EP3455575B1

EP3455575B1 - Fin for a finned pack for heat exchangers as well as a heat exchanger

Info

Publication number: EP3455575B1
Application number: EP17735621.9A
Authority: EP
Inventors: Michelangelo SASSANELLI; Matteo LEONI
Original assignee: Stefani SpA
Current assignee: Stefani SpA
Priority date: 2016-05-13
Filing date: 2017-05-12
Publication date: 2021-03-10
Anticipated expiration: 2037-05-12
Also published as: WO2017195157A1; US20190145716A1; EP3455575A1; ITUA20163433A1; CN109477704A

Description

TECHNICAL FIELD OF THE INVENTION

The present invention regards a fin for a finned pack for heat exchangers, a finned pack and a heat exchanger including the latter.

STATE OF THE PRIOR ART

Heat exchangers are used in many applications for heating or cooling a first fluid by placing it in heat exchange communication with a second fluid. This is usually obtained by conveying a first fluid in tubes which cross passage zones of the second fluid.
Different types of heat exchangers have been proposed, including the so-called "finned pack" heat exchangers, which comprise a plurality of packed fins. Such fins comprise plate-like elements having a plurality of holes in which tubes for conveying a first fluid are inserted, while a second fluid is sent between the fins for the heat exchange with the first fluid.
The fins can have substantially smooth or corrugated geometry, i.e. in particular if it is desired to increase the surface area or the efficiency of the heat exchange.
Nevertheless, the efficiency of the heat exchange in the exchangers according to the state of the art is often limited and there is therefore the need to improve the performances obtainable in heat exchangers.
US2004/194936A1 , WO2014/104576A1 , WO2011/082922A1 , EP2072939A1 and CN102135388A1 teach solutions according to the state of the art.
GB 332 455 A discloses a fin for a finned pack for heat exchangers having the features in the preamble of claim 1.

OBJECTS OF THE INVENTION

One object of the present invention is to provide a new fin of a finned pack for heat exchangers as well as a new finned pack and a new heat exchanger obtainable starting from one such fin.
Another object of the present invention is to provide a new fin of a finned pack that is able to ensure a greater heat exchange efficiency.
Another object of the present invention is to provide a fin like the aforesaid claim 1.
The dependent claims refer to preferred and advantageous embodiments of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Other characteristics and advantages of the invention will be more evident from the description of embodiments of fins, of a finned pack and of heat exchangers, illustrated as an example in the enclosed drawings in which:

figure 1 is a plan view of a fin according to the present invention;
figure 2 is a view of an enlarged-scale detail of the fin of figure 1 with tubes inserted;
figure 3 is a view of a detail of figure 2 with indications regarding several angles and distances;
figure 4 is a sectional view of a detail of a finned pack according to the present invention;
figure 5 is a view similar to figure 2 of another embodiment of a fin in accordance with the present invention;
figure 6 is a slightly top perspective view that illustrates several components of a finned pack with fins according to figure 5;
figure 7 is a view of a finned pack according to the present invention and including a fin in accordance with the present invention; and
figures 8 to 10 are views of heat exchangers in which a finned pack is installable according to the present invention.

In the set of drawings, equivalent parts or components are marked with the same reference numbers.

EMBODIMENTS OF THE INVENTION

With reference to Figures 1 to 4, a fin 1 is illustrated for a finned pack for heat exchangers, which comprises a plate 2 in which a plurality of through holes 3 is obtained for the positioning of tubes 4 intended to convey a first heat exchange fluid, e.g. a liquid.
The plate 2 has an edge 5 as well as two main faces 6, each intended to be licked or hit by a second heat exchange fluid, such as air, in a crossing direction A-A from an inlet portion 5a to an outlet portion 5b of the edge 5 of the plate 2. For such purpose, the facing main faces 6 of two adjacent and successive fins 1 together delimit a respective area of passage or crossing of a second fluid, which hits respective sections of tubes 4 inserted in such fins.
The edge 5 actually constitutes a face of external connection between the two main faces 6 and the same can be provided with two main sides 5a, 5b, e.g. parallel, which are bridge connected by means of secondary or smaller sides 5c, 5d, also if desired parallel and orthogonal to the main sides. The main sides 5a, 5b actually constitute, respectively, the inlet portion 5a and the outlet portion 5b.
The holes 3 are delimited by a respective inner delimiting wall 7 of the plate 2, which includes a first portion 7a facing towards the inlet portion 5a and a second portion 7b (equal to or greater than the portion 7a) facing towards the outlet portion 5b. The delimiting wall 7 for the holes 3 can be substantially cylindrical.
The fin 1 then comprises one or more confinement units 8, 9 for the flow of the second fluid, each confinement unit being placed around a respective section of the second portion 7b of the delimiting wall 7 of a hole 3 of the plurality of holes so as to obtain or define a partially surrounded hole or better yet a respective partially surrounded hole 3. Preferably, a confinement unit 8, 9 is provided for each hole 3 of the fin 1 or in any case for most of the holes 3 of the fin itself.
More particularly, at least one confinement unit comprises two first baffles 8, 9 or two through recesses for housing second baffles placed on opposite sides from each other with respect to a respective partially surrounded hole 3, and each enclosing and spaced by a respective section of the second portion 7b of the delimiting wall 7 of the partially surrounded hole 3, so as to confine on the plate 2, during use, a first flow zone FZ1 of the second fluid between each baffle 8, 9 or recess and a respective section of the second portion 7b of the delimiting wall 7.
The configuration that will be described with reference to the first baffles is also applied in substance to the second baffles and vice versa, if it is considered that, once a finned pack is assembled, such components (first or second baffles) are intended to carry out the same task and substantially in the same manner.
The first flow zone FZ1 comprises a mouth for introducing the second fluid delimited between the plate 2, the first baffles 8, 9 and a part of the delimiting wall 7 as well as a mouth for delivering the second fluid leading into an area downstream of the respective hole 3, i.e. an area after the hole 3 in the sense of the crossing direction A-A. The first flow zone FZ1 or better yet the walls thereof are fluid-sealed so as to prevent leaks or outflows of liquid between the introduction mouth and the delivery mouth.
With regard to the introduction mouth, it is preferably delimited between the plate 2, a first end 8a, 9a of the first baffles 8, 9 or recesses and a part of the second portion 7b of the delimiting wall 7.
In addition, the distance of each baffle 8, 9 or of the recesses relative to a respective partially surrounded hole 3, with reference to the sense moving away from the inlet portion 5a and approaching the outlet portion 5b, has one of the following geometries or extensions:

it is constant for the entire extension of the baffle or recess 8, 9,
it is constant and then increases,
it decreases for the entire extension of the baffle or recess 8, 9,
it decreases and then increases,
it is constant and then decreases, or
it is constant, then decreases and finally increases.

Such distance is calculated on a plane orthogonal to the axis x-x of a partially surrounded hole 3 and along an axis that connects the center or central point of the partially surrounded hole 3 with the baffle 8, 9 or better yet with the intrados of the baffle 8, 9 or of the recesses, i.e. the section of the baffles 8, 9 or recesses directed towards or facing the respective partially surrounded hole 3.
More particularly, the first flow zone FZ1 has a section, evaluated with reference to a plane orthogonal to the plate 2 or in any case to the main extension plane thereof, and passing through the center or a central point of the respective partially surrounded hole 3, that is:

constant for the entire extension thereof,
constant and then diverging,
converging for the entire extension thereof,
converging and then diverging,
constant and then converging, or
constant, then converging and finally diverging.

In substance, the first flow zone FZ1 does not have stagnation areas, i.e. it does not have first areas with section, evaluated with reference to a plane orthogonal to the plate 2 and passing through the center or a central point of the respective partially surrounded hole 3, greater than areas downstream and upstream, with reference to the sense from the inlet portion 5a to the outlet portion 5b of the first areas. If for example, the section of the first flow zone FZ1 first increases, and then once again decreases, there would be a stagnation zone of the second fluid at the increase of the section, which would involve an alteration of the laminar flow of the second fluid.
With regard to the first end 8a, 9a of the first baffles 8, 9, identifying, in a plane orthogonal to the axis of symmetry x-x (axis entering into the sheet with reference to the enclosed figures) of a partially surrounded hole 3, an initial angle α0 between an initial axis S0 parallel to the crossing direction A-A and passing through the center or a central point of the partially surrounded hole 3 and a first axis S 1 that extends from the center or central point of the partially surrounded hole 3 to the inlet portion 8a of a baffle or recess 8, 9, the initial angle α0 is between 45° and 135°, preferably between 80° and 100°.
If desired, identifying, in a plane orthogonal to the axis of symmetry x-x (axis entering into the sheet with reference to the enclosed figures) of a partially surrounded hole 3, a first angle α1 between a first axis S1 that extends from the center or a central point of the partially surrounded hole 3 to the first end 8a, 9a of a baffle or recess 8, 9 and a second axis S2 that extends from the center of the partially surrounded hole 3 to the point of such baffle or recess 8, 9 defining the termination or end of the constant section, the first angle is between 45° and 135°, preferably between the value of the initial angle α0 and 100°.
In addition, if the section of the first flow zone FZ1 is constant and then converging or constant, then converging and finally diverging, identifying, in a plane orthogonal to the axis of symmetry x-x of the partially surrounded hole 3, a second angle α2 between a second axis S2 that extends from the center of the partially surrounded hole 3 to the point of a baffle or recess 8, 9 defining the termination or end of the constant section and a third axis S3 that extends from the center of the partially surrounded hole 3 to the point of such baffle or recess 8, 9 defining the termination or end of the converging section, the second angle is between 45° and 180°, preferably between the value of the second angle α2 and 150°.
Alternatively, if the section of the first flow zone FZ1 is converging for the entire extension thereof or converging and then diverging (such variant is not illustrated in the figures), identifying, in the orthogonal plane, a second angle α2 between a second axis S2 that extends from the center of the partially surrounded hole 3 to the point of a baffle or recess 8, 9 defining the first end 8a, 9a of a baffle or recess 8, 9 and a third axis S3 that extends from the center of the partially surrounded hole 3 to the point of such baffle or recess 8, 9 defining the termination or end of the converging section, the second angle is between 45° and 180°, preferably between 45° and 150°.
If the section is constant and then diverging, identifying, in a plane orthogonal to the axis of symmetry x-x of the partially surrounded hole 3, a third angle α3 between a second axis S2 that extends from the center of the partially surrounded hole 3 to the point of a baffle or recess 8, 9 defining the termination or end of the constant section and a fourth axis S4 that extends from the center of the partially surrounded hole 3 to the point of such baffle or recess 8, 9 defining the termination of the diverging section, the third angle α3 is between 45° and 180°, preferably between the value of the first angle α1 and 165°.
If instead the section is converging and then diverging or constant, then converging and finally diverging, identifying, in a plane orthogonal to the axis of symmetry x-x of the partially surrounded hole 3, a third angle α3 between a third axis S3 that extends from the center of the partially surrounded hole 3 to the point of a baffle or recess 8, 9 defining the termination of the converging section and a fourth axis S4 that extends from the center of the partially surrounded hole 3 to the point of such baffle or recess 8, 9 defining the termination of the diverging section, the third angle α3 is between 45° and 180°, preferably between the value of the second angle α2 and 165°.
Advantageously, the first baffles 8, 9 or the recesses can also be extended beyond a respective hole, i.e. they have terminal sections closer to the outlet portion 5b relative to a respective hole and hence define a second flow zone FZ2, that actually constitutes a continuation of the first flow zone FZ1, and such second flow zone FZ2 is delimited between terminal sections of the first baffles 8, 9 or recesses. The second flow zone FZ2 is not extended around the respective partially surrounded hole 3.
In such a manner, one obtains a confinement of the second fluid downstream of the partially surrounded hole 3, with the expression confinement "downstream" indicating a confinement of the second fluid in the area or zone of the fin 1 that such fluid crosses after having hit the hole 3 or better yet the tube 4 inserted in the hole 3.
The second flow zone FZ2 has a feeding mouth corresponding to the delivery mouth of the first flow zone FZ1 as well as a mouth for discharging the second fluid towards successive holes or parts of the fin with reference to the crossing direction A-A. The second flow zone FZ2 or better yet the walls thereof are fluid-sealed so as to prevent leaks or outflows of fluid between the delivery mouth and the discharge mouth.
The second flow zone FZ2 has a section that is divergent, evaluated with reference to a plane orthogonal to the plate and passing through the center of the hole 3 partially surrounded by the respective baffle 8, 9 or groove.
With regard instead to the extrados 8d, 9d of the baffles 8, 9 or recesses, i.e. the section of the baffles or recesses directed away from the respective partially surrounded hole 3, this is substantially rectilinear or slightly curved and does not have stagnation zones for the second fluid. The concavity/convexity of the extrados 8d, 9d depends on the velocity field that is established due to the presence of other tubes.
More particularly, the extrados 8d, 9d is substantially tilted with respect to the crossing direction A-A by an angle between -45° and 45°, preferably between 0° and +20° or between -15° and 45°, with an initial end 8a, 9a proximal to the inlet portion 5a and distal from the outlet portion 5b and a final end 8b, 9b distal from the inlet portion 5a and proximal to the outlet portion 5b, the initial ends 8a, 9a of the extradoses 8d, 9d of the baffles or recesses 8, 9 of a partially surrounded hole 3 being at a distance from each other greater than the distance between the final ends 8b, 9b of the extradoses 8d, 9d of such baffles or recesses 8, 9.
Preferably, the baffles 8, 9 or recesses have a configuration, with reference to the travel sense or crossing direction A-A of the second fluid, with a first section 8e with preferably constant width, a second section 8f with preferably increasing width and then a third section 8g with preferably decreasing width. The second section 8f has initial width equal to the first section 8e and final width equal to 2-5 times the first section, preferably 3-4 times the first section 8e.
Advantageously, the holes 3 are each extended around a respective axis of symmetry x-x, with the axes of symmetry x-x of the holes 3 being substantially parallel to each other, while the first baffles 8, 9 or the housing recesses for second baffles of a confinement unit 8, 9 are substantially symmetric to each other with respect to a plane passing through the crossing direction A-A from an inlet portion 5a to an outlet portion 5b of the edge 5 and (passing) through the axis of symmetry x-x of the at least partially surrounded respective hole 3.
In addition, the delimiting wall 7 can have a collar section 7c projecting upward with respect to one of the main faces 6, while the first baffles 8, 9 of the partially surrounded hole 3 with collar section 7c are extended around at least one part of the collar section 7c distal from the inlet portion 5a and facing towards the outlet portion 5b, the first or second baffles having height or thickness equal to or greater than the collar section 7c. The collar section 7c of the delimiting walls 7 also carries out, in addition to the function of heat transfer between fin and tube, also the function of spacer between two adjacent and successive fins 1 of a finned pack.
Advantageously, the first baffles 8, 9 or the recesses of one or more confinement units 8, 9 have a first end 8a, 9a proximal to the inlet portion 5a as well as a second end 8b, 9b distal from the inlet portion 5a of the plate 2. The first proximal 8a, 9a of the first baffles 8, 9 or housing recesses are at a first distance D1 from each other, while the distal ends 8b, 9b of the first baffles 8, 9 or recesses of a confinement unit are at a second distance D2 from each other which is advantageously smaller than the first distance D1, such that the first baffles or recesses together delimit a first area that is substantially tapered moving away from the inlet portion 5a. In addition, in such case, preferably there are no intermediate sections of the first baffles 8, 9 with distance from each other greater than the first distance D1 between the first ends 8a, 9a.
If desired, the distance between the first baffles 8 could initially decrease moving away from the inlet portion 5a and then, having reached a minimum value at an intermediate portion of the first baffles, where the distance D3 between the baffles 8, 9 or recesses is minimal, once again increase up to the second end 8b, 9b; according to such variant, the distance D2 between the first baffles at the respective second end 8b, 9b could also be greater than the distance D1. In such case, the area between the proximal ends and the intermediate portions of the first baffles or of the housing recesses is substantially tapered in the sense moving away from the inlet portion 5a, while a second area would be provided between the intermediate portions and the second ends of the first baffles or of the housing recesses with an initial section with decreasing cross section and then a terminal section with cross section increasing moving away from the inlet portion 5a.
More particularly, the distance between the baffles 8, 9 or recesses in the sense moving away from the inlet portion 5a can initially progressively decrease and then, once a minimum value at an intermediate portion of the baffles or recesses has been reached, progressively increase once again up to the second end 8b, 9b.
In addition, the (first and/or second) baffles can have a tubular body or solid block body, which at the intrados 8h, 9h, i.e. the section of the baffles 8, 9 or recesses directed towards or facing the respective partially surrounded hole 3, is substantially flat or slightly curved with trim, preferably, orthogonal or projecting upward with respect to the plate 2. In addition, the (first and/or second) baffles are, preferably, fluid-sealed (if desired they are not perforated) so as to prevent the passage of the second fluid therethrough. In addition, each baffle is preferably formed in a single piece.
In substance, the intrados 8h, 9h of the baffles 8, 9 or of the second baffles is substantially continuous, so as to ensure the passage from one section of the first flow zone FZ1 to another (from constant to converging, from converging to diverging or from constant to diverging) in a gradual and progressive manner, i.e. there are no sudden passages or steps from one section of such first flow zone to another or along the extension of each of the same.
More particularly, the intrados 8h, 9h along the first flow zone FZ1 comprises a curved or substantially curved surface, better yet slightly curved with concavity directed towards the first flow zone FZ1 itself at the areas with constant section and/or converging section thereof, and a curved or substantially curved surface, better yet slightly curved with concavity directed away from the flow zone itself at possible areas with diverging section thereof.
If a second flow zone FZ2 is also provided, the intrados 8h, 9h of the baffles 8, 9 or of the second baffles is made in a manner such that the passage from a terminal section of the first flow zone FZ1 to the second flow zone FZ2 occurs in a gradual and progressive manner, i.e. there are no sudden passages or steps between such zones. More particularly, the intrados 8h, 9h at the passage from the first FZ1 to the second FZ2 flow zone comprises a curved surface or better yet slightly curved surface with concavity directed towards the extrados 8d, 9d.
The intrados 8h, 9h is therefore not flat or rectilinear.
If desired, the first baffles comprise a first drawn or cut and bent portion 2a of the plate 2, i.e. the baffles 8, 9 are obtained by means of drawing of the plate 2 itself. If a collar section 7c is provided, then both the first baffles 8, 9 and the collar sections 7c are obtained by means of drawing a respective plate 2.
The at least one drawn portion 2a of the plate 2 can be tapered moving away from the main extension plane of the plate 2, such that such drawn portion has a tip or free end 2a1 of lower width with respect to the base or end thereof for constraining 2a2 to the plate.
As defined in claim 1, said baffles have a substantially tubular structure so as to delimit at least one first opening or channel (11).
Each drawn portion 2a preferably has two separate and drawn sections 2a3, 2a4 defining the channel or opening 11 therebetween, e.g. substantially tapered, the ends of which together defining the tip 2a1 and the base 2a2 of the drawn portion 2a. As will be understood, for the obtainment of such drawn portion 2a the drawing of a portion of plate 2 will be carried out followed by the removal of the end substantially parallel to the plate 2 by means of cutting or incision, in such a manner obtaining the two separate sections 2a3, 2a4. The separate sections 2a3, 2a4 preferably have thickness lower than the remaining part of the plate 2, since the drawing determines or can determine a "stretching" of the edges, so as to increase the exposed surface area thereof and reduce their thickness.
In such case, the plate 2 can have second drawn portions, each set to define a collar section 7c, which in this case could be tapered like the first drawn portions. Such second drawn portions ensure a good transfer of the heat between fin and tubes.
Alternatively, the (first and/or second) baffles 8, 9 can comprise a tubular body or solid block body with trim substantially orthogonal to the plate 2, and such tubular body or solid block body can be formed apart or separately with respect to the plate 2 and connected, if desired via welding or fitting with the plate 2. In addition, second baffles could be formed apart and inserted each in a respective recess for housing a confinement unit 8, 9, and such baffles could have a configuration and, during use, arrangement substantially corresponding to the baffles 8, 9.
For such purpose, the second baffles could be metal sections obtained via extrusion, molding or shaping and mechanically inserted in the fins of a finned pack or better yet in the plates thereof, for example with forced insertion or via interference or by means of use of welding materials or alloys that facilitate the adhesion and the transmission of the heat. Clearly, the second baffles entirely fill the respective recesses, such that after the insertion of the second baffles there are no remaining parts of the recesses still open or not filled.
The height or thickness of the (first and/or second) baffles 8, 9, or even the pitch of the fins or distance between two successive fins, could vary from about 0.1 mm to about 36 mm.
In addition, in order to define the position of the baffles, one or more holes 3 will be considered with substantially circular or even non-circular cross section, e.g. oval, elliptical, etcetera and the first portion 7a and the second portion 7b with cross section that is substantially semi-circular, semi-oval, semi-elliptical, etcetera.
In addition, each baffle 8, 9 or recess can be at a third distance D4 from the delimiting wall 7 and more particularly from a section of the second portion 7b of the delimiting wall 7 between about 0.05R and about 3R, where with R the radius of a tube 3 or of a partially surrounded hole is indicated.
A fin like that illustrated in figures 1 to 4 allows reducing the so-called "dead zone" downstream of the tubes, with reference to the direction A-A of the flow of the second fluid.
The baffles 8, 9 or in any case the baffles insertable in the housing recesses in fact determine, as can be verified, a conveyance or confinement of the second fluid on the second portion 7b of the respective delimiting wall 7 and hence towards the respective tube 4, which ensures that each portion of the delimiting wall 7 and hence of the respective tube is hit by the second fluid.
A fin according to the present invention preferably comprises one, two or more rows of holes 3, offset or aligned with respect to each other with respect to the crossing direction A-A, such that each row of holes 3 is at a distance from the inlet portion 5a that is different with respect to the other rows of holes 3.
As indicated above, a baffle 8, 9 according to the present invention can have tubular configuration defining an opening or first opening 11 (see figures 5 and 6), if desired extended substantially parallel to the axis of symmetry x-x of the respective hole 3.
Such opening 11 is typically used for the passage through the respective baffle, i.e. in a direction substantially parallel to the axis x-x, of a third fluid F3 such to increase the exchange efficiency of the exchanger. In addition, the opening 11 could also be fed with the first F1 or the second F2 fluid.
It should then be noted that also the baffles 8, 9 described above could have an opening or channel 11, such to have a structure that is substantially tubular with through opening extended substantially parallel to the axis of symmetry x-x of the respective hole 3.
The first opening 11 of one or more baffles could have a section with any suitable shape, e.g. circular, elliptical, rectangular or polygonal.
In addition, in each baffle, two or more openings or micro-channels 11 could also be provided. Regarding such aspect, one or more baffles could also delimit two or more channels or openings for the conveyance of two different fluids or for sending a same fluid between one channel and the next.
Clearly, an opening 11 as indicated above can be present in particular if the baffles comprise metal sections obtained - via extrusion, molding or shaping - apart with respect to the plates 2 and then mechanically inserted in the plates 2 themselves, or portions 2a obtained via drawing or shaping of the plate 2a.
In addition, the first opening 11 is delimited at the second 8f and third section 8g or at the first 8e, second 8f and third 8g section.
If desired, the baffles 8, 9 comprise a tubular body with thickness that is substantially constant, such that the delimiting wall for the opening 11 has constant thickness.
With reference now in particular to the geometry and distribution of the holes in a fin according to the present invention, the following will be defined:

line or row of holes 3 or of tubes 4 is the set of the holes of a fin or of the tubes inserted therein at a same distance from the inlet portion 5a;
A or PT is the pitch or distance of the holes 3 or of the tubes 4 of a same row of tubes times the number of tubes of such row; and
B or PR is the pitch or distance of the lines times the number of lines.

On the basis of such definitions, a fin according to the present invention could have AxB between 10 mm x 10 mm and 200 mm x 200 mm.
In the following table, several possible geometries and sizes are reported for a fin according to the present invention as well as for the tubes to be inserted in the same.
In addition, there could also be a fin with AxB equal to 48x41.75 or 50x40 with tubes of diameter equal to 12mm or 16 mm, or AxB equal to 20x20 with tubes with 5 mm diameter.
With regard instead to the definition "offset" of the tubes or of the holes, it is intended that the holes of adjacent and successive rows are offset with reference to the crossing direction A-A, while the definition "square" indicates that the holes or the tubes of adjacent and successive rows are aligned, still with reference to the crossing direction A-A. For such purpose, in a fin according to the present invention, each row of holes 3 comprises at least one hole aligned along the crossing direction A-A with a respective hole of the other rows of holes and/or at least one hole offset with respect to the holes 3 of the other rows of holes 3, still with reference to the crossing direction A-A.
In substance, a fin according to the present invention comprises two or more lines or rows of holes 3, i.e. groups of holes substantially at a same distance from the inlet portion 5a. In addition, the holes of adjacent and successive rows can be offset or aligned with reference to the crossing direction A-A.
In addition, in a fin according to the present invention, there may or may not be holes for the positioning of heating elements, e.g. through holes with diameter equal to 9.5 mm.
The thickness of a fin according to the present invention can vary between 0.1 mm and 2 mm.
The distance D5 of the intrados 8h, 9h of a baffle 8, 9 or recess at the first end 8a, 9a of the baffles or recesses from the initial axis S0 parallel to the crossing direction A-A, and passing through the center or a central point of the partially surrounded hole 3, can thus be as indicated hereinbelow: $(R 1 + 0.1 mm) \sin (α 0) < D 5 < PT / 2$
wherein R1 is the radius of a partially surrounded hole 3.
Preferably, D5 is greater than 1.2R1 and smaller than 2.2R1.
The distance D6 of the extrados 8d, 9d of a baffle 8, 9 or recess at the first end 8a, 9a of the baffles or recesses from the initial axis S0 parallel to the crossing direction A-A, and passing through the center or a central point of the partially surrounded hole 3, can thus be as indicated hereinbelow: $(R 1 + 0.1 mm) \sin (α 0) < D 6 < PT / 2$
wherein R1 is the radius of a partially surrounded hole 3.
Preferably, D6 is greater than D5 and smaller than D5 + 2 mm.
With regard to D2, this can thus be as indicated hereinbelow: $D 3 / 2 < D 2 / 2 < PT / 2$
Preferably, D2/2 is greater than D3/2 and smaller than D6.
The length D8 of the extrados 8d, 9d of the baffles or recesses can be as indicated hereinbelow: $R 1 < D 8 < PR$
Preferably, D8 is greater than 0.8PR and smaller than 1.2PR.
In addition, if the first flow zone FZ1 has a section, evaluated with reference to a plane orthogonal to the plate 2 and passing through the center or a central point of the respective partially surrounded hole 3, constant and then converging, or constant, then converging and finally diverging, or always constant or always converging, then, having considered D9 to be the value of the distance of the partially surrounded hole 3 from a baffle 8, 9 or recess at the termination of the constant section and, if provided, the start of the converging section, and D10 to be the value of the distance of the partially surrounded hole from a baffle 8, 9 or recess at the termination of the converging section, D9 and D10 can be as indicated hereinbelow: $0.1 mm < D 9 < PT / 2 - R 1$
$0.1 mm < D 10 < D 9$
Preferably, D9 is greater than 0.9(D5/sin(α0)-R1) and smaller than D5/sin(α0)-R1, while D10 is greater than 0.6(D5/sin(α0)-R1) and smaller than 0.9(D5/sin(α0)-R1).
With regard to D3, this can be as indicated hereinbelow: $(R 1 + D 10 + 0.1 mm) \sin (α) (3) < D 3 / 2 < PT / 2$
Preferably, D3/2 is greater than 0.4(D5/sin(α0)-R1) and smaller than D5/sin(α0)-R1.
The pitch or distance between the fins can vary between 1.2 and 36 mm.
With regard instead to FZ2, this is a zone with a section which varies between completely constant and completely diverging, with constant and divergent sections alternating with each other and dependent on the mutual position of the tubes 4 and on their shape. The length of the zone FZ2 is extended from 0 up to a line distance of 0.2 mm, with typical range of 0 to 3/4 the line distance. The region between two baffles of two rows of tubes defines a further channel that has a section which can be a combination of straight, converging and diverging sections so as to guide the flow (there could be a line offset with the tube that is in the middle). Each section will have a length comprised between 0 and the overall length of the baffle.
A fin 1 according to the present invention can then have a smooth surface or so-called "w_vaffle", "pyramid" or "turbulence" surface. Such fin can also have an edge so-called "cap-like" or "smooth".
The fin 1 could be made of any suitable material, e.g. aluminum, aluminum alloys, copper, copper alloys, steel, stainless steel made of different alloys, such as AISI 304, AISI 316, etcetera.
In addition, the fin 1 could be finished with surface treatments, e.g. painting, cataphoresis or other treatments.
With reference now to figure 7, a finned pack 10 is illustrated according to the present invention for heat exchangers, which comprises a plurality of fins 1 according to the present invention, placed in succession one after the other or one alongside the other and substantially parallel to each other. Each fin 1 also has its through holes 3 aligned with the through holes 3 of the other fins 1.
The finned pack 10 then comprises an opening 10a for introducing a second fluid between pairs of fins of the plurality of fins, and an outlet opening 10b for the second fluid between the pairs of fins. The fins 1 have the inlet portions 5a thereof at the introduction opening 10a and the outlet portions 5b thereof at the outlet opening 10b.
In the exchanger, provision is also made for a plurality of tubes 4 inserted in the aligned through holes of the plurality of fins 1, the tubes 4 having a first sector 4a directed towards the inlet opening 10a as well as a second sector 4b directed towards the outlet opening 10b, the fins 1 having the confinement unit(s) 8, 9 around a portion of a second sector of a respective tube 4.
If the finned pack 10 is provided with two or more adjacent and successive fins with drawn portions 2a, then the tip 2a1 of the drawn portions 2a of a plate of one of such fins 1 is fit in the base 2a2 or better yet in the opening defined by the base 2a2 of the drawn portions 2a of an adjacent and successive fin 2.
As already stated above, the facing main faces 6 of two adjacent and successive fins 1 together delimit a respective area of passage or crossing of a second fluid that hits respective sections of tubes 4 inserted in such fins, and such tubes 4 as well as the baffles are extended through the passage areas so as to be hit by the flow of the second fluid.
The finned pack 10 can then comprise an upper tile 10c, a lower tile 10d and in addition at one side, manifolds 10f for the tubes 4, and on the other side forks 10g for transmitting the first fluid between two tubes 4.
If desired, each fin has at least one confinement unit with two through recesses for positioning baffles and each through recess of each confinement unit is aligned with a respective recess of the other fins. In such case, the finned pack 10 also comprises two baffles for each confinement unit, each inserted in a respective series of aligned through recesses of the fins 1, preferably of all the fins of the finned pack 10.
According to such variant, the baffles or bars could constitute a mechanical load-bearing element of the finned pack 10.
In addition, if the baffles delimit an opening 11, the finned pack 10 or better yet the respective heat exchanger could comprise means for feeding a third fluid or the first fluid into the opening 11 of one or more baffles 8, 9. In such case, at the end of the baffles 8, 9, outlets could be provided, along with tubular connection elements between the end of a baffle and a respective end of another baffle. In substance, in such case a circuit can be provided for feeding a third fluid constituted by the baffles connected with each other in series and/or in parallel. Alternatively, the baffles could be connected in series and/or in parallel with each other and with the tubes 4, such that baffles and tubes would be fed with the first fluid.
Alternatively, the opening 11 could be simply placed in communication with the outside without providing for feeding the first or a third fluid within the same.
The tubes 4 of a finned pack 10 could be made, for example, of copper and its alloys, stainless steel and its alloys, iron and its alloys, aluminum and its alloys or other suitable materials.
The tubes could also have an internal wall that is smooth, grooved, e.g. tilted grooved, helical grooved or grooved with cross spirals.
The tubes could then have a diameter between 4 and 90 mm, advantageously between 5 and 22 mm, preferably 5 mm, 6.35 mm, 7.2 mm, 7.9 mm, 9.5 mm, 12 mm, 14, 16 mm or 22 mm.
The thickness of the tubes instead preferably varies between 0.15 and 3 mm, and, still more preferably, is equal to 0.25 mm, 0.28 mm, 0.32 mm, 0.35 mm, 0.4 mm or 0.5 mm.
A finned pack according to the present invention can be integrated or installed in:

a condenser, fluid cooler (dry cooler), gas cooler 13 (see figures 8-9), i.e. a machine intended for the heat exchange between a fluid to be condensed (if two-phase) or cooled and the environment, which can employ liquid, aeriform or gaseous coolant fluids;
an evaporator or air cooler, i.e. a machine intended for the heat exchange between a coolant fluid being evaporated/heated and a secondary fluid (air) to be cooled, which can employ liquid, two-phase or gaseous coolant fluids;

As will be understood, a fin and a finned pack according to the present invention allow conveying the second fluid around the entire surface of the holes and hence of the tubes of the fin, also in the zone of each tube that is directed towards the outlet portion.
Indeed, for such purpose, it has been verified that with fins and finned packs according to the state of the art, the second fluid correctly and uniformly hits and affects the part of the tubes directed towards the inlet portion of the fins, but in the zone between the tubes of one row and the tubes of a successive row, the second fluid "detaches" from the external surface of the tubes, hence it does not affect the part of the tubes directed towards the outlet portion of the fins. Naturally, this involves a considerable reduction of the heat exchange efficiency since most of the external face of the tubes crossed by the first fluid is not in heat exchange contact with the second fluid.
Due to the confinement units of a fin according to the present invention and of a respective finned pack, the second fluid is instead actually guided and maintained close to the tubes even in the zone downstream thereof, so as to affect and place the second fluid in heat exchange with the entire external face of the tubes and the portion of the fin 2 downstream of the tube 3, considerably improving the obtainable heat exchange efficiency.
In order to demonstrate the capacities and advantages obtainable by means of a fin according to the present invention, hereinbelow the heat conduction in general and then through the same fin will be analyzed.
As can be understood, in order to facilitate the cooling and the heating of the fin surfaces, baffles have been proposed that are intended to be licked by a fluid current (e.g. air), which are provided with the same object of increasing the thermally active surface and, hence, reducing the overall thermal resistance of the fin.
Such solution addresses a thermo-fluid-dynamic problem that has two aspects:

conduction through the baffles;
convection between the surface of the baffles and the fluid or second fluid.

First, with regard to the conduction through the baffles, the base of the baffles, in particular when the same are obtained by means of drawing of a plate, is in direct contact with a surface (the plate 2) at high temperature, T_w, while the lateral skirt thereof is hit with a fluid current (second fluid) that is cooler, which maintains the surface of the skirt of the baffles at a temperature T_m(x) lower than that of the hot body (main body of the plate 2) and variable as a function of the distance x from the body itself. This temperature difference causes a conductive heat flow, qx(cond), through the base of the baffles: $q_{x (cond)} = - k \frac{δT}{δx}$
which assumes the form $q_{x (cond)} = - k \frac{δθ}{δx}$
wherein θ=T(x)-T_α is the temperature difference between baffle and fluid.
The energy that, in this manner, enters within the baffles is removed via convection through the lateral skirt and the terminal surface thereof. The convective heat flow can be evaluated with the following expression:
From the comparison of the above-reported expressions, it will be understood that the problem of the conductive flow is of greater interest, so that the problem desired to be resolved is that of finding a geometry that optimizes this heat exchange.
Having considered the geometric complexity of baffles or recesses for a fin according to the present invention, for a more thorough and complete description, three zones are identified that are indicated FZ0, FZ1 and FZ2, in which FZ0 is the initial flow zone around a tube 4 before or upstream of the inlet portion 8a, 9a or of the first flow zone FZ1.
With reference to the zone FZ0, the part relative to the problem of the separation of the limit layer will be discussed; such problem is manifested at about the maximum radius (diameter) of the cylinder or tube 4 hit by the flow. As widely documented in fluid mechanics, when a tube is hit with a flow, a flow dead zone is determined that is characterized by a region of stationary recirculation, which is formed downstream of the tube itself, thus allowing the complete separation of the dynamic flow at the geometric region affected by the vortical-stationary recirculation.
With reference to the two tubes 4 of a fin illustrated in figure 2, indicating as the first "Tube 1" that on the right in the figure and "Tube 2" that on the left in the figure, the flow of the second fluid after having hit tube 1 is once again stabilized after having exceeded the domain due to the stationary recirculation, by linking with the front part 4a of a successive cylinder or tube placed in another line or successive line (Tube 2). Hence, the dead zone downstream of tube 1 licked by the stationary recirculation unequivocally deteriorates the convective heat transfer between the second fluid and the first fluid that crosses tube 1.
With reference to the second flow zone FZ2, the geometric role performed by the thermo-fluid-dynamic flow baffles (in passive or active mode, i.e. without or with opening 11) will instead be described as a new solution for reducing the stationary recirculation (dead zone) so as to increase the transfer of convective heat.
Finally, with reference to the first flow zone FZ1, the assembly of the three zones will be described as well as the thermo-fluid-dynamic solutions brought thereby.
The increase of the heat convection essentially regards the study of the heat exchange between a solid surface and a fluid that is moving with respect thereto.
For such purpose, considering the tube 1 on the right in figure 2 as a two-dimensional cylindrical geometric surface correlated with a pair of fluid- dynamic baffles 8, 9, the characteristics and the function of such baffles determine the working mode of the fin and hence of a respective exchanger.
As a consequence of the particular geometry of the baffles, part of the flow that licks the tube 4 and the baffles 8, 9 will be obliged to be channeled along the "trajectory/conduit" generated or defined therebetween.
Due to the viscosity of the second fluid, the more the second fluid channeled into the trajectory/conduit approaches the wall of the tube 4 or of the baffles 8, 9, the more the fluid-wall relative speed decreases (but the total speed does not decrease, rather this is increased), until it is nearly canceled at the wall interface, where a sudden structural change is geometrically generated in the system of fluid-dynamic baffles such to determine an increase of the useful heat exchange section, with corresponding and consequent decrease of the speed and increase of the pressure of the second fluid.
In light of the latter consideration, it is clear that between the walls defined by the particular geometry (trajectory/conduit), there is a clear increase of the heat conduction, due to the increase of the heat exchange surface areas (baffles) and, if desired, also due to the increase of speed if the section is converging (with consequent decrease of pressure that can therefore be rebalanced as a function of the load loss caused by the conduit converging downstream of the diverging section of the tube/baffles system) generated by the walls of the tube/baffles conduit, which determines a separation of the fluid thread much further downstream of the tube, thus considerably decreasing the vortex of stationary recirculation downstream of the tube itself.
This therefore translates into a further increase of the useful heat exchange between the geometric structures (tube/baffles). The outlet section of the baffles is designed so as to determine a realignment and directional linking of the exiting flow with the tube of the successive line, in such a manner exploiting the increase of pressure generated in the section with possible divergence.
It should also be underlined that the temperature gradient that appears in the equation q = Aq̈ = hAΔT(1'), proportional to the quantity of heat removed from or transferred by the fluid, depends on the macroscopic motion of the fluid itself. For this reason, it is clear in this geometric case that it is necessary to use the equations of fluid-dynamics together with the principle of energy conservation in describing the phenomenon of convection.
In addition, the type of fluid motion has such an effect on the heat exchange that it is possible to obtain various convection types. In particular, in the present description, the presence of forced convection will be considered.
In the modality of convective exchange between tube 4 and baffles 8, 9 in passive mode (i.e. without hole or opening 11 in the baffles), the relation commonly employed for expressing the heat flow is indicated in (1'), in which the specific heat flow q̈ is proportional to a suitable temperature difference ΔT between flow and wall (naturally, both in the passive case - lack of openings 11 in the baffles system - and in the active case - presence of openings 11 in the baffles - the temperature difference ΔT considerably changes as a function not only of the presence/absence of the openings 11 in the baffles, but also as a function of the geometry thereof, also taking under consideration the fact that the baffles do not necessarily have internal/external symmetry, i.e. between the internal part or intrados, e.g. converging/diverging, and the external part or extrados, e.g. linear part of the baffles).
The equation (1') is known as Newton's Law and the proportionality constant h[W/(m²K)] is termed coefficient of convective heat exchange or, more simply, convective coefficient. It is considered that h, unlike the heat conductivity, is not a thermo-physical property of the fluid, but it should be considered as an "easy" operating definition, useful in evaluating the quantity of heat exchanged in a convective manner.
Another dimensionless ratio of considerable importance in the description of the particular geometry of baffles in passive mode, employed for convective heat exchange, is the Nusselt number, Nu, which represents the ratio between the convective heat flow and the conductive heat flow in the fluid. In order to determine the mathematic expression, a fluid layer is considered with thickness L and moving with respect to a solid wall.
Given the considerable complexity of the calculation for describing the phenomena affected by the particular geometry, work will be mainly conducted in ideal and symmetry mode only in the geometric part where such symmetry exists between tube and baffles, and passive mode (absence of openings in the baffles). The presence of the opening 11 in the baffles considerably complicates the calculation, given the possibility to generate not only different temperature gradients between the walls of the tube conduit/baffles, but also different densities before and after the constancy/convergence/divergence system, with the consequence that for a correct development of the calculation, average quantities must be used as a function of the geometry of the considered system.
In this situation, only the geometric part of the system in passive mode will be analyzed, hence with baffles without openings 11.
Hence, we assume that the second fluid placed at distance L from the solid surface (tube conduit/baffles), at temperature T_p, is at temperature T_∞. As already seen above, the heat flow can be expressed by means of the equation q = Aq̈ = hAΔT as:
If the fluid layer was (macroscopically) immobile, there would also be conduction and the specific conductive heat flow could be expressed, by means of Fourier's law, as: $\ddot{q} (cond) = \frac{k}{L} (T_{p} - T_{\infty})$
From the definition of Nusselt number $Nu ≜ \frac{\overset{..}{q_{conv}}}{\overset{..}{q_{cond}}} = \frac{hL}{k}$
Therefore, a high value of the Nusselt number, Nu, indicates a high efficiency of the convective process of heat exchange with respect to the merely conductive heat exchange of the fluid. As already stated, the fluid adheres to the wall and, then, in proximity thereto there is also conduction. For this reason, the specific convective heat flow can also be expressed, by means of Fourier's law, as:
Combining the equations (4') and (5'), one obtains: $Nu = \frac{hL}{k} = \frac{- (\frac{δT}{δy})}{Δ T} per y = 0$
from which it is inferred that the coefficient of convective heat exchange, h, depends on the temperature gradient of the wall fluid (in our case, the coefficient of heat exchange depends not only on the previously claimed conditions, but also on the nature of the structural material of the device used for the heat exchange).
As previously stated, the forced convection used in the tube/baffles system subjected to technical/analytical description assumes the existence of a fluid in relative motion with respect to a solid surface. As a function of the geometry of the latter, it is possible to make a distinction within the forced convection. Indeed, it is possible to distinguish between:

forced convection of the external motion;
forced convection of the internal motion, within ducts.

In the present case, there is a partial mixture of both convections, and further calculation difficulties arise therefrom.
Such classification is important since the different parameters characterizing the system (e.g. the Reynolds number, Re) assume different expressions in the two cases.
In the external outflows (i.e. those which pass outside the baffles or the extradoses thereof), for example, the motion of the fluid occurs in an unlimited region (or one that approaches this), around or in proximity to a solid surface. Usually, in this case, it is assumed that the speed µ_∞, and the temperature T_∞ of the fluid in the undisturbed region are known. The temperature difference that appears in the expression q = Aq̈ = hAΔT must in this case be assumed as equal to: $Δ T = T_{p} - T_{\infty}$
while the Reynolds number, Re, is defined as: $Re ≜ {Re}_{x} = \frac{u_{\infty}}{v}$
With regard to the internal outflows (e.g. within a duct or within the region that comprises the first FZ1 and the second FZ2 flow zone), the temperature difference of the equation (1') is assumed equal to: $Δ T = T_{p} - T_{b}$
Where T_b is the so-called bulk temperature or average temperature. The latter is also termed mixing cup temperature, since it is the temperature which would be obtained by placing the entire fluid in an adiabatic container and mixing so as to eliminate any thermal gradient. This is very important in the internal outflows since there is no analogous undisturbed temperature T_∞.
The bulk temperature in a given section of the duct is defined as in equation 5: $T_{b} ≜ \frac{\int_{A_{s}} ρ {uc}_{v} {TdA}_{s}}{\dot{m} c_{v}}$
If it is set that the fluid is incompressible, (in the case of air, the fluid is compressible, but we can use the assumption of incompressibility given the operating conditions involved) and the physical properties are known and constant, equation 5 becomes: $T_{b} ≜ \frac{\int_{A_{s}} {uTdA}_{s}}{\dot{V}}$
In the case of constant heat flow, after a first zone, termed of heat development, the difference between wall temperature and average temperature is maintained constant. However, in the case of constant wall temperature, the average temperature tends asymptotically to become that of the wall.
Regarding the Reynolds number, Re, this is defined: $Re ≜ {Re}_{D} = \frac{u_{m} D_{h}}{v}$
wherein

u_m is the average speed of the fluid,
v is the kinematic viscosity of the fluid, and
D_h is the hydraulic diameter defined as: $D_{h} ≜ \frac{4 A}{P}$
wherein with A it is intended the area of the section of the duct with wet perimeter P. Other aspects that distinguish the two types of forced convection are the formation and development of the speed and thermal limit layers.

First of all, one considers an external outflow such as that of a fluid on a flat surface. The distance δx from the flat wall in orthogonal direction y is termed thickness of the limit layer and is defined as that value for which there is: $u_{y} = 0.99 u_{\infty}$
where

u_y is the speed of the fluid at distance y from the wall which increases with the increase of x.
uoo is the speed of the undisturbed fluid

The quantity δt is termed thickness of the thermal limit layer and is defined as that value of y for which one has: $\frac{T_{p} - T_{(y)}}{T_{p} - T_{\infty}} = 0.99$
If the wall temperature T_p is constant and independent from x, the thickness of the thermal limit layer increases with the increase of x. As a consequence, the temperature gradient along y progressively decreases in moving away from the leading edge of a plate or sheet. Therefore, the coefficient of convective heat exchange h, and hence the heat flow q̈, decrease with the increase of x. In the case of internal outflows, the presence of the border surfaces conditions both the formation and the shape of the speed and thermal limit layers, and in this motion type it is possible to identify two regions: that of the inlet, where the motion is not developed, and that where the motion is completely developed. It is necessary at this point to better specify what is intended by completely developed motion.
Considering the inlet speed profile to be uniform, as soon as the fluid enters into a channel, the particles closest to the wall delimiting such channel undergo, due to the viscosity of the fluid, a deceleration while the particles at the center of the channel, in order to maintain the flow rate constant, are accelerated. In such a manner, two limit layers are formed which tend to be thickened along the direction of the motion and that, if the distance L between the plates defining the channel is not high with respect to the length of the channel, are joined together at a certain distance x_v from the inlet edge. After this point, a parabolic speed distribution is created, typical of the fully developed laminar profile of Couette motion, which no longer varies with the increase of the distance on the inlet edge.
The distance x_v is termed length of dynamic development or theoretical initial length, and it can be evaluated with different empirical formulas, such as the following $\frac{x_{v}}{D} = 0.0575 Re$
due to Langhaar:
valid for ducts of circular section with diameter D and for Reynolds numbers less than 2300.
With regard to the heat field, the entering fluid is at the uniform temperature T while the walls can be considered at the uniform and constant temperature T_p and subject to a constant heat flow q̈.
In such case, as the fluid proceeds along a duct, a thermal limit layer is formed, in proximity to both interfaces, which is identical to that of the isolated profile. Nevertheless, continuing in the sense of the motion, these two tend to be thickened until they are joined at a distance x_t, from the inlet edge, which is termed thermal development length, and finally defined as that distance from the inlet for which the Nusselt number differs by 5% from the value corresponding to the developed thermal operating conditions.
In laminar operating conditions, the value of xt depends on the thermal conditions at the wall and can be evaluated with the empirical expression 12, in the case of assigned wall temperatures, and 13, in the case of imposed heat flow. $\frac{x_{t}}{D_{h}} = 0.033 {Re}_{D_{h}} \Pr$
$\frac{x_{t}}{D_{h}} = 0.045 {Re}_{D_{h}} \Pr$
The Prandtl number, $\Pr = \frac{ν}{α} = \frac{c_{p} μ}{k},$
can assume values that are extremely different from each other based on the type of fluid selected. This dimensionless group is given by the ratio between the molecular properties of transport of the quantity of motion and heat and can be interpreted as the ratio between the thermal limit layer and the thermal viscous layer. If the Prandtl number, as with air, is close to one, then the two development lengths are of the same order of magnitude. If however it is much lower than one, the length of fluid-dynamic development is much greater than the thermal length. Indeed, in this case the transmission of heat is so efficient that the problem may sometimes be treated as a merely conductive one (case of liquid metals).
Finally, if the Prandlt number is much greater than one, or the viscosity of the fluid is very high, the fluid-dynamic limit layer is much thicker than the thermal limit layer.
From that stated above, it is observed that the temperature, unlike the speed, continues to vary with the increase of the distance from the inlet edge of the baffle. This would lead to the assumption that it is impossible to attain condition of complete development. Nevertheless, if one considers the dimensionless ratio (which can be considered a dimensionless temperature): $\frac{T_{p} - T}{T_{p} - T_{b}}$
it can be demonstrated that, in suitable conditions, this becomes independent from x. It can be verified that, even if the temperature T varies along the duct, the shape of its profile in the channel remains constant. In these conditions, then, one can speak of complete thermal development, and there is: $\frac{δ}{δx} [\frac{T_{p} - T}{T_{p} - T_{b}}] = 0$
Since, according to equation 15, the ratio between the temperature differences is independent of x, the same must hold true for its derivative with respect to y. In addition, by evaluating the aforesaid derivative in proximity to the wall and recalling that T_p and T_b are by definition independent from y, one obtains: $\frac{δ}{δx} [\frac{T_{p} - T}{T_{p} - T_{b}}] = \frac{- \frac{δT}{δy}}{T_{s} - T_{b}} \neq f (x) per y = 0$
from Fourier's law, one obtains
while from Newton's law $q_{p} = \ddot{h} (T_{p} - T_{b})$
Combining the equations, one obtains $\frac{h}{k} \neq f (x)$
Therefore, in the internal outflows, in conditions of complete thermal development, for a fluid with constant physical properties, the local convective coefficient is constant and independent. Given that the Nusselt number, Nu, is strictly tied to the convective coefficient, the length of thermal development can also be defined as that distance from the inlet edge for which the Nusselt number differs by 5% from the value corresponding to the developed thermal operating conditions.
Therefore, a solution with passive baffles, hence without openings 11 (see figure 2) determines:

a reduction of the dead zone (region in which the fluid does not wet the tube), with consequent increase of the heat exchange efficiency; given the same number of tubes, there can be an increase up to a theoretical maximum of the exchange surface area of about 50%;
an optimization of the flows within the exchanger and improved exploitation of the fluid flow, since the second fluid is channeled and conveyed on the walls of the tube, minimizing the paths that do not have heat exchange;
an increase of the exchange surface areas if there is a fin/baffle thermal contact, with consequent increase of the exchange and hence of the efficiency;
an increase of the efficiency since there is an increase of the convective exchange in the duct or flow zones created by the baffle.

The increase of performances is obtained with a marginal increase of the expenses necessary for the creation of the baffles, which can be obtained by means of fitting of the surfaces directly drawn from the surface of the existing fin.
In the case of baffles with drawn portions, the increase of the exchange surface area is in any case ensured and the geometry of the duct (and hence the shape of the baffle) can be reproduced with high accuracy.
The improved situation with the technical solution of figure 2 can be further optimized by employing an active strategy with regard to the baffles, i.e. by providing for baffles with openings 11.
In the case of baffles without openings, the baffles behave as passive elements, since their temperature is determined by the situation of equilibrium that is created between the heat transferred from the fin and that exchanged with the fluid. In such case, the baffles 8, 9 have the double function of increasing the exchange on the main tube 4 and increasing the total surface area of heat exchange of the fin.
The calculations are possible in the case of passive baffles, since the boundary conditions for the heat transmission differential equation are simple (uniform temperature given by the conduction through the baffles).
An increase of efficiency of the system can be obtained if the baffles are no longer employed only for deflecting the flow and increasing the exchange surface area, but also for increasing the forced exchange of heat. According to the solution of figure 5, two further channels or openings 11 are created, for which there can be the following possible use solutions:

a) no fluid within the channels, i.e. the first fluid; in such case, it is possible to exploit, in the case of natural convection, the stack effect created within the channels in order to have a passive exchange, in any case surely more efficient than the exchange given by just the fins;
b) fluid within the channels 11 equal to the fluid within the tubes 4, with temperature equivalent or different;
c) fluid within the channels 11 different from that within the tubes 4, with temperature equivalent or different between such fluids.

The proposed system has various applications.
An application of type c) with fluid in the channels 11 different from that of the tubes 4 is obtained in the applications of cooling the second fluid by means of a first fluid moving within the tubes 4. In such case, in particular when the temperature of the second fluid falls below 0°C, there is the formation of frost or ice around the tube 4 and on the fins 2. In order to remove such formation of frost or ice, so to prevent reducing the heat exchange, various systems are used including the presence of rod-like electrical heating elements suitably inserted between the tubes 4 in suitable holes created in the fins 2, or by means percolation systems for percolating water at suitable temperature, higher than 0°C, from the upper part of the exchanger, or by means of cycle inversion, in the case of the evaporators, by making hot gas condense within the tubes 4 or by passing water suitably mixed with compounds adapted to lower the cryoscopic point of the mixture itself within the tubes 4. Within baffles 8-9, a fluid at suitable temperature can then be passed that can operate the defrosting of the tubes 4 and fin 2 in a localized manner, with the advantage of:

operating defrosting in a dedicated circuit without having to modify the circuit of the first fluid within the tube 4;
increasing the efficiency of the defrosting, given that the defrosting circuit is potentially localized in proximity to all the tubes 4;
having the possibility of regulating the defrosting power as a function of the zone to be defrosted (i.e. where there is a greater formation of frost or ice).

If the fluid within the channels 11 is different from that in the tubes, consequences are not obtained from the operating or functional standpoint with respect to the case in which the fluid is the same, unless the temperature in the tubes 4 and in the channels 11 is different. Hereinbelow, the temperature difference between the fluid in the tubes and that in the channels will be considered, all considerations remaining valid whatever the fluid used.
In case a), the calculations exactly follow the same line traced for the system with baffles of passive type, since the boundary conditions are the same.
In such case, there is the possibility of a second heat exchange within the channels 11 (in free convection) which could lead to an increase of efficiency of the system due to the stack effect, that could naturally lead to a further fraction of heat outside the exchanger. The Nusselt number is no longer a function of the Reynolds number since the air present within the channels 11 has zero or in any case negligible speed, while the floating forces are those which start to play a fundamental role.
In cases b) and c), the complication in the calculation of the heat exchange is provided by the boundary conditions which in this case provide for the internal surface of the baffle at a new constant temperature T_d with respect to the rest of the exchanger. Once again, there is a conductive exchange between tube 4 and baffles 8, 9 and there is a forced convective exchange between tube 4 and second fluid, but in this case the temperature is no longer constant within the channel 11 and uniform at the edges. A temperature gradient is established in the duct between the walls of the tube+fin and that of the baffle at different temperature. There is an asymmetry of the temperature field and, consequently, of those of density and speed. The two cases b) and c) provide different (and symmetric) solutions in accordance with the sign of the temperature difference between channels 11 and tube 4. The simplification proposed for the passive case can be employed herein if the temperature differences are small.
We assume, as a first case, that the temperature of the fluid within the channels 11, and consequently T_d, is lower than that of the wall of the tube T_p. In such case, the conductive heat flow will lead to an elimination of the heat from the tube 4 towards the $q_{x (cond)} = - k \frac{δT}{δx}$
baffle, which increases with the increase of temperature gradient that one is able to establish. The system will function as a double-flow exchanger in which the transfer of heat between the two fluids (in the tube 4 and in the channels 11) occurs via pure conduction. Together with this conduction, however, we also have the convective part within the flow zones created by the baffles. The calculation complication is given by the boundary conditions which depend on the conduction equation. The thermal gradient that is established leads to having a complex temperature field, determined by the two wall temperatures, by their thermal connection and by the temperature of the fluid which passes inside the channels.
In order to compare the problem of the exchange, we have the possibility to execute some approximations. We can reasonably assume that due to the temperature gradient, the fluid carries out two independent heat exchanges with the two surfaces (in realty, there is a further exchange with the fin, which we can consider similar to that of the passive case or that without the baffles). Indeed, in laminar operating conditions, the duct can be divided into two semi-ducts in which the (undisturbed) temperature end point is not reached at the center line, but at a distance from the walls proportional to the temperature difference between wall and fluid. The point will be situated closer to the colder wall than from the warmer wall. In a first approximation, we can therefore consider the two exchanges independent, treating them with the formalism proposed for the passive baffle. The movement of the thermal well from the center line towards the colder wall uses a greater quantity of fluid for the heat exchange, thus increasing the machine output.
The system can then be employed for any type of exchanger. In particular, each tube of an existing geometry can be substituted with the tube+baffles assembly. From the structural standpoint, the system can be easily made by means of cutting and drawing the existing fin so as to create a continuous and load-bearing system of channels for the structure.
Therefore, a solution with active baffles, hence with openings 11 (see figures 5 and 6) determines:

a reduction of the dead zone, with consequent increase of the heat exchange efficiency, this being obtained due to the presence of the baffles 8, 9, independent of the auxiliary function thereof;
an increase of the efficiency since there is an increase of the convective exchange in the duct 11 created by the baffles 8, 9;
an optimization of the flows within the exchanger and improved exploitation of the fluid flow, since the fluid is channeled and conveyed on the walls of the tube and the paths which do not have heat exchange are minimized;
a more effective transfer of heat from the tube 4 towards the fluids which circulate in the system (in the flow zones and within the baffles), in particular when the temperature of the fluid in the baffle is lower than that of the tube;
an increase of the output due to the greater surface areas of heat exchange, if the temperature in the tubes 4 and in the baffles 8, 9 is the same, for example if the same circuit supplies both the tubes 4 and the channels 11; and
an increase of the performances, even if there is the structural requirement to construct a secondary circuit.

Modifications and variations of the invention are possible within the protective scope defined by the claims.

Claims

Fin for a finned pack (10) for heat exchangers, comprising a plate (2) in which a plurality of through holes (3) is obtained for the positioning of tubes (4) intended to convey a first heat exchange fluid, said plate (2) having an edge (5) as well as two main faces (6) each intended to be licked by a second heat exchange fluid in a crossing direction (A-A) from an inlet portion (5a) to an outlet portion (5b) of said edge (5) of said plate (2), said holes (3) being delimited by a respective inner delimiting wall (7) of said plate (2) including a first portion (7a) facing towards said inlet portion (5a) and a second portion (7b) facing towards said outlet portion (5b), said fin comprising at least one confinement unit (8, 9) of said second fluid arranged around a hole (3) of said plurality of holes (3) so as to obtain at least one partially surrounded hole (3), said at least one confinement unit comprising two baffles (8, 9) or two through recesses for housing baffles (8, 9) arranged one opposite the other with respect to a respective partially surrounded hole (3) as well as each surrounding and spaced from a respective section of said second portion (7b) of said delimiting wall (7) of said partially surrounded hole (3), so as to confine, during use, on said plate (2) a first flow zone (FZ1) of said second fluid between each baffle (8, 9) or recess and a respective section of said second portion (7b) of said delimiting wall (7),
wherein said first flow zone (FZ1) has section, evaluated with reference to a plane orthogonal to said plate (2) and passing through the center or central point of the respective partially surrounded hole (3), that is
constant for the entire extension thereof,
constant and then diverging,
converging for the entire extension thereof,
converging and then diverging,
constant and then converging, or
constant, then converging and finally diverging,
and wherein the intrados (8h, 9h) of said baffles (8, 9) or said recesses along said first flow zone (FZ1), i.e. the section of said baffles (8, 9) or recesses facing towards or facing the respective partially surrounded hole (3), comprises a curved or substantially curved surface with concavity facing towards said first flow zone (FZ1) at the areas with constant and/or converging section of said first flow zone (FZ1), and a curved or substantially curved surface with concavity facing away from said first flow zone (FZ1) itself at the optional areas with diverging section of said first flow zone (FZ1),
characterised in that said baffles (8, 9) have a substantially tubular structure so as to delimit at least one first opening or channel (11).
Fin according to claim 1, wherein said first flow zone (FZ1) does not have stagnation areas, i.e. it does not have first areas with section, evaluated with reference to a plane orthogonal to said plate (2) and passing through the center of the respective partially surrounded hole (3), greater than areas downstream and upstream of said first areas.
Fin according to any one of the preceding claims, wherein by identifying, in a plane orthogonal to the symmetry axis x-x of a partially surrounded hole (3), an initial angle (α0) between an initial axis (S0) parallel to said crossing direction (A-A) and passing through the center or a central point of the partially surrounded hole (3) and a first axis (S1) which extends from the center or central point of the partially surrounded hole (3) to the inlet portion (8a, 9a) of a baffle or recess (8, 9), said initial angle (α0) is between 45° and 135°, preferably between 80° and 100°.
Fin according to claim 3, wherein by identifying, in a plane orthogonal to the symmetry axis (x-x) of a partially surrounded hole (3), a first angle (α1) between a first axis (S1) which extends from the center or a central point of the partially surrounded hole (3) to the first end (8a, 9a) of a baffle or recess (8, 9) and a second axis (S2) which extends from the center of the partially surrounded hole (3) to the point of such baffle or recess (8, 9) defining the termination or end of said section constant, the first angle is between 45° and 135°.
Fin according to claim 4, wherein said first angle (α1) has a value between the value of the initial angle (α0) and 100°.
Fin according to any one of the preceding claims, wherein
if said section of said first flow zone (FZ1) is constant and then converging or constant, then converging and finally diverging, by identifying in a plane orthogonal to the symmetry axis (x-x) of the partially surrounded hole (3) a second angle (α2) between a second axis (S2) which extends from the center of the partially surrounded hole (3) to the point of a baffle or recess (8, 9) defining the termination or the end of the constant section and a third axis (S3) which extends from the center of the partially surrounded hole (3) to the point of such baffle or recess (8, 9) defining the termination or the end of the converging section, said second angle (α2) is between 45° and 180°, whereas
if the section of said first flow zone (FZ1) is converging for the entire extension thereof or converging and then diverging, by identifying in the plane orthogonal a second angle (α2) between a second axis (S2) which extends from the center of the partially surrounded hole (3) to the point of a baffle or recess (8, 9) defining the first end (8a, 9a) of a baffle or recess (8, 9) and a third axis (S3) which extends from the center of the partially surrounded hole (3) to the point of such baffle or recess (8, 9) defining the termination or the end of the converging section, the second angle (α2) is between 45° and 180°, preferably between 45° and 150°.
Fin according to claim 4 and 6 or 5 and 6, wherein said section is constant and then converging or constant, then converging and finally diverging, and wherein said second angle (α2) has a value comprised between the value of said first angle (α1) and 150°.
Fin according to any one of the claims from 4 to 7, wherein
if said section is constant and then diverging, by identifying in a plane orthogonal to the symmetry axis (x-x) of the partially surrounded hole (3) a third angle (α3) between a second axis (S2) which extends from the center of the partially surrounded hole (3) to the point of a baffle or recess (8, 9) defining the termination or the end of the section constant and a fourth axis (S4) which extends from the center of the partially surrounded hole (3) to the point of such baffle or recess (8, 9) defining the termination of the diverging section, the third angle (α3) is between 45° and 180°, whereas
if the section is converging and then diverging or constant, then converging and finally diverging, by identifying in a plane orthogonal to the symmetry axis (x-x) of the partially surrounded hole (3) a third angle (α3) between a third axis (S3) which extends from the center of the partially surrounded hole (3) to the point of a baffle or recess (8, 9) defining the termination of the converging section and a fourth axis (S4) which extends from the center of the partially surrounded hole (3) to the point of such baffle or recess (8, 9) defining the termination of the diverging section, the third angle (α3) is between 45° and 180°.
Fin
according to claim 4 and 8 or 5 and 8, wherein said section is constant and then diverging, wherein said third angle (α3) has a value comprised between the value of said first angle (α1) and 165°, or
according to claim 6 and 8 or 7 and 8, wherein said section is converging and then diverging or constant, then converging and finally diverging, and wherein said third angle (α3) has a value comprised between the value of said second angle (α2) and 165°.
Fin according to any one of the preceding claims, wherein said baffles (8, 9) or said housing recesses are extended beyond a respective partially surrounded hole (3), i.e. said baffles (8, 9) or said housing recesses have terminal sections closer to said outlet portion (5b) with respect to a respective partially surrounded hole (3) and defining a second flow zone (FZ2) constituting a continuation of said first flow zone (FZ1), said second flow zone (FZ2) not extending around said partially surrounded hole (3), said second flow zone (FZ2) having a supply mouth corresponding to the dispensing mouth of said first flow zone (FZ1) as well as a discharge mouth for said second fluid towards parts of said fin subsequent in the direction of said crossing direction (A-A), said second flow zone (FZ1) having a section, evaluated with reference to a plane orthogonal to said plate and passing through the center of the respective partially surrounded hole (3), that is diverging.
Fin according to any one of the preceding claims, wherein the baffles (8, 9) or the housing recesses of a respective confinement unit have a first end (8a, 9a) proximal to said inlet portion (5a), a second end (8b, 9b) distal from said inlet portion (5a) of said plate (2) and wherein the distance between said baffles (8, 9) or said recesses in the direction moving away from the inlet portion (5a) initially progressively decreases and then, once a minimal value has been reached at an intermediate portion of said baffles or recesses (8, 9), progressively increases once again up to said second end (8b, 9b).
Fin according to any one of the preceding claims, wherein the extrados (8d, 9d) of said baffles (8, 9) or said recesses, i.e. the section of said baffles or said recesses facing away from the respective partially surrounded hole (3), is substantially rectilinear or slightly curved and does not have depression or stagnation zones for said second fluid.
Fin according to claim 12, wherein said extrados is substantially tilted with respect to said crossing direction (A-A) for an angle between -45° and 45°, with an initial end (8a, 9a) proximal to said inlet portion (5a) and distal from said outlet portion (5b) and a final end (8b, 9b) distal from said inlet portion (5a) and proximal to said outlet portion (5b), the initial ends (8a, 9a) of the extradoses (8d, 9d) of the baffles or recesses of a partially surrounded hole being situated at a distance from each other greater than the distance between the final ends (8b, 9b) of the extradoses (8d, 9d) of such baffles or recesses.
Fin according to claim 12 or 13, wherein each baffle (8, 9) or recess of said at least one confinement unit has intrados (8h, 9h) that is not parallel to the respective extrados (8d, 9d), i.e. the section of the baffles (8, 9) or recesses facing away from the respective partially surrounded hole (3).
Fin according to any one of the preceding claims, wherein said baffles (8, 9) or recesses have a configuration, with reference to the travel direction of said second fluid on said plate (2), with a first section (8e) with constant width, a second section (8f) with increasing width and then a third section (8g) with decreasing width.
Fin according to any one of the preceding claims, wherein said at least one first opening or channel (11) is substantially extended parallel to the symmetry axis (x-x) of the respective hole (3) and is set to allow the passage through the respective baffle and in a direction substantially parallel to said symmetry axis (x-x) of a third fluid or of said first fluid or is set to be arranged in communication with the outside.
Fin according to claim 15, wherein said first opening (11) is delimited at said second (8f) and said third (8g) section or at said first (8e), said second (8f) and said third (8g) section.
Fin according to any one of the preceding claims, wherein said baffles (8, 9) comprise a tubular body with substantially constant thickness.
Fin according to any one of the preceding claims, wherein said baffles (8, 9) comprise at least one drawn portion (2a) of the plate (2), i.e. said baffles (8, 9) are obtained by means of drawing of said plate (2).
Fin according to claim 19, wherein said at least drawn portion (2a) of said plate (2) is tapered moving away from the main extension plane of said plate (2), such that said at least one drawn portion (2a) has a free end or tip (2a1) with lower width than its base or end (2a2) for constraining to the plate (2).
Finned pack for a heat exchanger, comprising:
- a plurality of fins (1) according to any one of the preceding claims arranged in succession one after the other and substantially parallel to each other, each fin (1) having its through holes (3) aligned with the through holes (3) of the other fins (1);

- a introduction opening (10a) for introducing a second fluid between pairs of fins (1) of said plurality of fins (1), said fins (1) having their inlet portions (5a) at said introduction opening (10a);

- an outlet opening (10b) for said second fluid between said pairs of fins (1), said fins (1) having their outlet portions (5b) at said outlet opening (10b);

- a plurality of tubes (4) fitted in the aligned through holes (3) of said plurality of fins (1), said tubes (4) having a first sector (4a) facing towards said inlet opening (10a) as well as a second sector (4b) facing towards said outlet opening (10b); and
said fins (1) having a confinement unit (8, 9) around a portion of a second sector (4b) of at least one of said tubes (4).
Finned pack according to claim 21 when provided with at least two adjacent and successive fins according to claim 20, wherein said tip (2a1) of the drawn portions (2a) of a plate (2) is fitted in the base (2a2) or better yet in the opening defined by the base (2a2) of the drawn portions (2a) of an adjacent and successive fin (2).
Heat exchanger with finned pack comprising at least one finned pack according to claim 21 or 22.