell depending on the sign of the velocity (e.g., on whether the fluid ascends or descends in the central part of the cell). It will be appreciated that very small alterations in the physical conditions, or small variations in the physical properties of the fluid, can result in radical changes in the structure of convection patterns.

Although G-cell formations may be more common in observed gases and L-cells may be more common in observed liquids, all or portions of the fluid in the vessel106may include one or more L-cells and/or G-cells. Direction and circulation may depend upon the derivatives of viscosity or density with temperature. It will be appreciated that ascending fluid in a convection cell may be warmer than the descending fluid. As a result, the central part of the L-cell may be less viscous or less dense for liquids and the peripheral part of a G-cell may be less viscous or less dense for gases.

There may be transitions of patterns in a fluid of the vessel106. For example, all or a portion of the fluid may start in a motionless state and transition to a pattern of hexagonal cells. All or part of the fluid may transition from a pattern of hexagonal cells to a pattern of rolls. Any or all transitions may be related to the density and/or the viscosity of all or a portion of the liquid and/or temperature (e.g., depending on heat transfer).

FIG.19is a two-armed spiral in a fluid that rotates clockwise in some embodiments. It will be appreciated that variation(s) of one or more characteristics of the fluid with temperature may play a role in fluid rotation or convection, such as the variation of density and/or viscosity with temperature. Dependencies may be based on kinematic viscosity, thermal conductivity, and/or heat at constant pressure. Transitions (e.g., to the two-armed spiral or the like) may begin closer to the walls of the vessel and subsequently involve regions closer to the center. For example, a roll pattern may be ordered into a left- or right-handed spiral with the number of arms varying from run to run. The outer part of such a pattern may comprise concentric circular rolls. Each arm of the spiral may terminate in a pattern defect called a dislocation and, as a result, the spiral may be mismatched with outer rings (see dislocations1902and1904inFIG.9). The direction of spiral rotation may be the result of waves propagating from the spiral core (e.g., from the center of the vessel106). The formation of a “global” spiral pattern fitting into container geometry may be an effect of a small horizontal temperature gradient near the wall of the vessel (e.g., producing sidewall forcing).

It will be appreciated that if the fluid layer has an appreciable asymmetry of the physical condition with respect to the midplane (e.g., z=½ or an up-down asymmetry), then three-dimensional cells may form. If, however, the layer is symmetric, then two-dimensional rolls may arise. A transition from some roll set to a mirror reflection about the midplane may be equivalent to a uniform translation of the entire pattern in the direction of a vector. Three-dimensional cells may not share this property. It is therefore not surprising that rolls may be typical for the case where the top and bottom part of a layer are indistinguishable. Alternately, the existence of hexagonal L- and G-cells is compatible with the presence of non-uniformity of viscosity (e.g., the direction of circulating may be such that the viscosity is minimum in the region of the highest strain rates which may be in the central part of a cell).

It will be appreciated that there may be no convection pattern, that convection patterns appear or disappear over time, and/or convection patterns change based on changes in heat transfer, variations or fluctuations in localized temperatures, and fluid characteristics.

FIG.20AandFIG.20Bare roll patterns with boundaries of the rolls depicted by dotted and solid lines.FIG.20Adepicts texture in a rectangular container (the neighborhoods of the short container walls are not visible).FIG.20Bdepicts a schematic image of a texture in a circular container (dashed lines indicate the main features of the structure of the large scale flow). As depicted inFIGS.20Aand B, there may be a tendency of rolls to approach the sidewalls at a right angle.

In various embodiments, if there are no complicating factors, roll flows may represent a basic form of steady-state convection. It will be appreciated that rolls are typically not quite straight and the roll flow may not be strictly two-dimensional. This may be due, at least in part, because the flow involves only a portion of a layer and the presence of sidewalls may considerably affect the flow of the fluid and its structure.

It will be appreciated that flows within a fluid may be affected by: 1) situations where the sidewall thermal regime dictates a certain character of flows in the region near the wall; and/or 2) non-uniformities (however insignificant) of heating from below and/or cooling from above.

FIG.21A-Cdepict roll patterns in a circular container.FIG.21Adepicts concentric rolls formed with stronger forcing. In some embodiments, the wall that exerts stronger forcing may create an axisymmetric system of rolls (seeFIG.21A). The effect of the less forcing wall may also be sufficient for axisymmetric convection but may not be strong enough for circular rolls next to the wall to be stable. Cross-roll instability may occur, resulting in development of a secondary flow in the form of short roll segments directed along container radii and abutting against the wall. These cross rolls may occupy an annular region of width as seen inFIG.21B.FIG.21Bdepicts concentric rolls formed with weaker forcing and superposed by short crossed rolls near the wall.

FIG.21Cdepicts straight rolls formed from a disordered pattern. In some embodiments, it may be possible to obtain a set of almost straight rolls even if the wall with stronger forcing is used. If fluid pattern motions are sufficiently vigorous (developing initially little ordered flow), formed rolls that are weakly curved may appear; and in those near-wall regions, the rolls may make small angles with the wall thereby creating short cross rolls.

FIG.22depicts eccentric annular rolls in a cylindrical vessel106in some embodiments. Axisymmetric roll patterns may be susceptible to a particular instability which may manifest itself more appreciably as the Rayleigh number increases.

It will be appreciated that the use of shapes or surfaces within or on the base and/or walls of the vessel may promote bubble nucleation for the onset of more rapid boiling. Square edges such as those depicted inFIGS.7B,8, and14Bmay assist as nucleation points. Barbs, points, and/or roughened surfaces on the inner base or inner walls of the vessel may also be utilized as nucleation points. Bubble nucleation may also contribute to, or induce, convection in the contained fluid.

The present invention is described above with reference to exemplary embodiments. It will be appreciated that various modifications may be made and other embodiments can be used without departing from the broader scope of the present invention. Therefore, these and other variations upon the exemplary embodiments are intended to be covered by the present invention.