Abstract:
An article of manufacture including a wall portion having a wall inner surface and a wall outer surface. The article of manufacture also includes a base portion having a base inner surface and a base outer surface. At least a portion of the wall portion and the base portion form a vessel to retain a fluid therein. At least one of a shaped portion of the base outer surface is shaped to have substantially more surface area in thermal contact with a heating source than a flat base outer surface so as to allow the retained fluid to receive additional heat from the heating source, or, a shaped portion of the base inner surface is shaped to have substantially more surface area in thermal contact with the substance than a flat base inner surface so as to transfer additional heat from the heat source to the retained fluid.

Description:
BACKGROUND 
       [0001]    Vessels are used to contain substances such as fluids. A vessel is any hollow container including, for example, a container manufactured to hold a fluid (e.g., water, liquid, substance, or liquid/solid mixtures) and to facilitate the transfer of thermal energy to the substance (e.g., fluid) contained within. Examples of such vessels include pots, kettles, and the like. 
         [0002]    Such vessels in the prior art such as pans or skillets typically include a flat bottom or a bottom that is indented around a perimeter of the bottom. Even with such an indentation, the bottom of such vessels is primarily flat. The bottom of the vessel is generally set against a heat source (e.g., flame or heating element). The heat source transfers thermal energy through the flat bottom of the vessel and into the fluid therein. There may be design elements or reinforcement elements on the vessel or the bottom of the vessel. 
         [0003]    Essentially, the same vessel has been used worldwide. Differences in vessels of the same type are generally cosmetic, based on durability, based on ergonomics, or different choices of fabrication material. 
       SUMMARY 
       [0004]    An article of manufacture configured to transfer thermal energy to a contained substance such as a liquid or liquid/solid mixture. In some embodiments, the article of manufacture includes a wall portion having a wall inner surface and a wall outer surface; a base portion having a base inner surface and a base outer surface, at least a portion of the wall portion and the base portion forming a vessel to retain fluid therein, at least a heating surface portion of the base outer surface positioned to receive heat from a heating source, and at least one of: a shaped portion of the base outer surface being shaped to have substantially more surface area in thermal contact with the heating source than a flat base outer surface to receive additional heat from the heating source, or a shaped portion of the base inner surface shaped to have substantially more surface area in thermal contact with the fluid than a flat base inner surface to transfer additional heat from the heat source to the fluid. 
         [0005]    In some embodiments, a shaped surface is corrugated to include a plurality of ridges and furrows. In some embodiments the ridges and furrows are shaped as a sinusoidal wave. In some embodiments, the ridges and furrows are shaped as a square wave. The ridges and furrows causing a surface area of the shaped surface to be substantially increased. 
         [0006]    In some embodiments, a shaped surface includes a plurality of protrusions and/or indentations. In some embodiments the protrusions are shaped and positioned as a sinusoidal wave. In some embodiments the plurality of protrusions are shaped and positioned as a square wave. The protrusions may cause a surface area of the shaped surface to be substantially increased. 
         [0007]    In various embodiments, the shaped portion of the base outer surface is shaped to have 1.2 or more times the surface area than the flat base outer surface. The shaped portion of the base inner surface may be shaped to have 1.2 or more times the surface area than the flat base inner surface. 
         [0008]    These and other advantages will become apparent to those skilled in the relevant art upon a reading of the following descriptions and a study of the several examples shown in the drawings. The drawings are included for illustrative purposes and are not intended to limit possible or potential shapes, patterns, or locations of protrusions and/or indentations. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]      FIG. 1  depicts a perspective view of an example of a kettle for transferring thermal energy to a contained substance. 
           [0010]      FIG. 2A  is a planar view of an example kettle bottom surface with a cavity defined between an edge of the base of the kettle and a thick metal encapsulated base in the prior art. 
           [0011]      FIG. 2B  is a cross section view of an example kettle bottom surface with a cavity defined between an edge of the base of the kettle and a thick metal encapsulated base in the prior art. 
           [0012]      FIG. 2C  includes dimensions for the cross section view of  FIG. 2B . 
           [0013]      FIG. 3  is a cross sectional view of a vessel (e.g., a portion of the kettle) in some embodiments. 
           [0014]      FIG. 4  is a planar view of an example shaped surface that is corrugated according to an example pattern. 
           [0015]      FIG. 5  is a planar view of an example shaped surface that is corrugated according to another example pattern. 
           [0016]      FIG. 6  is a planar view of an example shaped surface that is corrugated according to another example pattern. 
           [0017]      FIG. 7A  is a cross-sectional view of a shaped surface that includes ridges and furrows shaped according to a sinusoidal wave. 
           [0018]      FIG. 7B  is a cross-sectional view of a shaped surface that is corrugated with ridges and furrows shaped according to a square wave. 
           [0019]      FIG. 8  is a planar view of a shaped surface that is corrugated according to another example pattern. 
           [0020]      FIG. 9  is a planar view of a shaped surface that is corrugated according to another example pattern. 
           [0021]      FIG. 10  is a planar view of a shaped surface with a plurality of protrusions according to a protrusion pattern. 
           [0022]      FIG. 11  is a planar view of a shaped surface with a plurality or protrusions according to another protrusion pattern. 
           [0023]      FIG. 12  is a planar view of a shaped surface with a plurality or protrusions according to another protrusion pattern. 
           [0024]      FIG. 13  is a planar view of a shaped surface with a plurality or protrusions according to another protrusion pattern. 
           [0025]      FIG. 14A  is a cross-sectional view of a shaped surface with protrusions shaped as a sinusoidal wave. 
           [0026]      FIG. 14B  is a cross-sectional view of a shaped surface with protrusions shaped as a square wave. 
           [0027]      FIG. 15A  depicts interlocking elbow shaped surfaces in some embodiments. 
           [0028]      FIG. 15B  depicts conical shaped surfaces in some embodiments. 
           [0029]      FIG. 15C  depicts conical shaped indentations in some embodiments. 
           [0030]      FIG. 15D  depicts triangular shaped surfaces in some embodiments. 
           [0031]      FIG. 15E  depicts triangular shaped indentations in some embodiments. 
           [0032]      FIG. 15F  depicts dimple shaped indentation in some embodiments. 
           [0033]      FIG. 15G  depicts dimple shaped surfaces in some embodiments. 
       
    
    
     DETAILED DESCRIPTION 
       [0034]      FIG. 1  depicts a perspective view of an example of a kettle  100  for transferring thermal energy to a contained fluid such as water, a liquid, a substance, or a liquid/solid mixture (e.g., soup). While the kettle  100  is 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. For example, a surface area of a cooking implement may be substantially increased thereby allowing for thermal energy to be absorbed and/or transferred at a substantially increased rate. 
         [0035]    The kettle  100  includes a base portion  102  and a wall portion  104 . The base portion  102  and the wall portion  104  may 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 the base portion  102  to the wall portion  104 . The base portion  102  and the wall portion  104  may 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 kettle  100  to the inside of the kettle  100 . 
         [0036]    The kettle  100  may comprise any kind of material. For example, the base portion  102  and/or the wall portion  104  may comprise material such as, but not limited to, steel, copper, ceramic(s), and/or the like. The base portion  102  and/or the wall portion  104  may comprise an alloy or any combination of materials. In some embodiments, the base portion  102  and the wall portion  104  may include a sandwich structure of various layers of materials. For example, the base portion  102  and/or the wall portion  104  may be clad and include a layer of copper, aluminum, or other metal(s) sandwiched between layers of steel. 
         [0037]    The base portion  102  and the wall portion  104  may combine to create a vessel  106  that functions to contain a volume of a substance. In various embodiments, the kettle  100  may be referred to as a vessel or, in some embodiments, the kettle may comprise a vessel. The vessel  106  is a portion of the kettle  100  that may contain or hold the substance. In various embodiments, the kettle  100  receives heat from an external heat source and transfers heat through the base  102  to the contained substance. 
         [0038]    In various embodiments, the base portion  102 , and potentially, the wall portion  104  are in thermal contact with the substance (e.g., fluid) contained within the kettle  100 . In some embodiments, the thermal contact enables thermal energy to transfer from or through the base portion  102  and/or the wall portion  104  to the contained substance (e.g., held by the container  106 ). For example, the substance is in thermal contact with the base portion  102  because the substance within the kettle  100  is in physical contact with the base portion  102  and/or wall portion  104 . In transferring thermal energy to the contained substance, the base portion  102  and/or the wall portion  104  may, 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, or induction heating). Further in transferring thermal energy to a contained substance, the base portion  102  and/or the wall portion  104  can transfer energy absorbed from the thermal energy source to the contained substance. Those skilled in the art will appreciate that the thermal energy source may be external to the kettle  100  (e.g., a stove or fire) or be internal to the kettle  100  (e.g., an electric kettle  100  or any other electric container). 
         [0039]    In an example of operation, the base portion  102  and/or the wall portion  104  may absorb thermal energy from many different types of thermal energy sources. In various embodiments, the base portion  102  and/or wall portion  104  may receive thermal energy from, but not limited to, conduction, convection, induction, or radiation heating. Additionally, the base portion  102  and/or the wall portion  104  can transfer absorbed thermal energy to the contained substance and/or facilitate convection in the contained substance. 
         [0040]    The kettle  100  includes a receiving aperture  108 . The receiving aperture  108  is an opening through which the substance (e.g., fluid) may be passed out of and/or into the vessel  106 . In some embodiments, once the substance is contained within the vessel  106 , thermal energy can be transferred from the external heating source, through the base portion  102  and/or the wall portion  104 . 
         [0041]    The kettle  100  includes a dispensing aperture  110 . The dispensing aperture  110  is an opening through which the substance may be passed out from the vessel  106 . The dispensing aperture  110  may be shaped to allow for the pouring of the substance. In some embodiments, the dispensing aperture  110  passes heated fluid after a desired amount of thermal energy is transferred to the fluid. For example, the dispensing aperture  110  may be used to pass a contained liquid out of the vessel  106  after enough thermal energy is transferred to the liquid contained within the vessel  106  to cause the liquid to boil. 
         [0042]      FIG. 2A  is a planar view of an example kettle bottom surface with a cavity defined between an edge  208  of the base of the kettle and a thick metal encapsulated base  202  in 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 base  202  is flat and is a major portion (e.g., a predominant portion) of the bottom of the kettle. An encapsulated base edge  204  and edge  208  of the kettle may define a cavity  206  along the rim of the base of the kettle. A diameter  210  is a diameter of the base of the kettle. 
         [0043]    The edge  208  may allow for the thick metal encapsulated base  202  to be coupled to the bottom of the kettle. The edge  208  and cavity  206  may also 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. 
         [0044]      FIG. 2B  is a cross section view of an example kettle bottom surface with a cavity  206  defined between an edge  208  of the kettle and a thick metal encapsulated base  202  in the prior art. In this cross-sectional view, the cavity  206  is shown between the edge of the kettle  208  and the encapsulated base  202 . 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. 
         [0045]      FIG. 2C  includes dimensions for the cross section view of  FIG. 2B . Here, dimension “d 1 ” represents the diameter of the thick metal encapsulated base  202 . Dimension “d 2 ” represents the diameter of the base of the kettle (e.g., diameter  210 ). Dimension “h” represents the distance that the thick metal encapsulated base  202  extends perpendicularly from the base of the periphery of the kettle. Given these dimensions, the increase in surface area for the kettle bottom surface in  FIG. 2C  relative to a kettle with a flat bottom surface is: 
         [0000]      Δarea=(area of this example kettle bottom surface)−(area if the kettle bottom surface was flat)
 
         [0000]    With the dimensions shown in  FIG. 2C : 
         [0000]    
       
         
           
             
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         [0000]    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: 
         [0000]      (100%)(Δarea)/(area if the kettle bottom surface was flat)
 
         [0000]    For example, using the dimensions as labeled in  FIG. 2C , a kettle with approximate dimensions of d 1 =7 inch, d 2 =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) 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. 
         [0046]      FIG. 3  is a cross sectional view of a vessel  106  (e.g., a portion of the kettle  100 ) in some embodiments. The vessel  106  is formed by a base portion  102  and a wall portion  104 . The base portion  102  includes a base outer surface  302  and a base inner surface  304 . The base outer surface  302  is the surface opposite of the base inner surface  304 . 
         [0047]    In various embodiments, the base outer surface  302  is the surface of the base portion  102  through which thermal energy is received from the thermal energy source. The base outer surface  302  may include a heating surface portion that receives and absorbs heat from the thermal energy source. The base inner surface  304  is the surface of the base portion  102  through which absorbed thermal energy may be transferred to the contained substance (e.g., a fluid contained or held within the vessel  106 ). Thus, the base portion  102  may be thermally coupled to the substance contained within the vessel  106  through the base inner surface  304 . In various embodiments, the base inner surface  304  may physically contact at least some of the substance contained within the vessel  106 , and thereby be thermally coupled to the substance contained within the vessel  106 . 
         [0048]    In some embodiments, at least one of the base outer surface  302  and/or the base inner surface  304  includes a shaped portion. A shaped portion of the base outer surface  302  or the base inner surface  304  is shaped such that there is substantially more surface area when compared to a flat surface. A shaped portion of the base outer surface  302  may 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. The shaped portion may include raised portions of a surface, depressed portions in the surface, or a combination of raised portions and depressed portions of the surface. Substantially more surface area may, for example, include double 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 surface  302  and/or the base inner surface  304  includes shaped portions. 
         [0049]    The wall portion  104  includes a wall outer surface  306  and a wall inner surface  308 . The wall outer surface  306  is opposite the wall inner surface  308 . In some embodiments, all or a portion of the wall outer surface  306  may receive thermal energy from the thermal energy source. A portion of the wall inner surface  308  may transfer thermal energy from the wall outer surface  306  to the contained fluid. Thus, a portion of the wall portion  104  may be thermally coupled to the contained fluid. In various embodiments, the wall inner surface  308  may physically contact the fluid contained within the vessel  106 . 
         [0050]    In some embodiments, at least a portion of the wall outer surface  306  and/or at least a portion of the wall inner surface  308  include a shaped portion. A shaped portion of the wall outer surface  306  or the wall inner surface  308  is shaped such that the shaped portion has substantially more surface area than if the shaped portion of the corresponding wall outer surface  306  or wall inner surface  308  was flat. 
         [0051]    The shaped portion of the wall outer surface  306  and/or the shaped portion of the wall inner surface  308  may 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 indentions) 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 surface  306  and/or at least a portion of the wall inner surface  308  includes a shaped portion. 
         [0052]    A base outer surface  302  and/or a wall outer surface  306  with 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 vessel  106  (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 surface  308  and/or base inner surface  304 ). Increasing the surface area of the base inner surface  304  of the base portion  102 , and/or the wall inner surface  308  (e.g., with protrusions, ridges, fins, furrows, indentations, and/or the like) increases the surface area of contact between a contained substance in the vessel  106  and at least a portion of the base inner surface  304  and/or at least a portion of the wall inner surface  308 . Due to the (e.g., substantially) increased surface area between the substance and the base inner surface  304  and/or the wall inner surface  308 , the rate of heat transfer from heat absorbed by the vessel  106  (e.g., from a heat source via the base outer surface  302 ) may be (e.g., substantially) increased. 
         [0053]    Similarly, increasing the surface area of the base outer surface  302  of the base portion  102 , and/or the wall outer surface  306  (e.g., with protrusions, ridges, fins, indentions, 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 surface  302  of the base portion  102 , and/or the wall outer surface  306 . Due to the (e.g., substantially) increased surface area between the thermal energy of the heat source and the base outer surface  302  and/or the wall outer surface  306 , the rate of heat transfer from the thermal energy source to the vessel  106  (e.g., from the heat source) may be (e.g., substantially) increased. 
         [0054]    Increasing the amount of thermal energy that is absorbed by at least a portion of the base portion  102  and/or at least a portion of the wall portion  104  may increase the thermal difference between the base portion  102  and/or the wall portion  104  and a substance contained within the vessel  106 . Increasing the thermal difference between at least a portion of the base portion  102  and/or at least a portion of the wall portion and a substance contained within the vessel  106  may lead to an increased rate at which thermal energy is transferred from the base portion  102  and/or the wall portion  104  to the substance. As a result of increasing the rate at which thermal energy is transferred from the base portion  102  and/or the wall portion  104  to the substance contained within the vessel  106 , 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 increased surface area(s) of the base potion  102  and wall portion  104 . 
         [0055]    In some embodiments, in configuring a portion of a base inner surface  304  and/or a wall inner surface  308  to 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 vessel  106 . Increasing the surface area of the base inner surface  304  and/or the wall inner surface  308  may increase the amount of surface area that is in thermal contact with a substance contained within the vessel  106 . As a result of increasing the amount of surface area that is in thermal contact with a substance contained within the vessel  106  and/or the heat source, an increased amount of thermal energy may be absorbed by, or otherwise transferred to, the substance. 
         [0056]    Although  FIGS. 4-14  depict patterns of protrusions and indentions (e.g., ridges and furrows), the pattern of protrusions and indentions 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 indentions) to increase surface area. In one example, the random assortment increases the surface area by at least 1.2 times over the surface area of a flat surface. All or a part of a surface (e.g., base outer surface  302 , base inner surface  304 , wall outer surface  306 , or wall inner surface  308 ) may comprise patterns, random assortments, or a combination of patterns and random assortment of shapes. 
         [0057]    Further, although  FIGS. 4-14  depict patterns of protrusions and indentions, the protrusions and/or indentions (e.g., ridges, furrows, corrugations, or the like) may include any number of geometric shapes or forms. Width, depth, and/or other defining measurement(s) of protrusions and/or indentions may vary over its trajectory and/or may vary with respect to other protrusions and/or indentions that are formed on the inner or outer surfaces of the kettle  106 . 
         [0058]      FIG. 4  is a planar view of an example shaped surface  400  that is corrugated according to an example pattern. In various embodiments, all or a portion of the base inner surface  304 , the base outer surface  302 , the wall inner surface  308 , an/or the wall outer surface  306 , may be shaped according to at least a portion of the shaped surface  400  shown in  FIG. 4 . 
         [0059]    The shaped surface  400  includes a plurality of ridges  402 - 1  . . .  402 - n  (hereinafter referred to as “ridges  402 ”) and furrows  404 - 1  . . .  404 - n  (hereinafter referred to as “furrows  404 ”). By including ridges  402  and furrows  404 , the surface area of the shaped surface  400  is increased over a surface area of a flat surface of the same size as the shaped surface  400 . 
         [0060]    One or more of the ridges  402  may include portions that extend from the surface and one or more of the furrows  404  may be the lowest portion (e.g., at the bottom or in the surface such as an indentation) of the shaped surface  400 . In some embodiments, the shaped surface  400  has a surface area that is at least two times greater than if the shaped surface  400  was flat. In some embodiments, the shaped surface  400  has a surface area that is at least three times greater than if the bottom of the kettle  100  was flat. In another example, the shaped surface  400  has a surface area that is at least 1.2 times greater or more than if the bottom of the kettle was flat. In some embodiments, the ridges  402  and the furrows  404 , in the example pattern shown in  FIG. 4 , are parallel to each other. In various embodiments, all or some of the ridges  402  and the furrows  404  may, or may not, be parallel to each other. 
         [0061]    In some embodiments, adjacent ridges  402  and furrows  404  are shaped as a sinusoidal wave. In being shaped as a sinusoidal wave, ridge sides of the ridges  402  are curved towards ridge top planes at the top of the ridges  402 . The ridge top plane is a hypothetical flat surface which contains the top of each ridge  402 . For example, the ridge top plane may be a tangential plane containing the peak (e.g., highest amplitude value) point of all, some, or most ridges  402 . In some embodiments, the period, amplitude, phase angle, and/or symmetry of different portions of any number of sinusoidal waves may vary. 
         [0062]    Additionally, in being shaped as a sinusoidal wave, furrow sides of the furrows  404  are curved towards furrow top planes at the bottom of the furrows  404 . The furrow top plane is a hypothetical flat surface which contains the bottom of each furrow  404 . For example, the furrow top plane may be a tangential plane containing the trough (e.g., lowest amplitude value) point of all, some, or most furrows  404 . 
         [0063]    In some embodiments, adjacent ridges  402  and furrows  404  are shaped as a square wave. In being shaped as a square wave, the top portion of each of the ridges  402  (e.g., highest amplitude value) may be in a tangential plane (e.g., a ridge top plane). Similarly, bottom portions of each of the furrows  404  (e.g., lowest amplitude value) may be in a tangential plane (e.g., a furrow top plane). In various embodiments, symmetry of any or all of the square waves may vary. 
         [0064]    In various embodiments, regardless if the shaped portion is sinusoidal, is rectangular wave shaped, includes posts, includes indentions, and/or the like, one, some, or all of the shaped portions (e.g., ridges  402 ) 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., furrows  404 ) 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 all or a portion of any or all of the posts and/or indentations may vary. 
         [0065]    Although  FIG. 4  depicts eighteen (18) parallel shaped portions  400 , there may be any number of shaped portions that may be parallel, partially parallel, or not parallel. Those skilled in the art will appreciate that there may be any number of shaped portions  400  (including high portions and low portions of any shape or combination of shapes). 
         [0066]      FIG. 5  is a planar view of an example shaped surface  500  that 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 surface  500  shown in  FIG. 5 . 
         [0067]    The shaped surface  500  includes a plurality of ridges  502 - 1  . . .  502 - n  (hereinafter referred to as “ridges  502 ”) and furrows  504 - 1  . . .  504 - n  (hereinafter referred to as “furrows  504 ”). In including ridges  502  and furrows  504 , the surface area of the shaped surface  500  is increased over a surface area of a flat surface of the same size as the shaped surface  500 . In some embodiments, the shaped surface  500  has a surface area that can be at least two times or greater than if the shaped surface  500  was flat. In another embodiment, the shaped surface  500  has a surface area that can be at least three times or greater than if the shaped surface  500  was flat. In another example, the shaped surface  500  has a surface area that can be at least 1.2 times or greater than if the shaped surface  500  was flat. 
         [0068]    The ridges  502  and the furrows  504  are arranged adjacent to each other concentrically about a center  506  of the shaped surface  500 . The center  506  can 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 surface  500  shown in  FIG. 5 . 
         [0069]    In some embodiments, the ridges  502  and the furrows  504  can be shaped as a sinusoidal wave, as discussed with respect to  FIG. 4 . In another embodiment, the ridges  502  and the furrows  504  can be shaped as a square wave, as discussed above with respect to  FIG. 4 . 
         [0070]    Although  FIG. 5  depicts ten (10) concentric circles, there may be any number of concentric circles or partially concentric circles. Those skilled in the art will appreciate that there may be any number of shaped portions (including high portions and low portions of any shape or combination of shapes). 
         [0071]      FIG. 6  is a planar view of an example shaped surface  600  that 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 surface  600  shown in  FIG. 6 . 
         [0072]    The shaped surface  600  includes a plurality of ridges  602 - 1  . . .  602 - n  (hereinafter referred to as “ridges  602 ”) and furrows  604 - 1  . . .  604 - n  (hereinafter referred to as “furrows  604 ”). In including ridges  602  and furrows  604 , the surface area of the shaped surface  600  is increased over a surface area of a flat surface of the same size as the shaped surface  600 . In some embodiments, the shaped surface  600  has a surface area that can be at least two times or greater than if the shaped surface  600  was flat. In another embodiment, the shaped surface  600  has a surface area that can be at least three times or greater than if the shaped surface  600  was flat. The ridges  602  and the furrows  604  radiate out from a center  606 . The center  606  can be the center, or originate at one or more points distant from the 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 surface  600  shown in  FIG. 6 . In the pattern shown in  FIG. 6  the furrows  604  increase in furrow width  608  as the furrow extends out from the center  606 . In other embodiments, a ridge width of a ridge can increase as the ridge extends out from the center  606 . 
         [0073]    In various embodiments, different patterns may include different pattern centers any of which may be different than a center of a bottom surface (e.g., center  606  in  FIG. 6 ). For example, a bottom outer surface  302  may include any number of rings located next to each other, each ring 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 surface may be oriented around any number of pattern centers. 
         [0074]    In some embodiments, the ridges  602  and furrows  604  can be shaped as a sinusoidal wave, as discussed with respect to  FIG. 4 . In various embodiments, the ridges  602  and furrows  604  may be shaped as half circles. In another embodiment, the ridges  602  and the furrows  604  can be shaped as a square wave, as discussed with respect to  FIG. 4 . 
         [0075]    Although  FIG. 6  depicts twenty four (24) shaped portions radiating from a center, there may be any number of shaped portions radiating form the center. Those skilled in the art will appreciate that there may be any number of shaped portions (including high portions and low portions of any shape or combination of shapes). 
         [0076]      FIG. 7A  is a cross-sectional view of a shaped surface  700  that includes ridges  702  and furrows  704  shaped according to a sinusoidal wave. The shaped surface  700  shown in  FIG. 7A  can be formed in accordance with the example patterns shown in  FIGS. 4-6 . The shaped surface  700  can be formed on any combination of a base inner surface, a base outer surface, a wall inner surface, and a wall outer surface. In some embodiments, the shaped surface  700  shown in FIG.  7 A has 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. 
         [0077]    The ridges  702  include ridge sides  706  that are curved towards a ridge top plane  708  (e.g., a plane tangent to the peaks of the sinusoidal waves). In an embodiment, the ridges  702  can be shaped such that a cross section of a ridge of the ridges  702  exhibits reflection symmetry about a ridge axis of symmetry  710  that is normal to the ridge top plane  708 . 
         [0078]    The furrows  704  include furrow sides  712  that are curved towards a furrow bottom plane  714  (e.g., a plane tangent to the troughs of the sinusoidal waves). In an embodiment, the furrows  704  can be shaped such that a cross section of a furrow of the furrows  704  exhibits reflection symmetry about a furrow axis of symmetry  716  that is normal to the furrow bottom plane  714 . 
         [0079]    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 kettle  100  and a contained liquid): 
         [0000]        Q =( U )(Area)(Δ T )
 
         [0000]    Here, “Q” has units of energy per time (e.g., Joule per second). 
         [0080]    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: 
         [0000]    
       
         
           
             y 
             = 
             
               a 
                
               
                   
               
                
               sin 
                
               
                   
               
                
               bx 
             
           
         
       
       
         
           
             
               
                  
                 y 
               
               
                  
                 x 
               
             
             = 
             
               ab 
                
               
                   
               
                
               cos 
                
               
                   
               
                
               bx 
             
           
         
       
       
         
           
             
               
                 
                   
                     Arc 
                      
                     
                         
                     
                      
                     length 
                   
                   = 
                     
                    
                   S 
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     2 
                      
                     
                       
                         ∫ 
                         0 
                         
                           π 
                           b 
                         
                       
                        
                       
                         
                           
                             1 
                             + 
                             
                               
                                 ( 
                                 
                                   
                                      
                                     y 
                                   
                                   
                                      
                                     x 
                                   
                                 
                                 ) 
                               
                               2 
                             
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           x 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   S 
                 
               
             
             
               
                 
                   = 
                     
                    
                   
                     2 
                      
                     
                       
                         ∫ 
                         0 
                         
                           π 
                           b 
                         
                       
                        
                       
                         
                           
                             1 
                             + 
                             
                               
                                 a 
                                 2 
                               
                                
                               
                                 b 
                                 2 
                               
                                
                               
                                 
                                   cos 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   bx 
                                   ) 
                                 
                               
                             
                           
                         
                          
                         
                             
                         
                          
                         
                            
                           x 
                         
                       
                     
                   
                 
               
             
           
         
       
     
         [0081]    Assuming a=π and b=1 then: 
         [0000]        S= 2∫ 0   π √{square root over (1+π 2  cos 2 ( x ))} dx  
 
         [0000]        S= 2(7.21403)=14.482 
         [0000]    Assuming unit width, the area equals (S)(1) or S. 
         [0082]      FIG. 7B  is a cross-sectional view of a shaped surface  750  that is corrugated with ridges  702  and furrows  704  shaped according to a square wave. The shaped surface  750  shown in  FIG. 7B  can be formed in accordance with the example patterns shown in  FIGS. 4-6 . The shaped surface  750  can be formed on any combination of a base inner surface, a base outer surface, a wall inner surface, and a wall outer surface. In some embodiments the shaped surface  750  shown in  FIG. 7B  has at least 3 times greater surface area than a surface area of a flat surface. 
         [0083]    The ridges  702  include planar tops that form the tops of the ridges  702 . The ridges  702  include ridge sides  706  that extend linearly upwards towards a ridge top plane  708 . The ridge top plane  708  is formed along a planar top of a ridge with a corresponding ridge side  706  that extends linearly upwards towards the ridge top plane  708 . 
         [0084]    The furrows  704  include planar bottom that form the bottoms of the furrows  704 . The furrows  704  include furrow sides  712  that extend linearly downwards towards a furrow bottom plane  714 . The furrow bottom plane  714  is formed along a planar bottom of a furrow with a corresponding furrow side  712  that extends linearly downward towards the furrow bottom plane  714 . 
         [0085]    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): 
         [0000]        S= 4 a+ 2 b    
         [0086]    If a=b=π, S=4π+2π=6π=18.85 
         [0087]    Relative to a flat surface with length 
         [0000]      2 b= 2π=6.2832
 
         [0000]    Assuming unit width, the area equals (S)(1) or S.
 
For example:
 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
                   
               
               
                   
                   
                 Area (Assuming  
                 Area Relative to  
               
               
                   
                 Surface 
                 Unit Width) 
                 a Flat Surface 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Flat 
                 6.2832 
                 1.000 
               
               
                   
                 Sinusoidal in one dimension 
                 14.482 
                 2.305 
               
               
                   
                 with amplitude defined above 
                   
                   
               
               
                   
                 equal to half of the period 
                   
                   
               
               
                   
                 Rectangular in one dimension 
                 18.85 
                 3.000 
               
               
                   
                 with amplitude defined above 
                   
                   
               
               
                   
                 equal to half of the period 
               
               
                   
                   
               
             
          
         
       
     
         [0088]      FIG. 8  is a planar view of a shaped surface  800  that is corrugated according to another example pattern. In various embodiments, an applicable combination of a portion of a base inner surface, a base outer surface, a wall inner surface, and a wall outer surface may be shaped according to the shaped surface  800  shown in  FIG. 8 . 
         [0089]    The shaped surface  800  includes a plurality of ridges  802 - 1  . . .  802 - n  (hereinafter referred to as “ridges  802 ”) and furrows  804 - 1  . . .  804 - n  (hereinafter referred to as “furrows  804 ”). By including ridges  802  and furrows  804 , the surface area of the shaped surface  800  is increased over a surface area of a flat surface of a same size as the shaped surface  800 . In some embodiments, the shaped surface  800  has a surface area that is at least two times greater than if the shaped surface  800  was flat. In another embodiment, the shaped surface  800  has a surface area that is at least three times greater than if the shaped surface  800  was flat. The ridges  802  are shaped along the longitudinal length of the ridges  802  according to a planar square wave pattern. Similarly, the furrows  804  are shaped along the longitudinal length of the furrows according to an inverse of a planar square wave pattern of which the ridges  802  adjacent to the furrows  804  are shaped. 
         [0090]      FIG. 9  is a planar view of a shaped surface  900  that is corrugated according to another example pattern. In various embodiments, an applicable combination of a portion of a base inner surface, a base outer surface, a wall inner surface, and a wall outer surface may be shaped according to the shaped surface  900  shown in  FIG. 9 . 
         [0091]    The shaped surface  900  includes a plurality of ridges  902 - 1  . . .  902 - n  (hereinafter referred to as “ridges  902 ”) and furrows  904 - 1  . . .  904 - n  (hereinafter referred to as “furrows  904 ”). In including ridges  902  and furrows  904 , the surface area of the shaped surface  900  is increased over a surface area of a flat surface of a same size as the shaped surface  900 . In some embodiments, the shaped surface  900  has a surface area that is at least two times greater than if the shaped surface  900  was flat. In another embodiment, the shaped surface  900  has a surface area that is at least three times greater than if the shaped surface  900  was flat. The ridges  902  are shaped along the longitudinal length of the ridges  902  according to a planar sinusoidal pattern. Similarly, the furrows  904  are shaped along the longitudinal length of the furrows according to an inverse of a planar sinusoidal wave pattern of which the ridges  902  adjacent to the furrows  904  are shaped. 
         [0092]      FIG. 10  is a planar view of a shaped surface  1000  with a plurality of protrusions according to a protrusion pattern. In various embodiments, protrusions included in the protrusion pattern of the shaped surface shown in  FIG. 10  can include any combination of square shaped protrusions, trapezoid shaped protrusions, triangular shaped protrusions, sinusoidal shaped protrusions, and/or protrusions of any shape or pattern. 
         [0093]    The protrusion pattern shown in  FIG. 10  includes protrusion lines  1002 - 1  . . .  1002 - n  (hereinafter referred to as “protrusion lines  1002 ”), in which protrusions are formed to increase the surface area of the shaped surface  1000 . In the shaped surface shown in  FIG. 10 , the protrusion lines  1002  are parallel to each other. 
         [0094]      FIG. 11  is a planar view of a shaped surface  1100  with a plurality or protrusions according to another protrusion pattern. In various embodiments, protrusions included in the protrusion pattern of the shaped surface shown in  FIG. 11  can include any combination of square shaped protrusions, trapezoid shaped protrusions, sinusoidal shaped protrusions, and/or protrusions of any shape or pattern. 
         [0095]    The protrusion pattern shown in  FIG. 11  includes protrusion columns  1102 - 1  . . .  1102 - n  (hereinafter referred to as “protrusion columns  1102 ”) and protrusion rows  1104 - 1  . . .  1104 - n  (hereinafter referred to as “protrusion rows  1104 ”). Protrusions are formed within the protrusion columns  1102  and the protrusion rows  1104  to increase the surface area of the shaped surface  1100 . The protrusion columns  1102  and the protrusion rows  1104  intersect to form an array of protrusions on the shaped surface  1100 . 
         [0096]      FIG. 12  is a planar view of a shaped surface  1200  with a plurality or protrusions according to another protrusion pattern. In various embodiments, protrusions included in the protrusion pattern of the shaped surface shown in  FIG. 12  can include any combination of square shaped protrusions, trapezoid shaped protrusions, sinusoidal shaped protrusions, and/or protrusions of any shape or pattern. 
         [0097]    The protrusion pattern shown in  FIG. 12  includes protrusion rings  1202 - 1  . . .  1202 - n  (hereinafter referred to as “protrusion rings  1202 ”) concentrically formed about a center  1204  of the shaped surface  1200 . The center  1204  can 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 surface  1200  shown in  FIG. 12 . Protrusions are formed within the protrusion rings  1202  to increase the surface area of the shaped surface  1200 . 
         [0098]      FIG. 13  is a planar view of a shaped surface  1300  with a plurality or protrusions according to another protrusion pattern. In various embodiments, protrusions included in the protrusion pattern of the shaped surface shown in  FIG. 13  can include any combination of square shaped protrusions, trapezoid shaped protrusions, sinusoidal shaped protrusions, and/or protrusions of any shape or pattern. 
         [0099]    The protrusion pattern shown in  FIG. 13  includes protrusion radials  1302 - 1  . . .  1302 - n  (hereinafter referred to as “protrusion radials  1302 ”) formed to radiate out from a center  1304 , center area, or other focal points or areas, of the shaped surface  1300 . The center  1304  can 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 surface  1300  shown in  FIG. 13 . Protrusions are formed within the protrusion radials  1302  to increase the surface area of the shaped surface  1300 . The protrusion radials  1302  have protrusion radial widths  1306  that can be constant across the length of the protrusion radials  1302 , or they can change across the length of the protrusion radials  1302 . For example, protrusion radial widths  1306  of the protrusion radials  1302  can increase across the length of the protrusion radials  1302  as the protrusion radials  1302  extend out from the center  1304 . 
         [0100]      FIG. 14A  is a cross-sectional view of a shaped surface  1400  with protrusions  1402  shaped as a sinusoidal wave. In various embodiments, the protrusions  1402  shown in  FIG. 14A  can be arranged in the protrusion patterns shown in  FIGS. 10-13 . 
         [0101]    In being shaped as a sinusoidal wave, the protrusions  1402  have protrusion sides  1404  that curve upwards towards a protrusion plane  1406 . The protrusion plane  1406  is a plane formed across the tops (e.g., peaks) of the protrusions  1402  at a protrusion height  1408  of the protrusions  1402 . In the shaped surface  1400  shown in  FIG. 14A , the protrusions  1402  all have the same protrusion height  1408 . The protrusion cross-section of the protrusions  1402  exhibit reflection symmetry about a protrusion axis of symmetry  1410  normal to the protrusion plane  1406 . 
         [0102]      FIG. 14B  is a cross-sectional view of a shaped surface  1450  with protrusions  1452  shaped as a square wave. In various embodiments, the protrusions  1452  shown in  FIG. 14B  can be arranged in the protrusion patterns shown in  FIGS. 10-13 . 
         [0103]    In being shaped as a square wave, the protrusions  1452  have protrusion sides  1454  that extend upwards towards a protrusion plane  1456 . The protrusion plane  1456  is a plane formed across the top portions (e.g., peaks) of the protrusions  1452  at a protrusion height  1458  of the protrusions  1452 . In the shaped surface  1450  shown in  FIG. 14B , the protrusions  1452  all have the same protrusion height  1458 . 
         [0104]    The shaped portions (e.g., protrusions and/or indentions) may comprise any material or the like including, but not limited to alloys, ceramics, metals, or combination of 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. 
         [0105]      FIGS. 15A-G  depict 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 surface and base outer surface). 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. 
         [0106]      FIG. 15A  depict interlocking elbow shaped surfaces in some embodiments. The interlocking elbow shaped surfaces may project outward from the base of the kettle (or inside the kettle). In some embodiments, the elbow shaped surfaces may project inward (forming an indentation) from the base of the kettle (or inside the kettle). A kettle may include both projections and indentations. Those skilled in the art will appreciate that any shapes or combination of shapes may be used for protrusions and/or indentations. 
         [0107]      FIG. 15B  depicts conical shaped protrusions in some embodiments.  FIG. 15C  depicts conical shaped indentations in some embodiments.  FIG. 15D  depicts triangular shaped protrusions in some embodiments.  FIG. 15E  depicts triangular shaped indentations in some embodiments.  FIG. 15F  depicts dimple shaped indentation in some embodiments.  FIG. 15G  depicts dimple shaped protrusions in some embodiments. 
         [0108]    Although the shaped protrusions and indentations in  FIG. 15B-G  appear to be the same, 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 and in any pattern. 
         [0109]    The present invention is described above with reference to exemplary embodiments. It will be apparent to those skilled in the art 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.