Centring device for centring a turbomachine casing, turbomachine system comprising a centring device and method for centring a turbomachine casing

Abstract

A centering device (10) for centering a turbine housing (40) relative to a central axis (33) of a radial turbine of a turbine system is described. The centering device (10) comprises an annular body (11) having an outer diameter D1 and an inner diameter D2, wherein the ratio D1 / D2 is ≤ 2. In addition, the centering device (10) comprises two or more centering elements (16) arranged on a lateral surface (12) of the annular body (11) for engaging with corresponding complementary centering elements (21) arranged on a support housing (20). The two or more centering elements (16) are configured for allowing a radial thermal expansion of the annular body (11) during engagement of the two or more centering elements (16) with the corresponding complementary centering elements (21). Furthermore, a turbine system comprising such a centering device and a method of centering a turbine housing are described.

Description

TECHNICAL FIELD

[0001] Embodiments of the present disclosure relate to a centering device for centering a turbine housing. Furthermore, embodiments of the present disclosure relate to a turbine system, such as a turbocharger or a turbo compound device, having a centering device as described in the present disclosure. In addition, embodiments of the present disclosure relate to a method of centering a turbine housing, in particular a method of centering a turbine housing by using a centering device as described herein. BACKGROUND

[0002] A typical turbine system is a turbocharger or a turbo compound device. Nowadays, exhaust gas turbochargers are widely used to improve the performance of internal combustion engines. An exhaust gas turbocharger usually has a turbine in the exhaust tract of an internal combustion engine and a compressor upstream of the internal combustion engine. The exhaust gases of the internal combustion engine expand in the turbine. The obtained work is transmitted via a shaft to the compressor, which compresses the air supplied to the combustion process in the internal combustion engine. By using the energy of the exhaust gases to compress the air supplied to the combustion process in the internal combustion engine, the combustion process and the efficiency of the internal combustion engine can be optimized. A turbo compound engine is a reciprocating engine that uses a turbine to recover energy from the exhaust gas. This energy is not used to drive a turbocharger, but is sent to the output shaft to increase the total power delivered by the engine.

[0003] Generally, a turbine system, such as a turbocharger or a turbo compound device, comprises a turbine, in particular a radial turbine, which is enclosed in a turbine housing. The turbine housing has to be centered with respect to the center axis of the radial turbine. Usually, the centering of the turbine housing is done by hot gas centering, for example hot gas centering on a heat shield or a nozzle ring arranged between the turbine housing and the support housing. A problem of the conventional hot centering method is that an equally fast heat transfer from the exhaust gas to the hot centering element, such as the heat shield, cannot be guaranteed, so that for transient operating states a larger gap between the turbine wheel and the turbine casing is required. However, a larger gap between the turbine wheel and the turbine casing has a disadvantageous effect on the turbine efficiency.

[0004] Therefore, in view of the above, there is a need to provide an improved centering of a turbine housing. SUMMARY

[0005] In view of the above, a centering device for centering a turbine housing, a turbine system comprising a centering device as described herein and a method of centering a turbine housing according to the independent claims is provided. Other aspects, advantages and features are apparent from the dependent claims, the description and the drawings.

[0006] According to one aspect of the present disclosure, a centering device for centering a turbine housing relative to a central axis of a radial turbine of a turbine system is provided. The centering device comprises an annular body having an outer diameter D1 and an inner diameter D2, wherein a ratio of D1 / D2 is less than or equal to 2 (D1 / D2 < 2). In addition, the centering device comprises two or more centering elements disposed on a lateral surface of the annular body. The two or more centering elements are configured for engagement with corresponding complementary centering elements disposed on a support housing. The two or more centering elements are configured for allowing radial thermal expansion of the annular body during engagement of the two or more centering elements with the corresponding complementary centering elements.

[0007] Thus, in comparison to the prior art, the centering device of the present disclosure provides for an improved centering of the turbine housing relative to the central axis of the radial turbine. In particular, embodiments of the centering device as described herein provide for centering of the turbine housing under transient and steady state operation as well as for minimizing the gap between the turbine wheel and the turbine housing. Thus, in comparison to the prior art, turbine efficiency can be improved by employing the centering device as described herein. In particular, it has been found that with the centering device as described herein, a reduction of the gap and an increase of turbine efficiency can be achieved.

[0008] According to another aspect of the present disclosure, a turbine system is provided. The turbine system comprises a support housing, a turbine housing of a radial turbine, and a shaft extending along a central axis. The shaft is mounted in the support housing and a turbine wheel is arranged on the shaft. Further, the turbine system comprises an exhaust inlet passage formed in the turbine housing upstream of the turbine wheel. In addition, the turbine system comprises a centering device according to embodiments described herein. The support housing comprises centering elements complementary to the two or more centering elements of the centering device. The two or more centering elements of the centering device engage the corresponding complementary centering elements of the support housing. The two or more centering elements are configured for allowing radial thermal expansion of the annular body during engagement of the two or more centering elements with the corresponding complementary centering elements.

[0009] Thus, in comparison to the prior art, an improved turbine system is provided. In particular, embodiments of the turbine system as described herein provide for an optimized centering of the turbine housing under transient and steady state operation in combination with minimizing the gap between the turbine wheel and the turbine housing, such that turbine system efficiency can be improved.

[0010] According to another aspect of the present disclosure, a method of centering a turbine housing relative to a central axis of a radial turbine of a turbine system is provided. The method comprises transferring heat from an exhaust gas to a centering device according to embodiments described herein. Further, the method comprises centering the turbine housing via thermal expansion of the centering device.

[0011] Accordingly, embodiments of the method as described herein provide optimized centering of the turbine housing under transient and steady state operation compared to the prior art, enabling minimization of the gap between the turbine wheel and the turbine housing and enabling improved turbine system efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0012] A more particular description of the above-mentioned and other aspects of the present disclosure can be acquired by reference to one or more embodiments, shortly summarized hereinbelow and described in detail below with reference to the attached drawings. The drawings provided are directed to embodiments of the present disclosure and describe:

[0013] Fig. 1 shows a cross-sectional view of a portion of a turbine system having a radial turbine and a heat shield for centering the turbine housing according to the prior art:

[0014] Figure 2 A schematic isometric view of a centering device according to embodiments described herein is shown:

[0015] Figure 3 A schematic isometric view of a support housing comprising centering elements complementary to the centering elements of a centering device according to embodiments described herein is shown: and

[0016] Figure 4 A cross-section of a portion of a turbine system having a radial turbine comprising a centering device according to embodiments described herein is shown. DETAILED DESCRIPTION

[0017] Reference will now be made in detail to various embodiments, one or more examples of which are illustrated in each of the figures. Each example is provided by way of explanation of the subject matter and is not meant as a limitation of the subject matter. For example, features illustrated or described as part of one embodiment can be used with any other embodiment or in combination with any other embodiment to produce yet another embodiment. It is intended that the present disclosure include such modifications and variations.

[0018] In the following description of the drawings, like reference numerals indicate like or similar parts. Generally, only the differences with respect to the various embodiments are described. The description of a part or aspect in one embodiment applies equally to the corresponding part or aspect in another embodiment, unless otherwise indicated.

[0019] Fig. 1 shows a cross-sectional view of a turbosystem 100 according to the prior art having a radial turbine 35 and a heat shield 62 for centering the turbine housing 40. The radial turbine 35 comprises a turbine housing 40, a shaft 34 mounted in a support housing 20 and on which a turbine wheel 30 having rotor blades 31 is arranged. Further, Fig. 1 shows a heat shield 62 and a nozzle ring 61 arranged between the turbine housing 40 and the support housing 20. According to the prior art, as exemplarily shown in Fig. 1, hot gas centering of the turbine housing is implemented via the heat shield. The heat shield shown in Fig. 1 has one cold centering element 63 and two hot centering elements 64. As can be understood from Fig. 1, at low temperatures, the turbine housing 40 is centered via the cold centering element 63, while at high temperatures, i.e. upon thermal expansion of the heat shield 62, the turbine housing is centered via the hot centering elements 64. However, as can be understood from Fig. 1, in transient operating states, i.e. during start-up of the turbine, centering can not be optimal due to inhomogeneous thermal expansion of the entire heat shield. Furthermore, as exemplarily shown according to the prior art of Fig. 1, there is typically a gap 65 between the nozzle ring 61 and the heat shield 62, which can be detrimental for heat transfer from the exhaust gas to the heat shield for achieving hot centering.

[0020] With exemplary reference to Figures 2 to 4 A centering device 10 for centering a turbine housing 40 relative to a center axis 33 of a radial turbine of a turbosystem is described. According to embodiments which can be combined with other embodiments described herein, the centering device 10 comprises an annular body 11 having an outer diameter D1 and an inner diameter D2. The ratio D1 / D2 is less than or equal to 2 (D1 / D2 < 2). In particular, the inner diameter D2 of the annular body 11 typically provides a central opening 14. Typically, centering of the turbine housing in transient and high temperature operating states is achieved via the outer diametric housing surface of the annular body, i.e. at the outer diameter D1.

[0021] It is to be understood that the centering device described herein is typically a separate device. In other words, the centering device as typically described herein is not part of the support housing or the turbine housing. More specifically, the centering device according to the embodiments described herein is typically neither an integral part of the support housing nor an integral part of the turbine housing, but a separate device.

[0022] Further, as Figure 2 Exemplarily, the centering device 10 comprises two or more centering elements 16 arranged on a side surface 12 of the annular body 11. Typically, the side surface 12 of the annular body 11 is a support housing side on which the two or more centering elements 16 are arranged. As Figure 3 Exemplarily, the two or more centering elements 16 are configured for engaging with corresponding complementary centering elements 21 arranged on the support housing 20.

[0023] Furthermore, the two or more centering elements 16 are configured for allowing a radial thermal expansion of the annular body 11 during the engagement of the two or more centering elements 16 with the respective complementary centering elements 21. In other words, the two or more centering elements 16 are configured such that a contact between the two or more centering elements 16 and the complementary centering elements 21 is ensured during a thermal expansion of the centering device 10. More specifically, the two or more centering elements 16 are configured such that a guided movement of the two or more centering elements 16 relative to the complementary centering elements 21 is provided during a radial thermal expansion of the annular body 11.

[0024] Thus, by using the centering device 10 in a turbine system, for example, as Figure 4 As exemplarily shown, especially in transient and steady state operating conditions, an improved centering of the turbine casing can be provided. As a result, a gap R between the turbine blades 31 and the turbine casing 40 can be reduced such that a turbine efficiency can be improved.

[0025] According to embodiments which can be combined with other embodiments described herein, the two or more centering elements 16 have a first planar guiding surface 17. As Figure 2 and 3 As exemplarily shown, the respective complementary centering elements 21 have a complementary second planar guiding surface 18. Especially, the first planar guiding surface 17 and the second planar guiding surface 18 are configured for guiding a relative movement of the two or more centering elements 16 relative to the respective complementary centering elements 21 during a thermal expansion, in particular a radial thermal expansion, of the annular body 11.

[0026] For example, according to embodiments which can be combined with other embodiments described herein, the opposing surfaces of the first planar guiding surfaces 17 of the two or more centering elements 16 can be parallel to each other. Alternatively, the first planar guiding surfaces 17 of the two or more centering elements 16 can be inclined relative to each other. Especially, as Figure 2 As exemplarily shown, the first planar guiding surfaces 17 can be inclined towards the center C of the inner diameter of the annular body 11.

[0027] According to an example which can be combined with other embodiments described herein, the first planar guiding surfaces 17 are arranged on opposite sides of the centering element 16, wherein one of the first planar guiding surfaces 17 has a first surface normal N1 pointing in a clockwise circumferential direction and the other one of the first planar guiding surfaces 17 has a second surface normal N2 pointing in an anti-clockwise circumferential direction of the annular body 11.

[0028] Thus, as Figure 3As exemplarily shown, the opposing surfaces of one or more of the complementary second planar guide surfaces 18 of the respective complementary centering elements 21 can be parallel to each other or inclined relative to each other, such that during the thermal expansion of the annular body 11 of the centering device, relative movement of two or more centering elements 16 relative to the respective complementary centering elements 21 can be achieved.

[0029] According to alternative examples that can be combined with other embodiments described herein, one or more of the two or more centering elements 16 may have a circular shape (not explicitly shown). In particular, one or more of the two or more centering elements 16 may have a cylindrical shape (e.g., having a circular base, an egg-shaped base, or an elliptical base) extending from the side surface 12 of the annular body 11. Thus, it should be understood that the circular, particularly cylindrical, centering element 16 engaging with the corresponding complementary centering element 21 having a planar guiding surface 18 provides two relatively arranged contact points, particularly contact lines, between the centering element 16 and the corresponding complementary centering element 21. Therefore, during the thermal expansion of the annular body, the relative movement of the two or more centering elements 16 with respect to the corresponding complementary centering element 21 can also be achieved using the circular or cylindrical centering element 16 of the centering device 10. According to embodiments that can be combined with other embodiments described herein, the two or more centering elements 16 are notches and / or cams. Correspondingly, the corresponding two or more complementary centering elements 21 are cams and / or notches. In other words, two or more centering elements 16 can include one or more notches and one or more cams, two or more notches, or two or more cams. Corresponding complementary centering elements 21 can be configured. In other words, the corresponding complementary centering element 21 can include one or more cams and one or more notches, two or more cams, or two or more notches. Figure 2 An example is shown in which two or more centering elements 16 are three notches. Figure 3 An example is shown where the corresponding complementary centering element 21 is three cams.

[0030] According to embodiments that can be combined with other embodiments described herein, the centering device 10 is connected to or is part of the nozzle ring. In particular, the centering device 10 can be connected to the nozzle ring via a welded connection, a brazed connection, and at least one of one or more fasteners. Alternatively, the centering device 10 is a component of the nozzle ring. For example, the centering device and the nozzle ring can be made from a single cast or machined element.

[0031] like Figure 2 As exemplarily shown, the guide vane 15 can be arranged circumferentially around the central opening 14 on the turbine side 13 of the annular body 11.

[0032] According to examples which can be combined with other embodiments described herein, the two or more centering elements 16 comprise at least one cam having a receptacle 19 for accommodating a fixing element 51, in particular a lug, of the hot plate 50. Thus, advantageously, the two or more centering elements 16 can be configured to provide a dual functionality, namely centering on the one hand and fixing of the hot plate on the other hand.

[0033] According to embodiments which can be combined with other embodiments described herein, as Figure 2 Exemplarily shown, the two or more centering elements 16 are equally spaced apart in a circumferential direction around the central opening 14. Alternatively, the two or more centering elements 16 can be irregularly spaced apart in a circumferential direction around the central opening 14 (not explicitly shown).

[0034] Exemplarily with reference to Figure 2 According to another aspect of the present application, a turbine system is described. The turbine system comprises a support housing 20, a turbine housing 40 of a radial turbine, a shaft 34 extending along a central axis 33. The shaft is mounted in the support housing 20 and a turbine wheel 30 is arranged on or mounted to the shaft. Typically, as described herein, the shaft 34 extends through the central opening 14 of the centering device 10. The turbine system comprises an exhaust gas inlet passage 41 formed in the turbine housing 40 upstream of the turbine wheel 30. In addition, the turbine system comprises a centering device 10 according to any one of the embodiments described herein. The support housing 20 comprises centering elements 21 complementary to the two or more centering elements 16 of the centering device 10. The two or more centering elements 16 engage with the respective complementary centering elements 21 provided on the support housing 20.

[0035] According to embodiments of the turbine system which can be combined with other embodiments described herein, the centering device 10 is connected to the nozzle ring, in particular via at least one of a welded connection, a brazed connection and one or more fasteners. Alternatively, the centering device 10 is an integral part of the nozzle ring. As Figure 4 and Figure 2 Exemplarily shown, the nozzle ring can comprise vanes 15. For example, guide vanes 15 can be provided between a first annular sheet-like element 111 provided at the support housing side 12 and a second annular sheet-like element 112 provided at the turbine housing side 13. In addition, the second annular sheet-like element 112 can be connected to a seal ring 113.

[0036] Alternatively, the nozzle ring can be vaneless (not explicitly shown).

[0037] According to embodiments which can be combined with other embodiments described herein, the centering device 10 is made of a material having a higher coefficient of thermal expansion than the material of the turbine housing 40 and / or the material of the support housing 20.

[0038] According to embodiments, which can be combined with other embodiments described herein, the centering device 10 is made of a material having the same coefficient of thermal expansion as the material of the nozzle ring.

[0039] According to turbine system embodiments, which can be combined with other embodiments described herein, the centering device 10 is arranged between the support housing 20 and the turbine housing 40. The centering device 10 is arranged and configured such that heat from the exhaust gas is transferred to the centering device 10 during operation of the turbine system, and the heat flow from the exhaust gas to the centering device is a continuous function. The heat flow is AQ / At = -K-A-AT / Ax, where AQ is the net heat (energy) transfer, At is the time used, AT is the cold-hot side temperature difference, Ax is the thickness of the thermally conductive material (distance between cold-hot side), K is the thermal conductivity, A is the surface area over which the heat is dissipated. Thus, as long as the thermal conductivity K is continuous or constant over the heat flow path, the heat flow is a continuous function.

[0040] In other words, according to embodiments, which can be combined with other embodiments described herein, the centering device is configured and arranged in a turbine system as described herein such that along the heat flow path from the exhaust gas to the centering device, the thermal conductivity does not change abruptly. For example, as shown in the prior art of Fig. 1, the gap 65 between the nozzle ring 61 and the heat shield represents a change in thermal conductivity along the heat flow path at the interface of “solid to gas” and “gas to gas”, and thus provides a discontinuous function of the heat flow.

[0041] As Figure 4 Figure 4 According to turbine system embodiments, which can be combined with other embodiments described herein, the turbine system further comprises a heat plate 50 having a fixing element 51. In particular, the fixing element 51 (e.g. a lug) is generally arranged in the accommodation 19 of the cam of the centering device 10.

[0042] According to another aspect of the application, a method of centering a turbine housing 40 relative to a center axis 33 of a radial turbine of a turbine system is described. The method comprises transferring heat from the exhaust gas to a centering device 10 according to any of the embodiments described herein. In addition, the method comprises centering the turbine housing via thermal expansion of the centering device 10. More specifically, generally transferring heat from the exhaust gas to the centering device comprises providing a heat flow from the exhaust gas to the centering device, wherein the heat flow is a continuous function.

[0043] In view of the above, it will be appreciated that the embodiments described herein advantageously provide an optimized thermal centering of the turbine housing, and ensure optimal turbine efficiency by achieving a minimum clearance between the turbine, in particular the turbine impeller blades, and the housing, both at transient and steady state operation.

[0044] While the foregoing description has been directed to embodiments, other and further embodiments can be devised without departing from the basic scope, and the scope is determined by the claims that follow.

[0045] Reference numerals

[0046] 10 centering device

[0047] 11 annular body

[0048] 12 side surface

[0049] 13 turbomachine side

[0050] 14 central opening

[0051] 15 guide vane

[0052] 16 centering element

[0053] 17 first guide surface

[0054] 18 second guide surface

[0055] 19 housing

[0056] 20 support housing

[0057] 21 complementary centering element

[0058] 30 turbomachine wheel

[0059] 31 turbomachine blade

[0060] 33 central axis

[0061] 34 shaft

[0062] 35 radial turbine

[0063] 36 nozzle ring

[0064] 40 turbomachine housing

[0065] 41 exhaust gas inlet passage

[0066] 50 hot plate

[0067] 51 lug

[0068] 61 prior art nozzle ring

[0069] 62 prior art heat shield

[0070] 63 cold centering element

[0071] 64 hot centering element

[0072] 100 turbomachine system

[0073] 111 first annular sheet-like element

[0074] 112 second annular sheet-like element

[0075] 113 sealing ring

[0076] D1 outer diameter

[0077] D2 inner diameter

[0078] C center

Claims

1. A centering device (10) for centering a turbine casing (40) relative to a central axis (33) of a radial turbine of a turbomachinery system, the centering device comprising: - an annular body (11) having an outer diameter D1 and an inner diameter D2, wherein the ratio D1 / D2 < 2: and - two or more centering elements (16) provided on a lateral surface (12) of the annular body (11) for engaging with corresponding complementary centering elements (21) provided on a support casing (20), wherein the two or more centering elements (16) are configured for allowing a radial thermal expansion of the annular body (11) during engagement of the two or more centering elements (16) with the corresponding complementary centering elements (21), wherein the centering device (10) is connected to a nozzle ring for the radial turbine.

2. The centering device (10) according to claim 1, wherein The two or more centering elements (16) have first planar guiding surfaces (17) and the corresponding complementary centering elements (21) have complementary second planar guiding surfaces (18) for guiding a relative movement of the two or more centering elements (16) relative to the corresponding complementary centering elements (21) during a thermal expansion of the annular body.

3. The centering device (10) according to claim 2, wherein opposite surfaces of the first planar guiding surfaces (17) of one or more of the two or more centering elements (16) are parallel or inclined relative to each other and opposite surfaces of the complementary second planar guiding surfaces (18) of one or more of the corresponding complementary centering elements (21) are parallel or inclined relative to each other.

4. The centering device (10) according to any one of claims 1 to 3, wherein The two or more centering elements (16) are at least one of a notch and a cam and wherein the corresponding complementary centering elements (21) are at least one of a cam and a notch.

5. The centering device (10) according to any one of claims 1 to 3, wherein the centering device (10) is connected to the nozzle ring via at least one of a welded connection and one or more fasteners.

6. The centering device (10) according to any one of claims 1 to 3, wherein The centering device (10) is an integral part of the nozzle ring.

7. The centering device (10) according to any one of claims 1 to 3, wherein the two or more centering elements (16) are cams and wherein at least one of the cams comprises a receptacle (19) for accommodating a fixing element (51) of a thermal plate (50).

8. The centering device of claim 7, wherein, The fixing element (51) is a lug.

9. The centering device (10) according to any one of claims 1 to 3, wherein the two or more centering elements (16) are equally spaced in a circumferential direction around a central opening (14) or wherein the two or more centering elements (16) are irregularly spaced in a circumferential direction around the central opening (14).

10. The centering device (10) according to any one of claims 1 to 3, wherein the inner diameter D2 of the annular body (11) provides a central opening (14).

11. Centering device (10) according to any one of claims 1 to 3, further comprising an outer radial shell surface at the outer diameter D1 of the annular body (11) for centering the turbine housing in transient and high temperature operating conditions.

12. The centering device (10) according to any one of claims 1 to 3, wherein At least one of the two or more centering elements (16) has a cylindrical shape extending from the lateral surface (12) of the annular body (11).

13. The centering device (10) according to claim 12, wherein The at least one centering element has a base selected from a circular base, an egg-shaped base or an elliptical base.

14. A turbine system comprising: - a support housing (20): - a turbine housing (40) of a radial turbine: - a shaft (34) extending along a center axis (33), the shaft being mounted in the support housing (20) and having a turbine impeller (30) arranged thereon, - a waste gas inlet channel (41) formed in the turbine housing (40) upstream of the turbine impeller (30), and - a centering device (10) according to any one of claims 1 to 4 and 7 to 13, wherein the support housing (20) comprises centering elements (21) complementary to the two or more centering elements (16) of the centering device (10), and wherein the two or more centering elements (16) engage with the respective complementary centering elements (21).

15. The turbine system of claim 14, wherein, The centering device (10) is connected to the nozzle ring via at least one of a welded connection and one or more fasteners.

16. The turbine system according to claim 14, wherein the centering device (10) is an integral part of the nozzle ring.

17. The turbine system of any one of claims 14-16, wherein, The nozzle ring is made of a material having the same coefficient of thermal expansion as the material of the centering device (10).

18. The turbine system according to any one of claims 14 to 16, wherein the centering device (10) is arranged between the support housing (20) and the turbine housing (40), and wherein, The centering device (10) is arranged and configured such that heat from the waste gas is transferred to the centering device (10) during operation of the turbine system, and the heat flow from the waste gas to the centering device is a continuous function.

19. The turbine system according to any one of claims 14 to 16, further comprising a heat plate (50) having a fixation element (51) arranged in the accommodation (19) of the cam of the centering device (10) according to claim 4.

20. The turbine system of any one of claims 14-16, wherein, The centering device (10) is a separate device.

21. A method of centering a turbine housing (40) relative to a center axis (33) of a radial turbine of a turbine system, the method comprising: - transferring heat from the waste gas to a centering device (10) according to any one of claims 1 to 13, and - centering the turbine housing via thermal expansion of the centering device (10).

22. The method of claim 21, wherein, Transferring heat from the waste gas to the centering device comprises providing a heat flow from the waste gas to the centering device, wherein the heat flow is a continuous function.

23. The method of claim 21, wherein, The heat flow is AQ / At = -K-A-AT / Ax, wherein AQ is the net heat transfer, At is the time used, AT is the cold-hot side temperature difference, Ax is the thickness of the heat conducting material, K is the thermal conductivity, A is the surface area from which the heat is dissipated.

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