WIND TURBINE TOWER HEAT EXCHANGER
BACKGROUND OF THE INVENTION Field of the Invention
This invention relates to wind turbines housed in a nacelle atop a tall tower, and more particularly to an apparatus for removing heat from inside a wind turbine tower. Description of the Prior Art As wind generated electricity becomes commonplace in many locations around the world, there becomes a desire to make wind turbine installations more aesthetic. One specific concern has been the location of control cabinets, which are placed outside of the turbine towers where they become openly visible. To address this concern, it has recently become common to place the control system cabinets within the wind turbine tower. There typically is sufficient space to accommodate such cabinets, but there can be serious thermal management problems. For example, in variable speed wind turbines, where a power electronic converter control system is commonly used, there can be significant heat generation by the converter control system. Consider for example, a full converter system with 96% efficiency in a 1.5 MW turbine. This means that 4% of 1.5 MW, or 60 kW is dissipated by the converter. If the converter is placed in the tower without adequate air movement a large temperature rise within the tower can result. This high temperature can be detrimental to the life of the converter control system and other required components within the tower. To deal with this temperature rise, large air movement fans have been placed in the tower to exhaust hot air; however, removing materials by cutting holes
in the tower raises turbine cost and reduces the overall system reliability.
The use of coiled cooling tubes to transfer heat into the wind turbine tower inside wall has the drawback because of the small amount of surface area that they provide that contacts the inside wall of the turbine tower. At power levels of 30 kilowatts, large amounts of cross sectional area are needed to keep the overall thermal drop down to only a few degrees that is needed to transfer the heat flux from the inside wall of the cooling tube through to the outside wall of the turbine tower. Coils of aluminum tape could be used to increase the coiled cooling tube contact surface area, but this too is insufficient .
Wobben patent 6,676,122 discloses a method for supplying heat exchange to a wind energy apparatus, which comprises cooling a generator by flowing fluid through a nacelle cooling channel and near the generator and transferring heat from the fluid to an outer wall of a tower as the fluid flows downward through a tower cooling channel. This has the disadvantage of having to manufacture a tower to include the cooling channel. This is expensive and means that existing towers cannot be retrofitted with the cooling system.
The cooling system has the further disadvantage that no cooling liquid can be used but only cooling gases since adapting a cooling circuit which extends through the tower and the nacelle to a cooling liquid is cost-intensive and impractical. Furthermore, powerful pumps would be necessary to circulate a cooling liquid from the tower base to the nacelle. Due to the fact that only gaseous coolants can be utilized, which do not have a good heat capacity, large amounts of gaseous coolant have to be circulated.
It is desirable to find an improved method of moving heat flux generated by internal wind turbine systems inside a tower to the outside of the tower.
SUMMARY OF THE INVENTION
Briefly, the invention is concerned with a wind energy apparatus including a tower and a cooling system within the tower in which heat to be dissipated from the cooling system is dissipated by the tower. In particular, the invention relates to a wind turbine comprising a wind turbine tower resting on a foundation, heat-generating components within the wind turbine tower, a first heat receiving means being arranged to absorb heat generated by the heat-generating components, first heat emitting means, and a conduit system connecting the heat receiving means and the first heat emitting means and circulating a cooling fluid between the heat receiving means and the first heat emitting means.
The first heat emitting means is attached to a circumferential part of the inner surface of the wind turbine tower and transfers heat of the cooling fluid to the wind turbine tower which dissipates the heat of the cooling fluid to the environment.
The shape of the first heat emitting means is adapted to the inner surface of the turbine tower so that a good thermal flux from the heat emitting means to the inner surface of the tower is ensured. In a preferred embodiment the first heat emitting means has the form of a ring segment which is adapted to the circular inner surface of the wind turbine tower. Such a design of the heat emitting means provides for a great area of contact between the heat emitting means and the turbine tower and, concurrently, provides for a heat emitting means which is cost-effective since it is easy to manufacture.
The first heat emitting means can be attached to the inner surface of the wind turbine tower in a number of ways . For example, it can be screwed or adhered. Furthermore, the inner surface of the tower can be provided with mountings in which the heat emitting means can be placed or inserted. However, it is preferred that the first heat emitting means is pressed against the inner surface of the wind turbine tower by a clamping or expansion device. Such clamping or expanding of the first heat emitting means has the advantage that only one fastener, i.e. the clamping device, has to be used for fastening and releasing the heat emitting means. Furthermore, the heat emitting means must not be provided with additional openings or screws and the like and therefore the design of the heat emitting means is very simple and cost-effective. A further important advantage which is provided by pressing the heat emitting means against the surface of the tower is that the area of contact between the heat emitting means and the tower surface is maximized due to the tension in the clamping device / heat emitting means arrangement which presses the heat emitting means against the tower surface.
Even if the first heat emitting means is pressed against the inner surface of the turbine tower unavoidable irregularities in this surface cause a decrease of the thermal flux. To further enhance the thermal flux between the first heat emitting means and the inner surface of the wind turbine tower the surface of the first heat emitting means abutting against the inner surface of the wind turbine tower is interfaced with this surface by a thermally conductive material. This thermally conductive material, e.g. a thermal conductive paste, compensates for the irregularities in the surface of the wind turbine tower. Of course, the same applies for irregularities in the surface of the first heat emitting means .
After the heat has been transferred from the cooling fluid to the wind turbine tower it is dissipated by the tower to the environment. To enhance the tower heat dissipation the wind turbine tower outer surface comprises a plurality of fins arranged in the area where the first heat emitting means is arranged within the tower.
In a preferred embodiment at least the first heat emitting means surface opposing the surface adjacent to the inner surface of the wind turbine tower comprises a heat insulation layer. This heat insulation layer reduces the heat dissipation of the first heat emitting means into the tower itself and therefore the overall performance is enhanced. Depending on the temperature of the cooling fluid such an insulation layer also avoids harm to maintenance personnel when working inside the tower .
Depending on the installation site and the season, heat dissipation through the wind turbine tower might not be sufficient. Therefore, in a preferred embodiment the wind turbine comprises a second heat emitting means located under the foundation and being connected with the conduit system.
Heat generated within the wind turbine tower can be dissipated into the material beneath the foundation. The conduit system may connect the first heat emitting means and the second heat emitting means in series so heat can be dissipated to the environment by the wind turbine tower and the material beneath the foundation.
To achieve optimal heat dissipation the conduit system comprises a plurality of valves arranged in such a manner within the conduit system that the cooling fluid, depending on the valve positions, is circulated through one of the heat emitting means or both in series.
To achieve optimal valve positions, and therefore optimal heat dissipation, temperature sensors are arranged at the wind
turbine tower, in the area where the first heat emitting means is arranged, and at an outlet of the first heat emitting means detecting the temperature of the cooling fluid leaving the first heat emitting means. In case one temperature is too high the valves can be adjusted accordingly, for example they can be adjusted to connect the heat emitting means in series.
The invention also relates to a method for dissipating heat generated within a wind turbine tower from that tower, the method comprises the steps of: A. detecting the temperature of the wind turbine tower and/or the cooling fluid,
B. calculating the optimal cooling fluid flow path on the basis of the detected temperature (s ),
C. adjusting valves of a conduit system within the wind turbine tower for setting up the optimal flow path, said conduit system connects heat-generating means within the wind turbine tower and heat emitting means, and
D. depending on the flow path, circulating a cooling fluid transporting heat generated by heat-generating components arranged within the wind turbine tower by means of a conduit system fluid pump as part of the conduit system through
El. the first heat emitting means attached to a circumferential part of the inner surface of the wind turbine tower, E2. the second heat emitting means located under the foundation, or
E3. both heat emitting means in series.
Whether the cooling fluid is circulated through one of the heat emitting means or both depends on the detected temperature (s) . In case the temperature of the wind turbine tower is sufficient to dissipate the overall heat through the turbine tower the valves are adjusted so that the cooling fluid is circulated through the first heat emitting means only
since this flow path minimizes the load on the pump of the conduit system. In a preferred embodiment the method comprises the further step of, depending on the calculated optimal cooling fluid flow path, adjusting the flow direction of the cooling fluid by adjusting the conduit system fluid pump. By adjusting the flow direction the heat dissipation can be enhanced further.
The invention has the advantage of reduced manufacturing cost, since no external heat exchanger is needed. This also results in a smaller installation footprint and improves the visual aspect, i.e. the absence of an external heat exchanger.
The invention has the advantage of reduced system noise because the heat loss flux is dissipated by the turbine tower, allowing a reduction in the number of turbine fans being used as air movers.
The invention has the advantage of increased reliability, because fewer fans mean fewer moving parts.
The invention has the advantage of being part of an integral design because the heat emitting means can be manufactured and installed at the time of tower production.
The invention has the advantage that the heat emitting means can be manufactured separately and installed in existing towers .
The invention has the advantage that the heat emitting means can be removed from the tower for repair and reinstalled in situ.
The invention has the advantage of being part of an integral design because the foundation-based cooling system can be installed at the time of tower foundation construction.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be described in detail with reference to the drawings in which:
FIGURE 1 is a view of a prior art wind turbine tower which transfers heat onto the wind turbine tower;
FIGURE 2a is a perspective view of a wind turbine embodiment in which the present invention is embodied; FIGURE 2b is a perspective view of another wind turbine embodiment in which the present invention is embodied;
FIGURE 3 is a detail perspective view of the thermal management system of FIGURE 2a;
FIGURE 4 is a top view of the thermal management system of FIGURE 3;
FIGURE 5 is a cross-sectional view of an embodiment of the thermal management system of FIGURE 4 taken along the view line 5-5;
FIGURE 6 is a cross-sectional view of a further embodiment of the thermal management system of FIGURE 4; and
FIGURE 7 is a cross-sectional view of heat transfer piping imbedded in a substrate for the foundation-based cooling system shown in FIGURE 1 and FIGURE 4.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
Refer to FIGURE 1, which is a view of a prior art wind turbine tower which transfers heat onto the wind turbine tower, US Patent 6,676,122 to Wobben. Wobben discloses a wind energy facility 1 with a completely closed or at least partially closed cooling circuit, with which the heat to be dissipated from the cooling circuit is dissipated by the tower 3 or the nacelle 2 of the wind energy facility 1. The tower 3 has cooling channels 11, 12, and the coolant, preferably air, flows through these channels. Both the driving lines 3, 4 of the wind energy facility or parts of the driving lines and/or the electrical devices 8, 9 for converting the electrical energy are connected to the cooling circuit. The tower 3 is configured with two walls over at least two sections along its
longitudinal axis and a double-walled region forms a cooling channel 12, 11, with which the heated air introduced into the cooling channel dissipates its heat to the outer wall of the tower 3. The same air is used essentially for continuously cooling the main driving lines 3, 4, as well as the devices 8,
9 of the power electronics. The cooling channel includes a fan
10 that circulates air within the cooling circuit.
Refer to FIGURE 2a, which is a perspective view of a wind turbine embodiment in which the present invention is embodied. In FIGURE 2 a wind turbine is shown facing the incoming wind 8. This wind creates lift on the wind turbine blades 6 causing rotation of the entire rotor 7. Rotation of the rotor results in rotation of the low speed main shaft 5, which is the mechanical input to speed increaser 3. The mechanical output of the speed increaser is the high-speed shaft 4, which is connected to a high-speed generator 2.
The gear ratio of the gearbox 3 is selected to match the required speed of the low speed shaft 5 to that of the highspeed generator 2 and high-speed shaft 4. The wind turbine tower structure is identified as 1 in the figure. This structure is used to elevate the turbine and provide static and dynamic support for mechanical loads on the up tower structure. It is customary for the tower to have an entry door as shown at 9. Because the tower is a load carrying structure, cutting holes to allow for the removal of heat is highly undesirable .
Further in FIGURE 2a, in the case of a variable speed wind turbine, the generator is electrically connected to the heat generating means 11, which is a power electronic control system in this embodiment, via electrical pendant cables 15. The same is true for a constant speed wind turbine except that the control system 11 at the bottom of the tower is a more
conventional electromechanical or power electronic switchgear rather than a variable speed converter.
The wind turbine further comprises a first heat emitting means 20 which is attached to a circumferential part of the inner surface 25 of the wind turbine tower 1 and transfers heat of a cooling fluid to the wind turbine tower 1, which dissipates the heat of the cooling fluid to the environment.
The control system 11 sits on a platform and contains a (not shown) heat receiving means being arranged to absorb heat generated by the heat emitting means 11, i.e. the control system.
A conduit system 12, 13, 22, 24 connects the heat receiving means and the first heat emitting means 20 and circulates a cooling fluid between the heat receiving means of the control system 11 and the heat emitting means 20.
In detail, the conduit system comprises a tubing 13 and a circulating pump 12. The circulating pump 12 causes the cooling fluid, e.g. a cooling liguid, to flow across or through the heat-generating portion of the control system 11, i.e. the heat receiving means. This cooling liguid is heated up by the heat generated by the control system and exits the heat receiving means at an elevated temperature via tubing 13. According to the shown embodiment the circulating pump 12 is arranged downstream of the control system 11 and between the control system and the heat emitting means 20. The circulating pump 12 is connected with the heat emitting means 20 by a further tubing 22, the inlet to the first heat emitting means.
The liguid is made thermally conductive to the tower via the heat emitting means 20. In accordance with the shown embodiment the heat emitting means 20 is a cooling jacket. The conduit system further comprises a tubing 24 which connects an outlet of the heat emitting means 20 with the heat receiving means of the control system 11.
Wind 8 blowing over the tower 1 causes the heat that was supplied to the tower to be dissipated in the wind. Since the heat is finally carried away by the wind, no significant heat build-up within the tower occurs. Low temperature liquid at the other end of the cooling jacket 20 is then circulated back to the inlet of the heat receiving means of the control system 11 through tubing 24.
There are numerous methods for attaching the heat emitting means 20, i.e. the coolant jacket 20, to the wind turbine tower. For example, welding, brazing, or thermal bonding would all be acceptable methods. The heat emitting means can be sized based on the heat flux to be removed from the wind turbine systems. More height provides for the dissipation of more heat flux for a desired temperature rise. Depending on the wind turbine system power level, it is customary to remove from five to hundreds of kilowatts of heat flux while trying to maintain system temperature rises of 10 - 50 Degrees Celsius .
Refer to FIGURE 2b, which is a perspective view of another wind turbine embodiment in which the present invention is embodied. FIGURE 2b also shows the arrangement of the second heat emitting means (32) beneath the foundation (17) . In case two heat emitting means are used for heat dissipation, the conduit system comprises two further tubings 34, 36 for circulating the cooling fluid though the second heat emitting means. For further details in connection with the conduit system utilized for two heat emitting means refer to FIGURE 7.
FIGURE 3 shows a more detailed drawing of the heat emitting means for transferring the heat from components inside the tower to the inner surface of the turbine tower, which dissipates the heat to the environment.
In particular, FIGURE 3 shows the heat emitting means, which is designed as a cooling jacket 20. The coolant jacket
20 may be formed as a u-shaped channel being closed at its face sides, or as a self-contained enclosure. The cooling jacket may be compression bonded, welded and/or glued, or otherwise attached to the internal curvature of the tower itself. However, in accordance with the shown embodiment the cooling jacket 20 is pressed against the inner surface of the wind turbine tower 1 by a clamping device 26. In this case it is preferred that the cooling jacket 20 is formed as a self- contained enclosure to disperse the pressure imposed by the clamping or expansion device 26.
The cooling jacket 20 is formed to carry a cooling fluid, e.g. a cooling liquid like water or water/ethylene glycol mix that will enable heat transfer through the tower itself. To enhance the thermal flux through the tower it is preferred that at least the part of the tower where the heat emitting means is attached consists of metal or a metal alloy.
The coolant jacket is fitted to the interior wall of the tower during, for example, manufacture of the tower. With this embodiment of the invention the coolant jacket can be removed and repaired or replaced.
For a u-shaped coolant jacket the enclosure is not self- contained and the interior wall of the tower, to which the jacket is fitted, provides the heat-flux surface exit path of the coolant jacket. With this embodiment of the invention the interior wall of the tower comes in direct contact with the coolant (refer to FIGURE 6) . The outside of the tower may be formed with fins to increase the heat-dissipating surface.
Further, the inside of the tower base is shown in FIGURE 3 revealing the invention inside the tower. The tower 1 may have entry doors 9 and is fixed to a foundation 17 by bolts 19. The circular-shaped coolant jacket 20 fits against the inside of the tower to facilitate heat-flux injection into the wind turbine tower 1. The internal circular shaped coolant jacket
20 works with the wind turbine tower 1 to transport the turbine system loss in the form of heat flux to the inside of the turbine tower, where it is then conducted into the internal skin of the turbine tower for conduction from there through the skin of the turbine tower to the outside environment .
Tubing 22, acting as the inlet pipe, and tubing 24, acting as the outlet pipe, transfer heated cooling fluid to and cooled cooling fluid from the coolant jacket 20. The sizing of the tubings is determined by the amount of heat flux to be removed. The higher the heat-flux is, the larger the tubings have to be. The tubings may be thermally connected to the tower by means of welding, brazing, or thermal bonding in order to transfer the heat of components to a larger surface of the tower, i.e. also tubings 22, 24 transfer heat to the inner surface of turbine tower. As heated cooling fluid enters the inlet pipe 22 and passes through the coolant jacket 20 it gives up its heat to the tower 1, because heat tends to move from a high-temperature region to a low-temperature region. Wind blowing over the tower 1 causes the heat that is supplied to the tower to be dissipated in the wind. Since the heat is finally carried away by the wind, no significant heat build-up within the tower occurs. Low temperature cooling fluid at the outlet pipe 24 of the coolant jacket 20 is then circulated back to the inlet of the heat receiving means of the control system 11 through tubing 24.
FIGURES 4 and 5 show an embodiment of the heat emitting means, namely a cooling jacket 20 formed as a self-contained enclosure. The overall shape is circular, or in the shape of a toroid. The outside edge of the self-contained coolant jacket 20, which contacts the inside wall of the tower 1, is slightly curved at a radius matching the radius of curvature of the inside wall of the tower. This maximizes surface contact of
the self-contained coolant jacket 20 to the inside wall of the tower to provide low thermal resistance (or high thermal conduction) for the outside edge of the cooling jacket 20 that contacts the inside wall of the turbine tower 1. An expansion or clamping device 26 is provided for pressing the coolant jacket 20 against the inside wall of the tower 1. The expansion device 26 can be a turnbuckle or any type of expandable clamp that is used within a channel to compress a planar member within the channel against a wall of the channel. The clamp ensures uniform contact between the coolant jacket 20 and the inside wall 25 of the tower 1.
Given a curved, self-contained, toroidal tank design, with rectangular sides, and a length of 95% of the tower inside circumference, no vertical welds are needed, and no interference issues are involved with the lowest tower section main single vertical weld.
It is now referred to FIGURE 4 which shows optional tower manufacturer-installed support brackets 23 which can be used to provide low cost holding support for the coolant jacket 20, which also allows for coolant jacket removal and reinstallation by loosening the expansion device 26 should repair be necessary, since the cooling jacket is simply inserted into the support brackets 23
An overall side aspect ratio of 30:1 provides minimum thickness and sufficient surface area to allow the coolant jacket installation, just above the tower base 19, and below the base of the tower doors. This installation range allows for compact installation with minimum impact on all the other internal wind turbine electrical and mechanical systems. Furthermore, FIGURE 4 shows an exemplary arrangement of the second heat emitting means 32 beneath the foundation.
As shown in FIGURES 5 and 6, bolts 19 secure the turbine tower 1 to the foundation 17. The six sided coolant jacket 20
(FIGURE 5) is held in place by a support bracket 23. A variation using a u-shaped or five sided coolant jacket (FIGURE 6) 20 may also be held in place with epoxi, brackets, or other fastening methods such as 360 degree welding 26 of the coolant jacket 20.
A thermally conductive material 21, such as thermal grease, may be applied between the curved outside surface of the coolant jacket 20 and the inside diameter surface 25 of the turbine tower 1. Heat conduction is the transfer of thermal energy between substances due to a temperature gradient. It always takes place from a substance of higher temperature to a substance of lower temperature. Heat conduction acts to equalize a temperature difference. The thermal grease increases the thermal conductivity of the thermal interface 21 by compensating for the irregular surfaces of the coolant jacket and the inner wall 25. The thermal grease 21 should preferably provide low thermal resistance (or high thermal conduction) in the range of less than 0.6 degrees C per Watt per square inch once the expansion device (not shown in FIGURES 5 and 6) is adjusted after coolant jacket installation. Heat transfer therefore occurs from the hot coolant jacket 20 through the thermal grease 21 and the tower wall 1 where the heat is dissipated from the cooler outside wall 27 of the tower. The cooling fluid, which may be water or a mixture of Ethylene glycol and water, enters the coolant jacket 20 through the inlet line 22 at one end of the coolant jacket and exits through an output line 24 at the other end of the coolant jacket, for minimum pressure drop and maximum heat transfer. 304L Stainless Steel helps to keep fabrication costs down, as a minimum of additional labor steps are needed for the finishing and fabrication of the finished product with this type of material.
The coolant jacket 20 has the following typical size when used with a wind turbine that produces 2.5 Mw of power - 1 inch thick x 2.6 feet high x 40 feet long.
The coolant jacket 20 is located in the lowest tower section that is located at the base of the tower. There is a "keep out zone" which extends from 150 mm down from the bottom of the tower doorframes 9. The other "keep out zone" extends up one meter from the tower floor 17 so that enough room is provided for work that needs to be done to the tower bolts and nuts 19, and applicable cables (not shown) .
Refer to FIGURE 7 which is a cross-sectional view of an embodiment of the conduit system utilized in connection with two heat emitting means.
The tower 1 rests upon, for example, a concrete foundation 17. Heat-generating components 11 are arranged within the wind turbine tower 1 and (not shown) heat receiving means are arranged to absorb heat generated by the heat-generating components 11. The heat receiving means are a part of the heat generating means and hereafter it is only referred to heat generating means 11.
Hereafter, details of an embodiment of a conduit system are described. The heat-generating means are connected with a fluid pump 12 by a pipe or a tubing 13. A further tubing 36 connects second heat emitting means 32 with the pump 12, the tubing 36 being the inlet of the second heat emitting means. Along tubing 36 two three-way valves 46, 48, connected to bypass controls 44, are arranged. Valve 46 provides a connection to the first heat emitting means 20 (the cooling jacket), the connection being the inlet for the first heat emitting means. Valve 48 provides a further connection to the first heat emitting means 20, this connection being the outlet of the first heat emitting means. The conduit system comprises a further tubing 34 connecting the second heat emitting means 32
with the heat generating means 11. This valve tubing arrangement allows for two operating methods: connecting both heat emitting in series or circulating the cooling fluid through the second heat emitting means only. The shown embodiment comprises a third three-way valve 50 connecting the outlet tubing of the first heat emitting means 20 and tubing 34, and the outlet of the second heat emitting means 32. This three valve arrangement allows for a third operating method: circulating the cooling fluid through the first heat emitting means only.
Referring to FIGURE 7, an embodiment of the method in accordance with the invention is now described. To achieve optimal heat dissipation the temperature of the cooling fluid is detected with temperature sensor 52 which is connected with the by-pass controls 44. On the basis of the detected temperature, the optimal cooling fluid flow path is calculated and the valves 46, 48, 50 of the conduit system are adjusted accordingly. Depending on the flow path, the cooling fluid is circulated by means of the fluid pump 12 through the first heat emitting means 20 attached to a circumferential part of the inner surface of the wind turbine tower 1 or the second heat emitting means 32 located under the foundation 17, or both heat emitting means 20, 32 in series.
The following example emanates from the operating method in which the cooling fluid is circulated through the first heat emitting means 20 only. Due to changes in the environmental condition (temperature, solar irradiation on the tower) the temperature of the cooling fluid exceeds a given threshold. Depending on certain characteristics of a given wind turbine the optimal flow path for the cooling fluid is calculated (by the by-pass controls 44) and the valves 46, 48, 50 of the conduit system are adjusted accordingly. For example, the valves are adjusted so that the flow path
comprises both heat emitting means (both heat emitting means are connected in series) . Upon adjusting the valves the cooling fluid is circulated along the new flow path, which includes (in this order) : heat generating means 11, tubing 13, pump 12, tubing 36, valves 46, first heat emitting means 20, first heat emitting means outlet tubing, valve 48, second heat emitting means 32, tubing 34, heat generating means 11.
Furthermore, FIGURE 7 shows a preferred arrangement of the second heat emitting means 32. The heat emitting means 32, for example a coolant tubing network, is located in a filled excavation underneath the foundation and is installed before the foundation concrete is poured. The filled excavation includes a heat-conducting material 40 compacted around the coolant tubing network 32, the heat transfer coefficient of the compacted material being higher than the heat transfer coefficient of excavated material 41, so the total amount of heat transmitted from the tubing to the surrounding material is greater.
The features and advantages described in this specification are not all inclusive, and particularly, many additional features and advantages will be apparent to one of ordinary skill in the art in view of the figures, specification, and claims hereof. Moreover, it should be noted that the language used in the specification has been principally selected for readability and instruction purposes, and therefore resort to the claims is necessary to determine the inventive subject matter.