Patent Publication Number: US-2019195564-A1

Title: Heat exchanger

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority under 35 U.S.C. § 119 to Korean Patent Application No. 10-2017-0172756, filed on Dec. 15, 2017 and Korean Patent Application No. 10-2018-0154915, filed on Dec. 5, 2018, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference in its entirety. 
     TECHNICAL FIELD 
     The following disclosure relates to a heat exchanger, and more particularly, to a heat exchanger operated in a high-pressure environment and including a tube which is manufactured according to an extrusion method and optimized in pressure resistance and heat transfer performance. 
     BACKGROUND 
     A heat exchanger is a device for generating heat exchange between a working fluid and a surrounding environment such as ambient air and other fluids. Generally, a widely used heat exchanger includes a flow channel through which a working fluid passes and a tube including a tube wall for heat transfer to an external medium (fin, or the like). In the configuration of the heat exchanger, a plurality of tubes are generally arranged in parallel and fins are provided between the tubes to improve heat transfer performance. 
     The heat exchanger tubes generally each have a shape of a flat pipe, in which the fins are brazed to be coupled to the outside of the flat surfaces of the tubes, respectively. Such heat exchanger tubes may be formed in a variety of ways. For example, a method of bending a thin metal plate and joining the ends is commonly used. However, in the case of the tubes formed in the above-described manner, if a working fluid in the heat exchanger tubes flows at a high pressure, stress may be concentrated on a joint portion to break the joint portion, causing a problem of leakage of the working fluid. Thus, a high-pressure heat exchanger generally uses tubes formed according to an extrusion method that does not cause a joint portion. 
     An extruded tube may be easily manufactured to have a cross-section having a complicated shape, as compared with a tube manufactured in a plate bonding manner. Thus, the extruded tube is easier to manufacture to have a cross-section having a complicated shape, as compared with a tube manufactured according to a plate bonding scheme. Thus, in order to further enhance heat transfer performance in a flow channel in the tube, in the case of the extruded tube, a design of forming a plurality of partitions (hereinafter, referred to as ‘inner walls’) in a flow channel (i.e., tube inside space) is introduced in many cases. In this manner, the area of the tube inside space in contact with a working fluid (refrigerant) is increased to increase an amount of heat transferred from the working fluid to the tube, resultantly increasing heat transfer performance. 
     However, if too many inner walls are formed in the tube flow channel (that is, if too many holes are formed), a flow rate of the working fluid itself may be reduced to rather degrade heat transfer performance. In order to avoid such a problem, a design for reducing a thickness of the inner wall may be introduced. In this case, if the inner wall is too thin, the inner wall may burst due to internal pressure of the working fluid and design performance may not be realized. Also, if the thickness of the inner wall is too thin, substantial manufacturing itself is difficult. 
     In consideration of such various factors, it is necessary to maximize heat transfer performance in the inner wall thickness, the outer wall thickness, and the number of holes of the extruded tube, and at the same time, to have an optimal design satisfying appropriate pressure resistance and manufacturing characteristics. As an example of a technique for presenting such a design, Japanese Patent Laid-Open Publication No. 2007-093144 (“Heat Exchanging Tube and Heat Exchanger” published on Apr. 12, 2007) discloses a technique of limiting numerical values regarding various sizes of an extruded tube to maintain stiffness against an external impact, while ensuring heat transfer performance. Also, Japanese Patent Laid-Open Publication No. 2016-186398 (“Heat Exchanging Tube and Heat Exchanger Using the Heat Exchanging Tube” published on Oct. 27, 2016) discloses a technique regarding a shape and a size of an extruded tube capable of enhancing manufacturing characteristics, while ensuring a light weight. 
     However, there is a continuing need for an optimized design of a more systematic heat exchanger which may be easily applied to tubes of various sizes, while satisfying all of the heat transfer performance, pressure resistance, manufacturing characteristics, and the like, as desired. 
     RELATED ART DOCUMENT 
     [Patent Document] 
     1. Japanese Patent Laid-Open Publication No. 2007-093144 (“Heat Exchanging Tube and Heat Exchanger”, 2007 Apr. 12) 
     2. Japanese Patent Laid-Open Publication No. 2016-186398 (“Heat Exchanging Tube and Heat Exchanger Using the Heat Exchanging Tube”, 2016 Oct. 27) 
     SUMMARY 
     An embodiment of the present invention is directed to providing a heat exchanger having an optimal design satisfying appropriate pressure resistance and manufacturing characteristics, as well as maximizing heat transfer performance in an internal wall thickness, an outer wall thickness, and the number of holes of an extruded tube. Another embodiment of the present invention is directed to providing a heat exchanger having an optimal design formed based on a more systematic rule so as to be easily applied to tubes of various sizes. 
     In one general aspect, a heat exchanger includes: a pair of header tanks formed in parallel and spaced apart from each other by a predetermined distance; a plurality of tubes fixed to the pair of header tanks at both ends to form a flow channel of a refrigerant; and a fin interposed between the tubes, wherein the plurality of tubes are extruded tubes, and when each tube is formed such that a tube width is greater than a tube height and a flow channel in the tube is divided into a plurality of holes formed in parallel of the tube in a width direction by a plurality of inner walls extending in a height direction of the tube, the tube width, an outer wall thickness at an end portion of the tube in the width direction, a hole width, and an inner wall thickness have a size within a range in which the following formula is satisfied: 
       2.5&lt; A/B&lt; 4  Formula 1:
 
       0.07&lt; B&lt; 0.2 (mm)  Formula 2:
 
       0.2&lt; Tw ( A+B )/( Tw− 2 Tn )&lt;0.6 (mm)  Formula 3:
 
     (Here, Tw: tube width, Tn: outer wall thickness at end portion of tube in width direction, A: hole width, B: inner wall thickness). 
     Also, in the heat exchanger, a plurality of louvers may be formed on the fin, and the hole width, the inner wall thickness, a louver pitch may have a size within a range in which the following formula is further satisfied: 
         A+B&lt;Lp   Formula 4:
 
     (Here, A: hole width, B: inner wall thickness, Lp: louver pitch). 
     Also, in the heat exchange, the inner wall thickness B may have a size within a range in which the following formula is further satisfied: 
       0.1 &lt;B &lt;0.18 (mm).  Formula 2-11:
 
     Or, more preferably, in the heat exchanger, the inner wall thickness B may have a size within a range in which the following formula is further satisfied: 
       0.07 &lt;B &lt;0.18 (mm).  Formula 2-12:
 
     Or, in the heat exchanger, the inner wall thickness B may have a size within a range in which the following formula is further satisfied: 
       0.1 &lt;B &lt;0.15 (mm).  Formula 2-21:
 
     Or, more preferably, in the heat exchanger, the inner wall thickness B may have a size within a range in which the following formula is further satisfied: 
       0.07 &lt;B &lt;0.15 (mm)  Formula 2-22:
 
     The plurality of tubes may be formed of aluminum. 
     Other features and aspects will be apparent from the following detailed description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view of a general fin-tube heat exchanger. 
         FIG. 2  is a top view of an extruded tube and a louver-pin combination. 
         FIG. 3  is a view illustrating definition of each part of an extruded tube. 
         FIGS. 4(A) and 4(B)  illustrate simulation results of a relationship between hole width/inner wall thickness and burst pressure or heat transfer performance. 
         FIG. 5  illustrates simulation result of a relationship between a hole width, the number of inner wall thickness sets and heat transfer performance. 
         FIG. 6  illustrates a range of optimal design conditions for a hole width and an inner wall thickness. 
         FIG. 7(A) to 7(D)  illustrate ranges of optimal design conditions under these additional conditions. 
         FIG. 8  illustrates an area of optimal design condition range smaller than the area illustrated in  FIG. 6 . 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Hereinafter, a heat exchanger according to the present invention will be described in detail with reference to the accompanying drawings. 
       FIG. 1  is a perspective view of a general fin-tube heat exchanger. As illustrated in  FIG. 1 , a typical fin-tube type heat exchanger  100  includes a pair of header tanks  110  formed in parallel and spaced apart from each other by a predetermined distance, a plurality of tubes  120  fixed to the pair of header tanks  110  at both ends to form a flow channel of a refrigerant, and a fin  130  interposed between the tubes  120 . Here, the tube  120  is an extruded tube, which is formed by an extrusion method and does not have a joint. Further, a plurality of louvers  135  may be formed on the fin  130 , and  FIG. 2  illustrates a top view of a combination of the extruded tube and the louver. The heat exchanger  100  may be a condenser, and the tube  120  may be formed of aluminum. 
     In the present invention, an optimal design made by more systematic rules between the sizes of each part of the tube  120  is proposed to enhance performance of heat transfer from a refrigerant to an inner wall of the tube and ensure pressure resistance and manufacturing characteristics through appropriate inner and outer wall thicknesses of the tube. 
       FIG. 3  illustrates the definition of each part of the extruded tube, in which a tube width Tw, a tube height Th, the outer wall thickness Tn at an end portion of the tube  120  in a width direction, a hole width A, and an inner wall thickness B are illustrated. As illustrated in  FIG. 3 , in the tube  120  of the present invention, the tube width Tw is greater than the tube height Th, and a flow channel in the tube  120  is divided into a plurality of holes  122  formed in parallel in a width direction of the tube  120  by a plurality of inner walls  121  extending in a height direction of the tube  120 . 
     Condition for Ensuring Pressure Resistance 
     In order to improve performance of heat transfer from a refrigerant to the inner wall of the tube, it is necessary to increase a contact length with the refrigerant at an internal cross-section of the tube through which the refrigerant passes, further, a refrigerant passage sectional area. From this point of view, as the number of the holes  122  increases, as the thicknesses of the inner wall  121  and the outer wall decrease, heat transfer performance may be increased. 
     However, since the refrigerant flowing in the tube  120  has a significantly high pressure, if the inner wall thickness B is too thin, the inner wall  121  may burst. It is known that a maximum operating pressure of the refrigerant flowing in the tube  120  is 25 kg/cm 2 . Here, safety factor is generally 3 to 4 times greater, and thus, when pressure at which the inner wall  121  bursts is burst pressure Pb, the inner wall thickness B may be determined such that the burst pressure Pb is about 85 kg/cm 2 . The inner walls  121  are spaced apart from each other by a space corresponding to the hole width A, and although the inner wall thickness B is the same, pressure resistance increases as the hole width A decreases. Resultantly, pressure resistance may be determined collectively in consideration of the inner wall thickness B and the hole width A, rather than determined by only a single indicator of the inner wall thickness B. 
     In this point of view, it was assumed that a working space in which the pair of inner walls  121  were formed in a space having a height equal to the tube height Th, and a relationship between the hole width A/inner wall thickness B and pressure of the refrigerant flowing in the working space at a point in time when the inner wall  121  is burst, i.e., the burst pressure Pb, was simulated. 
     According to results illustrated in  FIG. 4(A) , the burst pressure Pb tends to decrease as the hole width A/inner wall thickness B increases. Here, the hole width A/inner wall thickness B when the burst pressure Pb corresponds to 85 kg/cm 2  (as described above) is approximately 2.5. Therefore, the hole width A/inner wall thickness B value may be determined to be larger than 2.5. 
     As described above, the pressure resistance is enhanced as the hole width A/inner wall thickness B value increases, but if this value is too large, another problem may arise. Details thereof are as follows. When the hole width A/inner wall thickness B value increases, it means that the inner wall thickness B decreases when the hole width A is fixed or the hole width A increases when the inner wall thickness B is fixed. In particular, when the hole width A excessively increases, the number of holes  122  which may be formed in the single tube  120  may decrease, and in this case, a contact sectional area between the refrigerant and the tube inner wall decreases to reduce heat transfer performance. The ultimate object of the present invention is to maximize heat transfer performance, and thus, the hole width A/inner wall thickness B value must be determined within a range in which heat transfer performance does not deteriorate. 
     From this point of view, a variation aspect of a heat transfer coefficient h over the increase in the hole width A/inner wall thickness B was simulated. 
     As illustrated in  FIG. 4(B) , as the hole width A/inner wall thickness B increases, the heat transfer coefficient h of the refrigerant side (i.e., the inside of the tube) tends to increase and start to decrease at a certain point. Of course, the hole width A/inner wall thickness B at a point where the value of the heat transfer coefficient h at the refrigerant side is maximized may be determined as a maximum value, but in this case, the degree of freedom of design may be excessively limited. Meanwhile, the hole width A/inner wall thickness B value at a point where the heat transfer coefficient (h) at the refrigerant side is about 75% of the maximum value is about 4. Actually, the heat transfer coefficients h at the refrigerant side (i.e., the inside of the tube) in a general tube without an inner wall and in a tube having the hole width A/inner wall thickness B of 4 were measured and results thereof shows that the heat transfer coefficient value at the refrigerant side in the tube according to the design of the present invention was enhanced to be about 650% higher than that of the general tube. That is, the heat transfer coefficient may be enhanced sufficiently remarkably even at a point where the heat transfer coefficient value is not a maximum value, as compared with the existing case. In consideration of this, the hole width A/inner wall thickness B value may be determined to be smaller than 4. 
     That is, the tube  120  may have a size within a range in which the following formula is satisfied: 
       2.5 &lt;A/B &lt;4  Formula: 1:
 
     Condition for Ensuring Manufacturing Characteristics 
     As described above in the condition for ensuring pressure resistance, the increase in the hole width A/inner wall thickness B value indicates the decrease in the inner wall thickness B when the hole width A is fixed. Heat transfer performance may be enhanced as the inner wall thickness B decreases within a range in which pressure resistance is satisfied. However, if the inner wall thickness B is excessively reduced, the inner wall  121  may not be properly manufactured in the process of manufacturing the tube  120  according to an extrusion scheme. That is, in order to ensure manufacturing characteristics, the inner wall thickness B must have a value equal to or greater than a thickness that can be manufactured by general extrusion, and here, a limit value of the thickness that can be manufactured in an extruding process is known to be 0.07 to 0.10 in the extrusion process technical field. Thus, the inner wall thickness B may be determined to be greater than 0.07 which is a manufacturing limit. 
     However, the above-mentioned manufacturing limit is a value that may be obtained using the best equipment, materials, conditions, etc., and practically, it is not easy to realize the manufacturing limit in a practical production field of a mass production system. That is, as the inner wall thickness decreases, the inner wall may be bent or burst in the process of manufacturing or thicknesses of several inner walls may not be uniform. That is, as the inner wall thickness decreases, a defect rate increases (a pass rate decreases), and conversely, as the inner wall thickness increases, the defect rate decreases (the pass rate increases). That is, it is preferred that the inner wall thickness decreases to an appropriate level at which the pass rate is not excessively lowered. In other words, a maximum value of the inner wall thickness may be determined according to the pass rate. It was reported that a pass rate was about 98% when the inner wall thickness B is 0.2 mm in a mass-production site of the extruded tube, and thus, the inner wall thickness B may be a maximum of 0.2 mm. To sum up, the inner wall thickness B may have a size within a range in which the following formula is satisfied: 
     (Pass Rate of 98% or Greater is Ensured in Mass Production) 
       0.07 &lt;B &lt;0.2 (mm).  Formula 2:
 
     As described above, the present manufacturing limit is known to be 0.07, but if the extrusion manufacturing technology develops, a less value may also be possible. However, when the inner wall thickness B decreases to the manufacturing limit in consideration of the development status of the current extrusion manufacturing technology, a minimum value of the inner wall thickness B may most preferably be 0.07. Here, when manufacturing ease is further considered, the minimum value of the inner wall thickness B may be 0.1 so that the inner wall thickness may be manufactured to have a value slightly greater than the manufacturing limit. Meanwhile, it was reported that a pass rate was 95% when the inner wall thickness B is 0.18 mm. From this point of view, the inner wall thickness B may have a size within a range in which the following formula is satisfied: 
     (Pass Rate of 95% or Greater is Ensured in Mass Production) 
       0.1 &lt;B &lt;0.18 (mm) (considering ease of manufacturing)  Formula 2-11:
 
       0.07 ≤B ≤0.18 (mm) (when manufactured to be as thin as manufacturing limit).  Formula 2-12:
 
     Furthermore, it was reported that when the inner wall thickness B is 0.15 mm, the pass rate is about 90%. From this point of view, as described above, the thickness of the inner wall is manufactured to be as thin as the manufacturing limit or ease of manufacturing is considered similarly, and the inner wall thickness B may have a size within a range in which the following formula is satisfied: 
     (Pass Rate of 90% or Greater is Secured in Mass Production) 
       0.1 &lt;B &lt;0.15 (mm) (considering ease of manufacturing)  Formula 2-21:
 
       0.07 &lt;B &lt;0.15 (mm) (when manufactured to be as thin as manufacturing limit).  Formula 2-22:
 
     Condition for Enhancing Heat Transfer Performance 
     In general, an outer size of the tube  120  may be determined in advance according to a required size of the heat exchanger  100  itself, or in order to replace the newly designed tube  120  of the present invention in the existing heat-exchanger, the outer size of the tube  120  may be determined in advance because it is to be the same as an outer size of the existing heat exchanger tube. Here, the outer size of the tube  120  includes the tube width Tw and the tube height Th. When the heat exchanger  100  is employed in a vehicle air conditioning system, there may be a risk of a collision of stone pieces bouncing from the ground. Considering such a risk, the outer wall thickness Tn at the end of the tube  120  in the width direction may also be determined in advance (as a specific value having sufficient stiffness against the above-described collision risk). Since the tube width Tw and the outer wall thickness Tn at the end portion of the tube  120  in the width direction are determined in advance as described above, a flow channel space in the tube  120  may be designed in consideration of the tube width Tw and the outer wall thickness Tn. 
     As described above, as the number of the inner walls  121  formed in the flow channel and the number of the holes  122  formed by the inner walls  121  in the tube  120  increase, a contact area between the refrigerant and the tube inner wall increases to increase heat transfer performance. If, however, the numbers of the inner walls  121  and the holes  122  are too large, an absolute flow amount of the refrigerant itself may be reduced to rather deteriorate the heat transfer performance. 
     That is, in this stage where conditions for improving heat transfer performance are considered, the numbers of inner walls  121  and the holes  122  included in the flow channel space are appropriately determined in consideration of the tube width Tw, the outer wall thickness Tn at the end of the tube  120  in the width direction, and the like, to thus maximize heat transfer performance. In detail, a value obtained by multiplying a value, which normalizes the tube width Tw as a value obtained by subtracting the pair of outer wall thicknesses Tn from the tube width Tw, to the hole width A and the inner wall thickness B set is set to as a determination indicator (Tw(A+B)/(Tw−2Tn)). 
       FIG. 5  illustrates simulation results of a relationship between the numbers of hole width and inner wall thickness sets and heat transfer performance. As the value of the determination indicator (Tw(A+B)/(Tw−2Tn)) increases, heat transfer performance tends to gradually increase and start to decrease at a certain point. From the similar point of view to the description of  FIG. 4(B) , the determination indicator (Tw(A+B)/(Tw−2Tn)) value may be determined as a value at which heat transfer performance is maximized, but in this case, the degree of freedom of design may be excessively limited. In consideration of this, a boundary value of the determination indicator (Tw(A+B)/(Tw−2Tn)) range at the point corresponding to about 75% of the maximum value of heat transfer performance may be about 0.2/0.6. Thus, the determination indicator (Tw(A+B)/(Tw−2Tn)) value may be determined as a value within the range of 0.2 to 0.6. 
     That is, the tube  120  may have a size within a range in which the following formula is satisfied: 
       0.2 &lt;Tw ( A+B )/( Tw− 2 Tn )&lt;0.6 (mm).  Formula 3:
 
     Associated Condition with Fin Shape 
     Heat transferred from the refrigerant to the inner wall surface in the tube  120  is transferred to the outer surface of the tube  120  and finally discharged as outside air. The fin  130  is provided to more efficiently transfer the heat transferred to the outer surface of the tube  120  to the outside air. That is, heat transferred to the outer surface of the tube  120  is transferred to the fin  130  so that the area in contact with the outside air is expanded to the outer surface of the tube  120  and the surface of the fin  130 , and as a result, performance of heat transfer to the outside air may be significantly improved. Here, as illustrated in  FIG. 2 , a plurality of the louvers  135  may be formed on the fin  130  to further increase the contact area with the outside air. 
     As illustrated in  FIG. 2 , a direction in which the louvers  135  are arranged in parallel and a direction in which the inner wall  121  and the hole  122  set are arranged in parallel are the same as a width direction of the tube  120 . The amount of heat transferred from the inside of the tube  120  to the outer surface of the tube  120  is slightly larger locally at a position corresponding to the position of the inner wall  121  and is less at a position corresponding to the position of the hole  122 . In view of this, in order to maximize heat transfer performance, preferably, at least one inner wall  121  and hole  122  set is included in the width range of one louver  135 . 
     That is, the tube  120  preferably has a size within a range in which the following formula is satisfied: 
         A+B&lt;Lp   Formula 4:
 
     (A: hole width, B: inner wall thickness, Lp: louver pitch). 
     Optimal Design Condition 
     The optimal design conditions for the hole width A and the inner wall thickness B in consideration of the pressure resistance, the manufacturing characteristics, and the heat transfer performance may be summarized as follows: 
       2.5 &lt;A/B &lt;4  Formula 1:
 
       0.07 &lt;B &lt;0.2 (mm)  Formula 2:
 
       0.2 &lt;Tw ( A+B )/( Tw− 2 Tn )&lt;0.6 (mm).  Formula 3:
 
       FIG. 6  is a graph illustrating a range of optimal design conditions for the hole width and the inner wall thickness. In  FIG. 6 , a pair of graphs indicated by {circle around ( 1 )} represents an upper limit value and a lower limit value of Formula 1, respectively, a pair of graphs indicated by {circle around ( 2 )} represents an upper limit value and a lower limit value of Formula 2, respectively, and a pair of graphs indicated by {circle around ( 3 )} represents an upper limit value and a lower limit value of Formula 3, respectively. A portion in which three areas, i.e., an area formed by the pair of graphs indicated by {circle around ( 1 )}, an area formed by the pair of graphs indicated by {circle around ( 2 )}, and an area formed by the pair of graphs indicated by {circle around ( 3 )}, overlap, that is, the area portion shown to be thickest in  FIG. 6 , is the optimal design condition range. 
     That is, the tube  120  according to the present invention may be designed to have the hole width A and the inner wall thickness B value within the optimal design condition range illustrated in  FIG. 6 . 
     Meanwhile, as described above with respect to the conditions for ensuring the manufacturing characteristics, the minimum value of A/B and the minimum value conditions may be narrowed more strictly. Formulas of additional conditions related to A/B are summarized as follows, and  FIG. 7(A) ˜ 7 (D) illustrate ranges of optimal design conditions under these additional conditions. That is,  FIG. 7(A)  illustrates an optimal design condition range according to Formula 2-11,  FIG. 7(B)  illustrates an optimal design condition range according to Formula 2-12,  FIG. 7(C)  illustrates an optimal design condition range according to Formula 2-21, and  FIG. 7(D)  illustrates the optimal design condition range according to Formula 2-22. 
       0.1 &lt;B &lt;0.18 (mm)  Formula 2-11:
 
       0.07 &lt;B &lt;0.18 (mm)  Formula 2-12:
 
       0.1 &lt;B &lt;0.15 (mm)  Formula 2-21:
 
       0.07 &lt;B &lt;0.15 (mm)  Formula 2-22:
 
     Meanwhile, Formula 4 may be further introduced in consideration of even the louver pitch Lp. 
         A+B&lt;Lp   Formula 4:
 
     In  FIG. 6 , the graph indicated by {circle around ( 4 )} represents Formula 4, and an area portion formed below the graph indicated by {circle around ( 4 )} is the design condition range according to the Formula 4. In the example of  FIG. 6 , since the graph indicated by {circle around ( 4 )} is located above an upper limit graph indicated by {circle around ( 3 )}, there is no change in the optimal design area. However, if the louver pitch Lp is reduced, the graph indicated by {circle around ( 4 )} comes below the upper limit value graph indicated by {circle around ( 3 )}, and in this case, the area of the optimal design condition range is smaller than the area illustrated in  FIG. 6 . Such an example is illustrated in  FIG. 8 . 
     According to the present invention, there is an effect of significantly improving performance of heat transfer from the refrigerant to the tube, as compared with the related art. More specifically, according to the present invention, performance of heat transfer from the refrigerant to the inner wall of the tube may be enhanced by increasing the contact length with the refrigerant at the internal cross-section of the tube and further increasing the sectional area of the refrigerant passage, and the inner wall and outer wall thicknesses of the tube may be optimized to ensure appropriate pressure resistance and manufacturing characteristics. 
     Also, according to the present invention, although an overall size of the heat exchanger or the heat exchanger tube is varied, dimensions at which heat transfer performance, pressure resistance, and manufacturing characteristics are optimized may be easily calculated. Therefore, it is possible to maximize design convenience in the process of designing a new heat exchanger or designing to improve an existing heat exchanger. 
     The present invention is not limited to the above-mentioned embodiments but may be variously applied, and may be variously modified by those skilled in the art to which the present invention pertains without departing from the gist of the present invention claimed in the claims.