[0001] The present invention relates to a heat exchanger, particularly to a thermal management
system for an Exhaust Gas Re-circulation (EGR) cooler.
Background of the invention:
[0002] An Exhaust Gas Re-circulation (EGR) cooler receives exhaust gases from an engine
and cools the exhaust gases before the exhaust gases are re-circulated back to the
engine's cylinder. By re-circulating the engine's exhaust gas back to the engine's
cylinder, the peak in-cylinder temperatures are regulated, specifically lowered to
reduce formation of NOx gases. The EGR cooler further reduces the combustion chamber
temperature, thereby preventing valve clatter, detonation and further reduces NO
x formation. As a result, the exhaust gas recirculation (EGR) system substantially
reduces vehicle emissions to enable meeting stringent vehicular exhaust emission norms
prevalent in most parts of the world.
[0003] In an EGR cooler, exhaust gas is received in a tank and from the tank the exhaust
gas pass through heat exchange tubes received inside the housing, coolant is delivered
by a coolant inlet pipe around the heat exchange tubes to cause heat exchange between
the exhaust gas and the coolant, thereby resulting in cooling of the exhaust gas and
reducing the temperature of the exhaust gas. The coolant inlet pipe is disposed at
sidewall of the EGR cooler. The EGR cooler handles high temperature exhaust gases
in the temperature range of 400 to 900 °C. Accordingly, temperatures at certain regions
inside the EGR cooler, particularly, a gas inlet area of the heat exchange tubes that
first comes into contact with the exhaust gas, exceeds acceptable limits and cause
formation of hot spots. The hot spots at the gas inlet area cause problems such as
boiling of the coolant, durability issues and excessive thermo-dynamical stresses
at the gas inlet area. To avoid such problems, the coolant from the coolant inlet
pipe is directed to the gas inlet area of the heat exchange tubes by using a baffle
disposed inside the coolant inlet pipe to avoid high temperatures at the gas inlet
area. However, such baffle extends inside the housing of the EGR cooler and interferes
with the other components, particularly, components such as for example, heat exchange
tubes disposed inside the housing of the EGR cooler. Further, packaging of the baffle
within limited space inside the coolant inlet pipe is a concern and such configuration
of the baffle inside the coolant inlet pipe may restrict coolant flow through the
coolant inlet pipe. Further, conventional method of providing baffle for directing
coolant to the gas inlet area through an inlet configured on the housing fails to
effectively regulate distribution and velocity of coolant directed to the gas inlet
area. Still further, the conventional baffle is a dedicated component and as such
there are product costs, inventory costs and process costs associated with configuring
the baffle.
[0004] Accordingly, there is need for an EGR cooler configured with a baffle that effectively
directs coolant to the gas inlet area of the EGR cooler, thereby preventing high temperature
hot spots at the gas inlet area and that is capable of addressing issues such as boiling
of coolant, durability issues and excessive thermo-dynamical stresses arising due
to hot spots at the gas inlet area of the EGR cooler. Further, there is a need for
an EGR cooler configured with a baffle that does not interfere with the other components,
particularly, components such as for example heat exchange tubes disposed inside the
housing of the EGR cooler. Further, there is a need for an EGR cooler configured with
a baffle that effectively directs coolant to the gas inlet area, thereby preventing
excessive temperatures and the problems associated with the excessive temperatures
at the gas inlet area. Further, there is a need for an EGR cooler configured with
a baffle that is configured by modifying an existing part of the EGR cooler, thereby
reducing product and process costs associated with configuring the baffle. Still further
there is a need for an EGR cooler configured with a baffle inside a diverging tank
secured to a side of housing of the EGR cooler, wherein the baffle can be conveniently
packaged without disrupting coolant flow to heat exchange tubes received inside the
housing, particularly, the gas inlet area. Further, there is a need for an EGR cooler
that exhibits extended service life, improved reliability and efficiency.
Description of the invention:
[0005] An object of the present invention is to provide an EGR cooler that obviates the
drawbacks associated with conventional methods for cooling a gas inlet area for an
EGR cooler that fails to effectively regulate distribution and velocity of coolant
directed to the gas inlet area.
[0006] Another object of the present invention is to provide an EGR cooler configured with
a baffle that effectively directs coolant to a gas inlet area of an EGR cooler to
achieve efficient cooling of the gas inlet area thereby addressing issues such as
boiling of coolant, durability issues and excessive thermo-dynamical stresses arising
due to hot spots at the gas inlet area of the EGR cooler.
[0007] Still another object of the present invention is to provide an EGR cooler configured
with a baffle that does not interfere with the other components, particularly, components
such as for example, heat exchange tubes disposed inside the housing of the EGR cooler.
[0008] Yet another object of the present invention is to provide an EGR cooler that can
be easily packaged and that do not interfere with the flow of coolant through the
coolant inlet pipe.
[0009] Still another object of the present invention is to provide an EGR cooler configured
with a baffle that is configured by modifying an existing part of the EGR cooler,
thereby reducing product, process and inventory costs associated with configuring
the baffle.
[0010] Yet another objective of the present invention is to provide an EGR cooler that exhibits
extended service life, improved reliability and efficiency.
[0011] In the present description, some elements or parameters may be indexed, such as a
first element and a second element. In this case, unless stated otherwise, this indexation
is only meant to differentiate and name elements which are similar but not identical.
No idea of priority should be inferred from such indexation, as these terms may be
switched without betraying the invention. Additionally, this indexation does not imply
any order in mounting or use of the elements of the invention.
[0012] A heat exchanger is disclosed in accordance with an embodiment of the present invention.
The heat exchanger includes housing, a heat exchanger core, a diverging tank and at
least one baffle. The heat exchanger core is received in the housing and includes
heat exchange tubes that receive hot gas. The coolant is received in the housing and
around the heat exchange tubes. The diverging tank is disposed at a side of the housing
and is diverging towards the housing. The diverging tank connects a coolant inlet
with the housing to enable fluid communication between the coolant inlet and an interior
of the housing. At least a portion of the at least one baffle is disposed inside the
diverging tank and divides an interior of the diverging tank into at least two volumes,
wherein at least one volume is in fluid communication with the interior of the housing
and the at least one baffle directs coolant flow to a gas inlet area inside the housing.
[0013] Generally, the housing includes at least one inlet formed thereon for enabling fluid
communication between the at least one volume of the diverging tank and the interior
of the housing.
[0014] Particularly, the diverging tank includes a first opening connected to the coolant
inlet and a second opening larger than the first opening and connected to the first
opening, the second opening is so disposed with respect to said at least one inlet
that said diverging tank covers said at least one inlet.
[0015] Generally, the at least one inlet and the at least one baffle is at least half the
dimension of the second opening.
[0016] In accordance with an embodiment of the present invention, a base of the at least
one baffle is disposed along at least a portion of a periphery of the at least one
inlet.
[0017] Specifically, the at least one baffle forms an angle in the range of 20 to 70 degrees
with respect to the side wall of the housing configured with the at least one inlet.
[0018] In accordance with an embodiment, the at least one baffle includes a plurality of
tabs configured thereon to secure the at least one baffle inside the diverging tank.
[0019] Alternatively, the at least one baffle includes lips configured along at least a
portion of a periphery thereof to secure the at least one baffle inside the diverging
tank.
[0020] Further, the at least one baffle includes a plurality of apertures formed thereon.
[0021] Generally, the at least one baffle is integrally formed with the housing.
[0022] Specifically, the at least one baffle as well as the at least one inlet is formed
by deforming a cut out portion of the housing that is integrally connected to the
housing.
[0023] Preferably, the at least one baffle is of a shape selected from group of shapes comprising
of rectangular, semi-circular and trapezoidal shape.
[0024] Generally, the heat exchange tubes are axially extending along the housing and the
gas inlet area is near a tank delivering hot gases to the heat exchange tubes, the
at least one inlet is disposed upstream of gas inlet area in direction of coolant
flow and the at least one baffle directs coolant to the gas inlet area via the at
least one inlet.
[0025] Other characteristics, details and advantages of the invention can be inferred from
the description of the invention hereunder. A more complete appreciation of the invention
and many of the attendant advantages thereof will be readily obtained as the same
becomes better understood by reference to the following detailed description when
considered in connection with the accompanying figures, wherein:
Brief description of the drawings:
[0026]
FIG. 1a and FIG. 1b illustrate an EGR cooler in accordance with an embodiment of the present invention,
particularly, a sectional view depicting internal details of a diverging tank disposed
at a side wall of a housing of the EGR cooler;
FIG. 2a illustrates the baffle configured with tabs for securing the baffle to inner walls
of the diverging tank of FIG. 1a and FIG. 1b;
FIG. 2b - 2c illustrate different views of the diverging tank with the baffle of FIG. 2a received and secured inside the diverging tank;
FIGS. 2d- 2e illustrate different configurations of the baffle received inside the diverging tank,
wherein the baffle is illustrated in different orientations with respect to an inlet
configuring fluid communication between an interior of the diverging tank and an interior
of the housing;
FIG. 2f illustrates the baffle received inside the diverging tank and in between two inlets
configuring fluid communication between the interior of the diverging tank and the
interior of the housing;
FIG. 3a illustrates the diverging tank of FIG.1 without the baffle received there inside;
FIG. 3b illustrates a sectional view of the diverging tank along the section line A-A of
FIG 3a;
FIG. 4a illustrates a baffle with a plurality of tabs formed thereon for securing the baffle
inside the diverging tank;
FIG. 4b illustrates a baffle in accordance with another embodiment with apertures formed
thereon; and
FIG 4c illustrates a baffle with lips formed thereon for securing the baffle inside the
diverging tank.
[0027] It must be noted that the figures disclose the invention in a detailed enough way
to be implemented, said figures helping to better define the invention if needs be.
The invention should however not be limited to the embodiment disclosed in the description.
Detailed description of the preferred embodiments:
[0028] The present invention relates to a thermal management system for an Exhaust Gas Re-circulation
(EGR) cooler, specifically to at least one baffle, hereafter simply referred to as
a baffle disposed inside a diverging tank. Wherein a diverging tank is disposed at
a side wall of a housing of the EGR cooler and is in addition to tanks disposed at
ends of the housing for delivering hot gases to and collecting hot gases from heat
exchange tubes received inside the housing. The baffle acts as a partition and divides
an interior of the diverging tank into at least two volumes, wherein at least one
volume is in fluid communication with an interior of the housing and the baffle directs
coolant to a gas inlet area of the heat exchange tubes received inside the housing
of the EGR cooler. Such configuration of the baffle, addresses issues such as boiling
of coolant, durability issues and excessive thermo-dynamical stresses, arising due
to hot spots forming at the gas inlet area of the EGR cooler. Although, the baffle
of the present invention is used for directing coolant directly to the gas inlet area
of the EGR cooler. However, the baffle of the present invention is also applicable
for any other applications, where coolant or any other fluid is required to be directed
at a particular region inside any other system such as for example a region that is
exposed to hot fluid and that is required to be cooled to address issues arising due
to formation of hot spots.
[0029] FIG. 1a and
FIG. 1b illustrate a heat exchanger particularly, an EGR cooler
100 in accordance with an embodiment of the present invention. The EGR cooler
100 is configured with a diverging tank
30 disposed at a side
wall 10a of a housing
10 of the EGR cooler
100, wherein the housing
10 receives a heat exchanger core
20. The diverging tank
30 is in addition to tanks (not illustrated) disposed at ends of the housing
10 for delivering hot gases to and collecting hot gases from a plurality of heat exchange
tubes
22 received inside the housing
10. The diverging tank
30 is in fluid communication with a coolant inlet
12 at one end and the housing
10 at the other end, thereby enabling fluid communication between the coolant inlet
12 and an interior of the housing
10. The diverging tank
30 includes a baffle
14 that is at least partially received therein for directing coolant directly to a gas
inlet area
16, such as for example portions of the heat exchange tubes
22 near inlet of the heat exchange tubes
22 and received inside the housing
10. The baffle
14 may also direct coolant to the areas adjacent to the gas inlet area
16 to prevent drawbacks associated with over-heating. The gas inlet area
16 is for example the portion of the heat exchange tubes
22 of the heat exchanger core
20 that first receive the exhaust gas and are first to come in contact with high temperature
exhaust gases and as such is prone issues such as boiling of coolant, durability issues
and excessive thermo-dynamical stresses arising due to formation of hot spots. With
the baffle
14 directing coolant to the gas inlet area
16 disposed inside the housing
10 of the EGR cooler
100, the formation of hot spots at the gas inlet area
16 of the EGR cooler
100 is prevented and issues arising due to hot spots forming at the gas inlet area
16 of the EGR cooler
100 are also avoided. The baffle
14 may extend sideways out of the diverging tank
30 but do not extend into the housing
10 and as such do not interfere with the heat exchanger core
20 disposed inside the housing
10. The heat exchange tubes
22 are axially extending along the housing
10 and the gas inlet area
16 is near the tank delivering hot gases to the heat exchange tubes
22, the at least one inlet
18 is disposed upstream of gas inlet area
16 in direction of coolant flow and the at least one baffle
14 directs coolant to the gas inlet area
16 via the at least one inlet
18.
[0030] The housing
10 receives the heat exchanger core
20 connected to and disposed between a pair of headers disposed at the opposite ends
of the housing
10. The heat exchanger core
20 includes the plurality of heat exchange tubes
22 that receive hot gas from the tank and through which the hot gas pass. The housing
10 further receives coolant around the heat exchange tubes
22 through the coolant inlet
12. Such an arrangement enables heat exchange between the hot gas flowing through the
heat exchange tubes
22 and the coolant around the heat exchange tubes
22. The portion of the heat exchange tubes
22 that receives the exhaust gases and as such that first comes in contact with high
temperature exhaust gases is the gas inlet area
16 that is prone to issues due to formation of hot spots.
[0031] The diverging tank
30 is disposed at side of the housing
10 and is diverging towards the housing
10. The diverging tank
30 receives at least a portion of the baffle
14 as illustrated in
FIG. 2a. Referring to the
FIG. 2b, the diverging tank
30 includes a first opening
30a connected to the coolant inlet
12 and a second opening
30b opposite to the first opening
30a, larger than the first opening
30a and connected to the first opening
30a by side walls of the diverging tank
30. The second opening
30b is further connected to the housing
10 along a flange
30c radially extending along the second opening
30b and as such the diverging tank
30 is diverging towards the housing
10. More specifically, the diverging tank
30 is disposed between the coolant inlet
12 and the housing
10, the second opening
30b of the diverging tank
30 is so disposed with respect to at least one inlet
18 formed on the housing
10 for configuring fluid communication between the diverging tank
30 and the interior of the housing
10, that the diverging tank
30 covers the at least one inlet
18. The diverging tank
30 is in fluid communication with the coolant inlet
12 and the housing
10, thereby enabling fluid communication between the coolant inlet
12 and the interior of the housing
10. Such configuration of the diverging tank
30 provides enough space for receiving the baffle
14. Accordingly, such configuration of the diverging tank
30 receiving the baffle
14 enables the baffle
14 to direct the coolant from the coolant inlet
12 to the gas inlet area
16 without disrupting coolant flow to the gas inlet area
16.
[0032] The baffle
14 is disposed inside the diverging tank
30 and acts as a partition to divide an interior of the diverging tank
30 into at least two volumes, wherein at least one volume is in fluid communication
with the interior of the housing
10. The at least one baffle
14 forms an angle in the range of 20 to 70 degrees with respect to the side wall
10a of the housing
10 configured with the at least one inlet
18. FIG. 2a illustrates the baffle
14 configured with a plurality of tabs
14b for securing the baffle
14 to inner walls of the diverging tank
30. The baffle
14 can also be secured to the inner walls of the diverging tank
30 by using a plurality of lips
14d configured along at least a portion of periphery of the baffle
14 as illustrated in
FIG. 4c. However, the present invention is not limited to any particular configuration of
attachment means and method for securing the baffle
14 to inner walls of the diverging tank
30. FIGS. 2b - 2c illustrate different views of the diverging tank
30 with the baffle
14 received and secured inside the diverging tank
30.
[0033] In accordance with an embodiment as illustrated in
FIGS. 2d and
2e, the two volumes are separated and isolated from each other by the baffle
14 and one of the two volumes is in fluid communication with the interior of the housing
10 via the inlet
18 formed on the housing
10. Specifically,
FIGS. 2d- 2e illustrate different configurations of the baffle
14 received and secured inside the diverging tank
30, wherein the baffle
14 is illustrated in different orientations with respect to the inlet
18 configuring fluid communication between the interior of the diverging tank
30 and the interior of the housing
10. More specifically, a base
14a of the baffle
14 is disposed along at least a periphery of the at least one inlet
18 and the baffle
14 can be at any angle, for example, angle "α" with the outside wall or the side wall
10a of the housing
10. Preferably, the baffle
14 is at an acute angle with respect to the side wall
10a of the housing
10. Further, the inlet
18 formed on the housing
10 can be of different dimensions "D1" and "D2". In accordance with an embodiment, the
inlet
18 and the baffle
14 is at least half the dimension of the second opening
30b. The orientation of the baffle
14 and the dimension of the inlet
18 formed on the housing
10 are based on the position of the gas inlet area
16 with respect to the inlet
18, and particularly, based on the direction in which the coolant is to be directed to
reach the gas inlet area
16 and amount of coolant to be supplied to the gas inlet area
16 for effective cooling of the gas inlet area
16.
[0034] In accordance with another embodiment as illustrated in
FIG. 2f, the two volumes are in fluid communication with each other. Further at least one
of the two volumes are in fluid communication with the interior of the housing
10 via at least one of the inlets
18. Specifically, both volumes are in fluid communication with the interior of the housing
10 via inlets
18 formed on the housing
10 and illustrated in
FIG. 2f, wherein one inlet supplies coolant to the gas inlet area
16, such as for example portions of the heat exchange tubes
22 near the inlet of the heat exchange tubes
22, whereas the other inlet
18 supplies coolant to the remaining portion of the heat exchange tubes
22. The baffle
14 directs coolant to the gas inlet area
16 inside the housing
10 via one of the inlets
18.
[0035] In one embodiment of the present invention, the baffle
14 is of a planar configuration. In accordance with another embodiment, the baffle
14 is an integral part of the housing
10, particularly, integral part of the side wall
10a of the housing
10. More specifically, the at least one baffle
14 as well as the at least one inlet
18 is formed by deforming a cut out portion of the housing
10 that is still connected to the housing
10. The cut out portion of the housing
10 is cut along a profile and is configured by stamping operation such that the cut
out portion is still connected to the side
wall 10a of the housing
10 along at least one edge of the cut out portion, wherein when the cut out portion
is lifted away from the side
wall 10a to form the inlet
18 on the side wall
10a, the lifted cutout portion acts as the baffle
14. More specifically, the baffle
14 can have different shapes such as rectangular, semi-circular and trapezoid shape,
with at least one edge connected to the housing
10. However, the present invention is not limited to any particular shape of the cut
out portion or the baffle
14 formed thereby and any particular method for forming the cut out portion until the
cut out portion is capable of being deformed for forming the at least one baffle
14 as well as the at least one inlet
18 simultaneously. With such configuration the at least one baffle
14 and the at least one inlet
18 are formed by a single step, thereby reducing the number of manufacturing steps required
for configuring the diverging tank
30 secured to the housing
10 and with the at least one baffle
14 and the at least one inlet
18 received there inside.
[0036] As the baffle
14 in accordance of the present invention is formed by modifying an existing part of
the EGR cooler, particularly, by modifying the housing
10, product, process and inventory costs associated with configuring the baffle as a
dedicated element are eliminated. Further, with such configuration of the baffle
14, the baffle
14 is disposed inside the diverging tank
30 and does not interfere with the other components, particularly, components such as
heat exchange tubes disposed inside the housing
10 of the EGR cooler
100. In accordance with another embodiment, the baffle
14 includes a plurality of apertures
14c configured thereon. The present invention is not limited to any particular placement
of the apertures
14c on the baffle
14. The baffle
14 is formed by deforming the cut out portion of the housing
10, particularly, the cut out portion from the side
wall 10a of the housing
10, such that the periphery of the cut out portion snugly fits with respect to inner
walls of the diverging tank
30. However, the present invention is not limited to any particular shape, configuration
and orientation of the baffle
14 inside the diverging tank
30 and method of forming the baffle
14 as far as the baffle
14 is capable of effectively directing coolant to the gas inlet area
16 disposed inside the housing
10. FIG. 3a illustrates the diverging tank
30 without the baffle
14 received there inside.
FIG. 3b illustrates a sectional view of the diverging tank
30 along the section line A-A of
FIG. 3a.
[0037] Several modifications and improvement might be applied by the person skilled in the
art to the heat exchanger and such modifications and improvements will still be considered
within the scope and ambit of the present invention, as long the heat exchanger includes
housing, a diverging tank and a baffle. The housing receives a heat exchanger core
that includes heat exchange tubes that receives hot gas. The diverging tank is disposed
at a side of the housing and is diverging towards the housing. The diverging tank
connects a coolant inlet with the housing to enable fluid communication between the
coolant inlet and an interior of the housing. The baffle is disposed inside the diverging
tank and divides interior of the diverging tank into at least two volumes, wherein
at least one volume is in fluid communication with the interior of the housing and
the baffle directs coolant flow to a gas inlet area inside the housing.
[0038] In any case, the invention cannot and should not be limited to the embodiments specifically
described in this document, as other embodiments might exist. The invention shall
spread to any equivalent means and any technically operating combination of means.
1. A heat exchanger (100) comprising:
• a housing (10);
• a heat exchanger core (20) adapted to be received in said housing (10) and comprising
heat exchange tubes (22) that are adapted to receive hot gas, coolant is received
in said housing (10) and around said heat exchange tubes (22);
• a diverging tank (30) disposed at a side of said housing (10) and diverging towards
said housing (10), said diverging tank (30) adapted to connect a coolant inlet (12)
with said housing (10) to enable fluid communication between said coolant inlet (12)
and an interior of said housing (10); and
• at least a portion of at least one baffle (14) disposed inside said diverging tank
(30) and adapted to divide an interior of said diverging tank (30) into at least two
volumes, wherein at least one volume is in fluid communication with said interior
of said housing (10) and said at least one baffle (14) is adapted to direct coolant
flow to a gas inlet area (16) inside said housing (10).
2. The heat exchanger (100) as claimed in previous claim, wherein said housing (10) comprises
at least one inlet (18) formed thereon for enabling fluid communication between said
at least one volume of said diverging tank (30) and said interior of said housing
(10).
3. The heat exchanger (100) as claimed in the claim 2, wherein said diverging tank (30)
comprises a first opening (30a) connected to said coolant inlet (12) and a second
opening (30b) larger than said first opening (30a) and connected to the first opening
(30a), said second opening (30b) is so disposed with respect to said at least one
inlet (18) that said diverging tank (30) covers said at least one inlet (18).
4. The heat exchanger (100) as claimed in the claim 2, wherein said at least one inlet
(18) and said at least one baffle (14) is at least half the dimension of said second
opening (30b).
5. The heat exchanger (100) as claimed in the claim 2, wherein a base (14a) of said at
least one baffle (14) is disposed along at least a portion of a periphery of said
at least one inlet (18).
6. The heat exchanger (100) as claimed in the previous claim, wherein said at least one
baffle (14) forms an angle "α" in the range of 20 to 70 degrees with respect to a
side wall (10a) of said housing (10) configured with said at least one inlet (18).
7. The heat exchanger (100) as claimed in any of the preceding claims, wherein said at
least one baffle (14) comprises a plurality of tabs (14b) configured thereon and adapted
to secure said at least one baffle (14) inside said diverging tank (30).
8. The heat exchanger (100) as claimed in any of the preceding claims, wherein said at
least one baffle (14) comprises lips (14d) configured along at least a portion of
a periphery thereof and adapted to secure said baffle (14) inside said diverging tank
(30).
9. The heat exchanger (100) as claimed in any of the preceding claims, wherein said at
least one baffle (14) further comprises a plurality of apertures (14c) formed thereon.
10. The heat exchanger (100) as claimed in any of the preceding claims, wherein said at
least one baffle (14) is integrally formed with said housing (10).
11. The heat exchanger (100) as claimed in any of the preceding claims, wherein said at
least one baffle (14) as well as the at least one inlet is formed by deforming a cut
out portion of said housing (10) that is integrally connected to said housing (10).
12. The heat exchanger (100) as claimed in any of the preceding claims, wherein said at
least one baffle (14) is of a shape selected from group of shapes comprising rectangular,
semi-circular and trapezoidal shape.
13. The heat exchanger (100) as claimed in any of the claim 2, wherein said heat exchange
tubes (12) are axially extending along said housing (10) and said gas inlet area (16)
is near a tank delivering hot gases to said heat exchange tubes (22), said at least
one inlet (18) is disposed upstream of gas inlet area (16) in direction of coolant
flow and said at least one baffle (14) is adapted to direct coolant to said gas inlet
area (16) via said at least one inlet (18).