The thread was started a year ago, of course you did not have a time to read it, especially that part where I wrote that I gave up the idea because naked lamps look prettier.
The funny thing is I got this 'deja vu' feeling thinking 'havent I seen this thread before?' I wouldnt be surprised if I've posted in it when it was fresh. Perhaps I'll read it tonite in it's entirety.
While I did at one time make such a heatsink, data on which you can download from here http://www.pearl-hifi.com/06_Lit_Archive/07_Misc_Downloads/RB300_3CX_Data_Sheet.pdf I no longer make the part and I know of no other source
I came across this thread and read it with much interest. Since the thread ended up kind of inconclusive, I looked for more information trying to answer the following questions:
Q1. How infrared radiation from hot plate depends on plate temperature, environment temperature, and other factors?
Q2. How much infrared radiation from hot plate passes through the glass, is absorbed by the glass, and transmitted back off the glass to the plate?
Q3. What factors contribute to heat dissipation from glass envelope and how envelope cooling can be improved?
A1. Power radiated by plate is governed by Stefan-Boltzmann equation:
P=KεA(Ta^4 – Te^4), where
K, Stefan-Boltzmann radiation constant;
ε, emissivity factor, values ranging from 0 to 1, the latter being emissivity of absolute black body;
A, radiating area of plate;
Ta, plate temperature in degrees of Kelvin;
Te, glass envelope temperature in degrees of Kelvin.
The factor having most influence on heat radiation is plate temperature, because heat transfer by radiation is proportionate to fourth power of absolute temperature. Glass temperature has lesser, but not negligible effect. At typical plate temperature of 400C and glass temperature of 200C, about 25% of energy is radiated by glass back to plate. If glass temperature is reduced to 100C, the energy radiated back to plate will be only about 10%. Accordingly, for a tube having 25W plate dissipation rating, keeping glass at 100C will allow safely increasing plate dissipation to 28.75W. This answers OP's question about whether tube cooling allows increasing plate dissipation. It does.
ε has profound effect on energy radiation. Shiny metal surface has ε of about 0.1, grey alumina-blasted metal is 0.3-0.4, black polished metal is 0.6-0.7, and black carbonized metal with matte surface may be as high as 0.98. Thus, examining plate appearance may tell something about power rating. It is not surprising why a 807 tube with black carbonized plate is rated 25W, but similar 6BG6G with shiny black plate is only 20W.
"A" seems straightforward - larger plate area will radiate more power. However, plate surface temperature may be not uniform, depending on tube construction. Iron or nickel plate alloys have relatively poor heat conductance (Ni is 2 times more conductive than Fe), which is exacerbated by low thickness of material (ca. 0.1-0.2mm). Beam power tubes have very uneven heat distribution across the plate, whereas true power pentodes are much more even in this respect, thus allowing more efficient use of radiating surface.
A2. At the typical working plate temperature of 400C, the wavelength of IR radiation is broadly distributed from 1.5 to over 10 microns, with peak at 4 microns. Soft glass typical of most tubes has transmissivity of about 0.55 at 4 microns, and virtually zero at 5 microns and above. About 35% of total 400C IR passes through soft glass. Roughly 5% is reflected back to plate (this is in addition to Stefan-Boltzmann heat transfer), and the remainder 60% is absorbed by the glass. It might be counterintuitive, but glass has ε of 0.92-0.94 for IR, so it radiates and absorbs heat quite efficiently despite its smooth surface.
Although glass is poor heat conductor (1/30 conductivity of steel), temperature gradient across 1 mm glass thickness does not exceed 2-3C under rated power conditions. However, temperature gradients along the glass envelope may be as high as 150C. This is not a practical concern though, as long as rated temperature at the hottest point is not exceeded.
A3. As discussed, 35% of plate's heat passes through, and the rest is absorbed by the glass. Of the absorbed portion, some is radiated into environment according to Stefan-Boltzmann law, and the remainder is dissipated by air convection. For a tube with 100 cm^2 surface area with average envelope temperature of 130C and environment of 30C (DIY amplifier without enclosure), the calculated power radiated from envelope is about 1W, and dissipated by convection is 15W. So, convection dominates heat dissipation by envelope. Under equal conditions, large envelope is more effective at dissipating heat than smaller envelope for both radiation and convection, with heat transfer proportionate to square of envelope's diameter.
A tube cooler like Pearl's changes the balance of tube cooling by virtually eliminating heat radiation into environment (40% of total) and substituting it for convection. To be effective, the cooler must have surface area much larger than envelope's, and made of highly conductive material. Heat transfer at the glass-cooler interface may be a problem. Because heat radiation plays minuscule role in cooler's function, black painting is not necessary, but providing for good air convection is. However, good air convection around naked tube may be sufficient for keeping glass at safe temperature without sacrificing the benefits of radiation cooling.
Sorry for being too long.
Q1. How infrared radiation from hot plate depends on plate temperature, environment temperature, and other factors?
Q2. How much infrared radiation from hot plate passes through the glass, is absorbed by the glass, and transmitted back off the glass to the plate?
Q3. What factors contribute to heat dissipation from glass envelope and how envelope cooling can be improved?
A1. Power radiated by plate is governed by Stefan-Boltzmann equation:
P=KεA(Ta^4 – Te^4), where
K, Stefan-Boltzmann radiation constant;
ε, emissivity factor, values ranging from 0 to 1, the latter being emissivity of absolute black body;
A, radiating area of plate;
Ta, plate temperature in degrees of Kelvin;
Te, glass envelope temperature in degrees of Kelvin.
The factor having most influence on heat radiation is plate temperature, because heat transfer by radiation is proportionate to fourth power of absolute temperature. Glass temperature has lesser, but not negligible effect. At typical plate temperature of 400C and glass temperature of 200C, about 25% of energy is radiated by glass back to plate. If glass temperature is reduced to 100C, the energy radiated back to plate will be only about 10%. Accordingly, for a tube having 25W plate dissipation rating, keeping glass at 100C will allow safely increasing plate dissipation to 28.75W. This answers OP's question about whether tube cooling allows increasing plate dissipation. It does.
ε has profound effect on energy radiation. Shiny metal surface has ε of about 0.1, grey alumina-blasted metal is 0.3-0.4, black polished metal is 0.6-0.7, and black carbonized metal with matte surface may be as high as 0.98. Thus, examining plate appearance may tell something about power rating. It is not surprising why a 807 tube with black carbonized plate is rated 25W, but similar 6BG6G with shiny black plate is only 20W.
"A" seems straightforward - larger plate area will radiate more power. However, plate surface temperature may be not uniform, depending on tube construction. Iron or nickel plate alloys have relatively poor heat conductance (Ni is 2 times more conductive than Fe), which is exacerbated by low thickness of material (ca. 0.1-0.2mm). Beam power tubes have very uneven heat distribution across the plate, whereas true power pentodes are much more even in this respect, thus allowing more efficient use of radiating surface.
A2. At the typical working plate temperature of 400C, the wavelength of IR radiation is broadly distributed from 1.5 to over 10 microns, with peak at 4 microns. Soft glass typical of most tubes has transmissivity of about 0.55 at 4 microns, and virtually zero at 5 microns and above. About 35% of total 400C IR passes through soft glass. Roughly 5% is reflected back to plate (this is in addition to Stefan-Boltzmann heat transfer), and the remainder 60% is absorbed by the glass. It might be counterintuitive, but glass has ε of 0.92-0.94 for IR, so it radiates and absorbs heat quite efficiently despite its smooth surface.
Although glass is poor heat conductor (1/30 conductivity of steel), temperature gradient across 1 mm glass thickness does not exceed 2-3C under rated power conditions. However, temperature gradients along the glass envelope may be as high as 150C. This is not a practical concern though, as long as rated temperature at the hottest point is not exceeded.
A3. As discussed, 35% of plate's heat passes through, and the rest is absorbed by the glass. Of the absorbed portion, some is radiated into environment according to Stefan-Boltzmann law, and the remainder is dissipated by air convection. For a tube with 100 cm^2 surface area with average envelope temperature of 130C and environment of 30C (DIY amplifier without enclosure), the calculated power radiated from envelope is about 1W, and dissipated by convection is 15W. So, convection dominates heat dissipation by envelope. Under equal conditions, large envelope is more effective at dissipating heat than smaller envelope for both radiation and convection, with heat transfer proportionate to square of envelope's diameter.
A tube cooler like Pearl's changes the balance of tube cooling by virtually eliminating heat radiation into environment (40% of total) and substituting it for convection. To be effective, the cooler must have surface area much larger than envelope's, and made of highly conductive material. Heat transfer at the glass-cooler interface may be a problem. Because heat radiation plays minuscule role in cooler's function, black painting is not necessary, but providing for good air convection is. However, good air convection around naked tube may be sufficient for keeping glass at safe temperature without sacrificing the benefits of radiation cooling.
Sorry for being too long.
That is not the Stefan-Boltzmann equation, Stefan–Boltzmann equation states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time is
E = σ T⁴
Where σ = 5.67 x 10⁻⁸ W/(m² ºK⁴) is the Stefan-Boltzmann constant, and T is the absolute temperature of the emitter surface.
For a black body of area A, radiated power across all wavelengths is
P = A σ T⁴
For other than ideal black bodies
P = ε A σ T⁴
Where ε is the emissivity, ε<1
If the body, at temperature T is radiating energy to its cooler surroundings at temperature Tc, then
P = ε A σ (T⁴ - Tc⁴)
Note that emissivity is also function of the temperature
ε = ε (T)
So we must cheat to derive that you stated as Stefan-Boltzmann equation.
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In the usual case that environment temperature Te is smaller than cooler temperature Tc, your statement is wrong because the cooler still radiates as
P = ε A σ (Tc⁴ - Te⁴)
And black painting is intended to make the cooler as "black" as possible, increasing ε, remind you that a black body is the best emitter and at the same time the best absorber, that is also the reason of carbonized anodes.
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Yours is the simplified equation for the case of absolute black body radiating into infinite space. My formula is for radiation energy exchange between two bodies with different temperatures. The Te component can be ignored with large temperature difference, but not when the difference is not so large.
sser2, you would need to provide some mathematical support for a few of the values you use, especially relating to power transfer through glass, as that is an integration across a frequency span, where the transmittance varies with frequency, and the power density is a function of frequency and source temperature.
There is also an issue with your description of radiation power flow - transfer is from hotter to colder surfaces, not the other way.
The glass thickness has a significant effect on transmission profile with frequency, as indicated in that app note AN109.
There is also an issue with your description of radiation power flow - transfer is from hotter to colder surfaces, not the other way.
The glass thickness has a significant effect on transmission profile with frequency, as indicated in that app note AN109.
If you read my post carefully, you will note that at 200C tube surface and environment at room temperature, heat transfer by radiation is only 1/15 of that by convection. For convection cooling, it doesn't matter if surface is shiny mirror or matte black.
trobbins: I deliberately omitted references to source materials and calculations - it would make my already long post so much longer. Specifically re. power transfer through glass, please look at Fig.1 of "Material Technology for Electron Tubes" by Walter H. Kohl, found in the compilation of literature at the Pearl web site. The graph in Fig.1 superimposes spectral transmissivity of glass and IR energy spectra at 500 and 300C. 400C curve can be approximately interpolated, and % of transmitted energy calculated by figuring areas under the curves.
This is a common misconception. Radiation energy is emitted and absorbed both ways according to the simplified Stefan-Boltzmann equations for hotter body and for cooler body, however, the net transfer of energy is from hot body to cold one.
Sure it does. If 1 mm of glass absorbs 40% of IR radiation of 3 microns, a thicker layer will absorb more according to Beer-Lambert law. The quoted Fig.1 shows absorbance graph for typical thickness of soft glass in tubes, about 1 mm.
I will be glad to provide other references and explanations.
Yours, sser2
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Can you help me out please to identify "Fig.1" in that 1951 referenced book:
http://www.tubebooks.org/Books/kohl_materials.pdf
With respect to net power flow by radiation being the outcome of interest, your post #225 was difficult to interpret for "At typical plate temperature of 400C and glass temperature of 200C, about 25% of energy is radiated by glass back to plate."
Ta, Tim
Ok I can see that Fig 1 in 1960 book Materials and Techniques for Electron Tubes is the linkage:
http://www.tubebooks.org/Books/Atwood/Kohl%201960%20Materials%20and%20Techniques%20for%20Electron%20Tubes.pdf
The text surrounding Fig 1 is from J.P.Welsh article "Techniques of cooling electronic equipment" 1958. I'll go search for that article, as the Fig.1 related text makes no clarification of glass thickness, and I'm having a hard time interpreting the energy curves.
The Fig.1 plot is for % total energy per micron passing through the glass. Does that mean the total area under the plot integrates to 100%? I don't see how that figure determines the % of plate power transfer that transmits through the glass, versus is transferred to the glass.
http://www.tubebooks.org/Books/Atwood/Kohl%201960%20Materials%20and%20Techniques%20for%20Electron%20Tubes.pdf
The text surrounding Fig 1 is from J.P.Welsh article "Techniques of cooling electronic equipment" 1958. I'll go search for that article, as the Fig.1 related text makes no clarification of glass thickness, and I'm having a hard time interpreting the energy curves.
The Fig.1 plot is for % total energy per micron passing through the glass. Does that mean the total area under the plot integrates to 100%? I don't see how that figure determines the % of plate power transfer that transmits through the glass, versus is transferred to the glass.
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I'm going to blow the idea of using heatsinks for tubes; it may look good, so I tried this on EL84's and within a few weeks the envelopes cracked. It's a complete sales fad as the tube cannot be thermally coupled to the heatsink without massive amounts of thermal paste. Hardly a reliable solution. Let's assume that not all tubes from yester-year use the same zero expansion grade glass compared to today's manufacturing, where corners are cut.
Good luck.
Good luck.
If you download the collection of papers seen here http://www.pearl-hifi.com/03_Prod_Serv/Coolers/PEARL_Tube_Coolers.pdf you'll find an extensive treatment of 'Heat Transfer in Vacuum Tubes' written by H. O. Schade Jr.
Regarding cooler 'black painting/emissivity': real world investigation does support your premise that, " . . . black painting is not necessary."
Using an 813 running at nearly 300C bare bulb hot-spot temperature and a fine wire thermocouple I measured hot-spot temp with a shiny copper cooler and an identical but oxide blackened cooler. The shiny cooler had no measurable effect whereas the blackened part reduced the hot-spot temp over 100 degrees C.
Your point in respect of contact area is well taken has been the object some considerable inquiry over the years. The present best solution is a thin, high metal content powder coat that with heat from the bulb and pressure from the silicone O-rings softens to conform to the surface-to-surface variations between bulb and cooler thereby greatly increasing the otherwise minute actual contact area.
Being a 'textured' finish the powder coat also enturbulates air flow near the coolers surface with an expected improvement in heat transfer.
I've looked into the notion Schlieren thermography but to my surprise haven't located any references
I have lately purchased a FLIR E8 thermographic camera and will provide further information in due course.
Regarding cooler 'black painting/emissivity': real world investigation does support your premise that, " . . . black painting is not necessary."
Using an 813 running at nearly 300C bare bulb hot-spot temperature and a fine wire thermocouple I measured hot-spot temp with a shiny copper cooler and an identical but oxide blackened cooler. The shiny cooler had no measurable effect whereas the blackened part reduced the hot-spot temp over 100 degrees C.
Your point in respect of contact area is well taken has been the object some considerable inquiry over the years. The present best solution is a thin, high metal content powder coat that with heat from the bulb and pressure from the silicone O-rings softens to conform to the surface-to-surface variations between bulb and cooler thereby greatly increasing the otherwise minute actual contact area.
Being a 'textured' finish the powder coat also enturbulates air flow near the coolers surface with an expected improvement in heat transfer.
I've looked into the notion Schlieren thermography but to my surprise haven't located any references
I have lately purchased a FLIR E8 thermographic camera and will provide further information in due course.
No, I did write correctly the Stefan-Boltzmann equation, your stated equation (formula) is a wrongly derived one supposing that emissivity is a constant.
Are you trying to say that Stefan and Boltzmann were two incompetent who published a wrongly derived equation?
As a researcher, you should know that throwing numbers randomly is not very useful.
Using your stated equation (which IS NOT Stefan-Boltzmann equation), assuming 30ºC room temperature
Tc = 273 ºC + 200 ºC = 473 ºK
Te = 273 ºC + 30 ºC = 303 ºK
P = ε A σ (Tc⁴ -Te⁴) = (2360 ε A) W
Put the numbers here and it still is a huge number.
Heat and temperature distribution, emission, conduction and convection are very difficult to calculate accurately, so please stop throwing random numbers for them.
This is a beautiful example on how does a cuasi-black body works in real world.
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Yes, there is, it is hard glass or, in extreme, fused silica. The problem with these materials is that they are hard to work with, and equipment used for soft glass is not suitable for them. Some later generation tubes, especially SQ ones, have hard glass envelopes.
"Hard glass" is Pyrex or an equivalent.
While almost all glass envelope transmitting tubes were/are hard glass, and I'm making an assumption in respect of present-day Chinese parts, the only power receiving tubes built that way were the old Raytheon Red Bank parts and the gone and much missed Svetlana Winged "C" parts; which also had the best evacuation seen, as evidenced by their lack of blue pulsations within, under power.
While almost all glass envelope transmitting tubes were/are hard glass, and I'm making an assumption in respect of present-day Chinese parts, the only power receiving tubes built that way were the old Raytheon Red Bank parts and the gone and much missed Svetlana Winged "C" parts; which also had the best evacuation seen, as evidenced by their lack of blue pulsations within, under power.