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Mike T., Swampeast MO
Member Posts: 6,928
Temp at 2" from floor: 61.2°
Temp at 8" from ceiling: 61.7 °
Ceilings 9', two SEPARATE digital thermometers. At same position (elevation) seem to have about .3° variance.
A bit more than half of the EXPOSED floor space is heated radiantly. No heat around toilet and built the old-fashioned tub up on a low "platform" for the hell of it--real nice decorative tile border on walls matched by vertical of the platform. Right at half of the floor if you count where the vanity sits (unheated as well).
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Room ALSO has electric fin-tube heat (called "Soft Heat" as it has an oil-immersed heating element).
Have set its' thermostat to 72°. (Previously it was completely off.) Will let you know the temperature variance after lunch.
Any guesses???? (Remember there was a 5° floor/ceiling temperature variance in a nearby room heated to about 68° about 75% or so by radiation--my best, most fair assumption.)
Temp at 8" from ceiling: 61.7 °
Ceilings 9', two SEPARATE digital thermometers. At same position (elevation) seem to have about .3° variance.
A bit more than half of the EXPOSED floor space is heated radiantly. No heat around toilet and built the old-fashioned tub up on a low "platform" for the hell of it--real nice decorative tile border on walls matched by vertical of the platform. Right at half of the floor if you count where the vanity sits (unheated as well).
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Room ALSO has electric fin-tube heat (called "Soft Heat" as it has an oil-immersed heating element).
Have set its' thermostat to 72°. (Previously it was completely off.) Will let you know the temperature variance after lunch.
Any guesses???? (Remember there was a 5° floor/ceiling temperature variance in a nearby room heated to about 68° about 75% or so by radiation--my best, most fair assumption.)
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Comments
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Re: Radiation from radiators
This imagineer most definitely disagrees with calculation showing about 1/1000 btu/hr for a 110° radiator!!!!
First: you didn't show the FULL formula; second I think you misplaced a decimal or two in there...
While I believe the application of the radiation formula to the real world is fundamentally flawed, it's the best we have.
The radiant output of a body is the difference between what it puts out and what it receives--yes, the hot body does still receive radiation from its cooler surroundings.
The formula I've been given is:
WHERE:
Q = btu/hr/sq.ft (radiant output)
TH = temp deg Rankine, hot surface, emitter
TL = temp deg Rankine, cool surface, reciever
e = emissivity
A = Area of the emitter in square feet
Q = 0.1714 * e * A *[(TH/100)^4 - (TL/100)^4]
(formula can be expressed in many ways, but this is likely the easiest to handle)
REMEMBER: this is ABSOLUTE temperature (degrees Rankine) so you MUST add 460° to Fahrenheit!
Emissivity = relative number where 1 is "perfection"--a so-called black-body. I will assume that the radiator is painted. The emissivity of "paint" is listed as .93 (VERY high) but I'm going to be kind and use .85
I'm going to use the office where I am sitting as an example.
The 75 sq.ft. radiator is currently about 92° (552° R) and it's about 25° outside. It is equipped with a TRV and setting has not changed for over 48 hours. Temperature 8" from the ceiling is 69°, 10" off floor 64°. Head level (seated) about 68°.
As with any REAL space, the temperature of the surfaces of the room varies considerably. Warmest are interior partions, coldest are the windows. Floor is quite cool as temp in rooms surrounding is about 55°. Remember that radiation is fundamentally linked to the difference in temperatures of the bodies! For an "average" temperature of surrounding areas I will use 63° (523° R). Glass is also a good emitter/absorber and there are large windows and even with good weatherstripping/storms they are QUITE cold...
Now to the formula for ONE square foot:
0.1713 * .85 * 1 ((552/100) ^ 4) - (523/100) ^ 4)
The .85 number is the emissivity of the rad.
This results in: 26.26 btu/hr/sq.ft.
Times 75 square feet = 1,970 btu/hr for the rad.
Heat loss of this room at this outside temp = 2,335 btu/hr. This number is VERY accurate as it is "reverse engineered." The actual temperature of the radiator is within one degree of what I predict.
Finally: of the 2,335 btu required, 1,970 (84%) is coming from radiation. Please don't tell me that this is not significant!
Since "EDR" means "Equivalence of Direct Radiation" I think it's relatively safe to use the EDR number for the square feet. In the "real world" though the calculations for radiation come from VERY SIMPLE constructions. As cast iron rad in a room is ANYTHING BUT simple. Calculating the true values would be nearly beyond comprehension as you would have to compute each tube or column of the rad separately and in relation to one another. Even if the true number of square feet in a rad is half of EDR, we're still taking 42% of the output as radiation!
Now for subjective observations:
1) The MOMENT I step into the room I am HIGHLY aware that heat IS RADIATING from the radiator. Yes, the air coming out of the top feels warmer because it is warm and moving, BUT even 14' or so away from the rad (sitting in my chair) I CAN tell an INSTANT difference if I put a cloth over the radiator...
2) The floor-ceiling difference in temperature is about 5°. The ceiling fan is NOT running. Yes, feet are a bit cooler but it's fine with shoes/socks. Floor is abnormally cold since the entire downstairs is very cool. Were the entire home heated to the same temp, I'm certain that the floor would be warmer. I'm wearing a light, short-sleeve shirt and am COMPLETELY unaware of any air movement--only the radiation from the rad on my bare skin.
3) A couple weeks ago I was working very late (about 4:00 a.m.)--generally much closer to the time I GO to work. (Had though been out drinking a bit earlier, but that's another matter.) Coldest day of the year so far--about 5° outside. Went out for a smoke and noticed the neighbor frat boys were still up and at it, and moseyed over for a chat/more beer. Their house was VERY cold--forced air turned as low as it goes--about 55° I guess.
One needed to use my phone as all their cells were out of juice/minutes--imagine that! Massive iron rad about 18' from the front door is in best "line of full sight" from front hall. It was REALLY cranking (about 130°) as wind high and from west--the wall it's on. (Temp sensor is also in a bit of a draft--not good I know but remember that downstairs is bare studs and hard to find a place without some draft when it's really windy...and have sensors where they won't get harmed more than where best suited.)
When he came in the house he said, "Oh, you have heat!" It was only 57° in the entry!
Again, DON'T try to tell me that you can't "feel" radiation. They don't call them "radiators" for nothing!
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AND when I start using this equation at higher outside temps the proportion of radiation INCREASES, i.e.,
@ 80 degree surface temp of rad (50° outside)
@ 65 degree surface temp of room
990 btu/hr from the rad where loss is 1,050 = 94% of output from radiation.
I've checked, double-checked and triple-checked these numbers and "made my own" formula from another source (same general info, just equation in a different format) and the numbers agree.
If you find something fundamentally wrong, let me know please.0 -
How this applies to radiant floors
You MUST remember that radiation increases as the fourth order of magnitude with difference between the temperature of the hot & cold surfaces.
In the "real" world, the temperature of exposed walls/windows (and even other surfaces) VARIES with the outside temperature--the colder it is outside, the colder the surfaces--particularly exposed walls and glass.
SO, if the temperature of the floor remains constant, the OUTPUT of the system INCREASES as it gets colder outside. All the while, the temp of the air remains nearly constant.
As I understand convection, it WILL NOT INCREASE under this circumstance.
SO, how can a floor of nearly constant temperature achieve a nearly constant air temperature in the space WHILE the temperature of the walls changes with outside temp? ONLY radiation can do this!!!!!!!!!!
Convection affects ONLY THE TIME required to heat a fluid or gas--the more convection the faster it heats.
Think now of the fin baseboard. It heats the air MUCH faster than radiant, right?
It ain't called "radiant floor heat" for nothing!!!!!
Am getting ready to take floor/ceiling temperature measurements in a room that IS QUITE LITERALLY "half-heated" by radiant...and with exposure & windows.
According to what was written there should be a BIG difference in temperature, right?
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Numbers DO lie!
When you don't know how to use a calculator that is! No Mike, I don't mean you, I mean me. I haven't been driving a desk much lately, so when I did that quick calc I did mess it up (open mouth, insert foot, and chew). Doing the calc properly yields similar results to yours. I apologise for posting my own mistakes and any confusion that I caused.
75 square feet EDR in one rad? That sounds like a real monster. My old rads were just over 3 square feet EDR per section. Is that radiator in your office over 20 sections? If it is a panel rad it must be huge!
Do you have any numbers for the emmisivity of various flooring materials? I am still wondering about radiant floor heating covered with wood or carpet versus tile and such.
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Actually one of the smaller rads in the house
The "monsters" are over 100! Those 5-tube Capitols really do put a lot of area in a relatively small space...
THAT'S why these rooms are so comfortable--HUGE amount of radiation!
Play with the equation at various temperatures and you'll see how you actually do get MORE radiation (proportional to heat loss) at LOW surface temperature!
Best thing I can say about emissivity is to do a google search for "emissivity table" or "emissivity" + whatever surface you want. There is QUITE a lot of variance between some surfaces (and sources) though! Copper is REALLY crazy--from near nothing to near perfect based on oxidation.
P.S. That equation is a TRUE pain with a calculator. It's best put in a computer program!0 -
Excel
When I put it into Excel is when I noticed my error. I only wish I had done it that way in the first place. Are you running Mathcad? There is a seriously detailed building heat loss model that you can get free for use with Mathcad. The calcs are so complex as you approach the real world situation that I think a PhD is a prerequisite for using it.
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Not there yet but...
Temp at ceiling: 69.3°
Temp at floor: 63.9°0 -
I'm just playing...
with simple equations in BASIC (actually Visual Basic right now).
Best explanation of conduction/convection/radiation I've found came from a college course on cooking of all things--like canned goods, cakes, etc. in/at INDUSTRIAL level. Sorry, but didn't write down the link--just printed a hundred pages or so...
Higher math and I only get along well when I have a REAL reason for using it, then it seems to come easily. Math for the sake of math to me is much more akin to hardcore art appreciation when you have to pretend to see the art itself. Too abstract for me...I do my art in more concrete terms. Probably why I'm very good at seeing "detail" in impressionism--it's not really there, just its perception...0 -
Approaching...
Ceiling: 71.3°
Floor: 65.5°
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Outdoor conditions
39° outdoor.
Completely overcast.0 -
Flubbed it...
Opened door too soon/too often.
Ceiling: 72.7°
Floor: 62.1° (a drop of 3.4°)
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Doh!
I know how that feels.
I've put together some temperature measuring gear to take home for the holidays. I'm going to do some similar measurements on my convectively heated residence. I'll look at the overall balance room to room as well as the gradient throughout each room. I have a good handle on my system flow rate and I should be able to get a resonable idea as to how much heat I am adding to the system. Should be fun!0 -
Got lucky
Two good measurements while MAINTAINING SETPOINT and at JUST the right times...
WITH BASEBOARD ON:
73.1° at ceiling
67.7° at floor
WITH BASEBOARD OFF:
71.8° at ceiling
67.9° at floor
Now, compare these temperature differences with the OTHER room mentioned (the one with the radiator), and with this room itself when heated solely by the floor.
Is the similarity in floor/ceiling temperature when the source of convection is on coincidence? (Remember the rad is ALWAYS "on" as it is proportionally controlled.)
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Next step in experiment
Will turn the radiant OFF on my way out to happy hour and won't check again until sometime tomorrow. Temp is supposed to hover around freezing all day tomorrow with sleet/freezing rain/snow.
I KNOW THIS IS NOT A LABORATORY-GRADE EXPERIMENT--probably not even close, BUT I have done my best to control things as well as possible.
The numbers are REAL. The constructions I mention are REAL. The devices for measuring temperature are REAL.
So far, the numbers seen to well support everything I have ever said here regarding radiant, radiators and TRVs.
What kind of temperature difference do you think there will be tomorrow (space heated ONLY by the "Warm Heat)? Remember--ceiling height is the same.
I have an idea, and if it's correct tomorrows' messages will tie everything together with a form of "resonance."
This has been FUN, but have used a bunch of brain cells and they're tired. Numbers are starting to "melt together." Glad I got to work at 3:30 a.m. today as that's the ONLY way I was able to do my REAL work as well.
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Door unopened
But returned walking through rain.
"Cranked" my office TRV for about 10 minutes as I draped my wet jacket on top. (One like a Boy Scout tent--dry on the outside as long as you don't touch it...)
Down to the Galileo thermometer on top of my desk for temperature measurements and it's slow and crude but...
Jacket drying nicely. Rad MUCH warmer than necessary given outside temp. Convection STOPPED as much as possible by the large, tall London Fog jacket. Do feel more radiation.
Galileo's floaters haven't moved yet...
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So much for \"resonance\"
TOTALLY off the easy track.
Opened the room. Radiant floor output now zilch.
Temp at ceiling: 74.7°
Temp at floor: 65.7°
"Warm Heat" B/B running.
Someone...anyone...PLEASE tell me how there was ANY appreciable convection when the room was heated solely by the floor.
Will try to correlate the two VERY DIFFERENT spaces together, but it's going to be one of my "it just happens this way dynamically" situations. The convective output of my computer monitor (big Sony) isn't too far from that of the rad in the office...add the 120 watts of ceiling light that was on at 0-dark-thirty and...
Engineers won't care because school taught them to "go around" the mountain using only theoretical numbers and they comprehend nothing but...
Applied engineers who have learned the ART don't need it anyway...
How could I have been so stupid as to think that it could be so easy?
Important note: TEMP NEAR FLOOR DROPPED WHILE TEMP AT CEILING ROSE. Space utterly undisturbed for by far the greatest period of time. SAME thermostat setting once the convective heater was added to the equation.
Am doing it again...have scratch pads filled with numbers with no reference after the fact. Saved for the near future only by these postings...0 -
Last Measurement w/\"Soft Heat B/B\"
Temp at ceiling: 73.6°
Temp at floor: 62.8°
Temp outside: 30° and raining
(Don't you love it when that happens?)
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Your grand experiment
Wow! You've certainly put a lot of thought into how your system is operating. Here's some other food for thought and a question
Generally, ratio of radiant/convective with a radiant floor is 2/3 radiant & 1/3 convective. This is certainly theoretical - I'm not sure how you'd actually measure the ratio there. In general, the higher the surface temp (of the floor, radiator, or fin-tube), the higher the percentage of convective energy transfer.
I had some trouble following when/where you measured temps. What were the ceiling and floor temps when you had ONLY the radiant floor running?
Merry Christmas0 -
I agree
With the convective part being a piece of the puzzle. No engineering here just real world experience on this one. We finished a 600 sq ft addition recently and it was interesting to talk to the home owner about how his system worked. The floor is gypcrete with tube spacing running from 6" on the 3 perimeter walls out to 12 and 15" in the interior of the room. It is running solely on outdoor reset with no indoor feedback at all to the Vitotronic 200 that's running this system. (against my wishes btw, but he didn't want a t-stat or sensor in that room).
Anyhow, I digress. Back to the radiant+convection theory. The HO stated that the forced air part of the system (boiler driven A/H) doesn't run nearly as much as the old furnace that we took out. He also stated that the whole house "feels" warmer with the T-87 set at the temp they have always had it. The addition opens up to the rest of the home through a door height opening that is 9' wide. His wife stated, and I noticed it immediately also, that when you walk past that opening between the two rooms you can really feel the radiant floor. Feels just like when you walk past a sunlit window to a milder degree. Just for kicks I checked the air temp in the room adjacent to the addition and found it to be a degree and a half higher than the rest of the home. It felt like it was more like 3-4 higher. Then I took the thermocouple probe of the Fluke and inserted it into the arm of the couch facing the radiant room. Temp of the couch was 75.2* with anbient air at 71. HHMMMMMMMmmmmmmmm?!?!?! I probed the arm on the side facing away from the room and found the temp there to be within tenths of ambient air.
Conclusion?? Radiant energy does travel until it hits something solid that absorbs it. The couch was approx 8' from the radiant room, which BTW was running at an even 80* floor temp with a 15* outdoor temp.
Conclusion #2. The floor was warming the air in that room also both by convective air flow and by re-radiation of energy by objects in the room giving up their absorbed energy to the air.
These are my gut feelings.What do you think? Why was the room warmer than the rest of the house? Why was the side of the couch facing the radiant floor 4 degrees above ambient indoor air temp?0 -
With ONLY radiant
61.2° 2" from floor
61.7° 8" from ceiling
Temperature measurements taken within a minute or two of the time posted. (Only exception is the post after "Flubbed It" that contained two sets of temperatures.) 2nd was taken at post time, 1st about 80 minutes before.0 -
Good gut...
"Radiant energy does travel until it hits something solid that absorbs it." Air is considered to be nearly transparent to radiation. Note nearly--not perfect like a vacuum.
"The floor was warming the air in that room also both by convective air flow and by re-radiation of energy by objects in the room giving up their absorbed energy to the air."
With a 9' opening it's kind of hard to think of the rooms as different spaces (for heating purposes). There was likely more convection in the radiant space than if the entire space were heated radiantly and more radiation in the convective space than if all were heated solely by forced air.
I like to think of conduction as playing the FINAL role in ALL heating systems: the air of a convective system finally conducts heat to the surfaces/objects in the room; the surfaces/objects finally conduct heat to the air with radiant systems.
"Why was the side of the couch facing the radiant floor 4 degrees above ambient indoor air temp?" Good question. I'll assume it was upholstered in fabric. If not something like a heat register close to that side or direct sun shining through the big opening, I'll offer a possibility. The fabric & cushioning (being of high air content) of upholstered furniture is good at "trapping" heat--particularly convection. You can "force" it in, but it has to come out naturally. Unless the couch is directly over a hot air register, you won't really notice this in normal circumstance--other than than the idea that it might be a bit warmer than SOLID surfaces in the same room. The added radiant heat could have put this effect "over the top" so to speak. Just a wild guess.
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Conclusions (flawed I'm sure)
Most striking is the ENORMOUS increase in floor-ceiling temperature difference between "pure" radiant heat (0.5°) and "pure" convective heat (13.5°). Both of these measurements after room completely undisturbed overnight.
Curious is the similarity in floor-ceiling temperature difference between that room when heated by a combination of radiant floor/BB and a MUCH larger, but same ceiling height room heated by standing iron. What seems most interesting is the way the difference zoomed to about 5° when the BB was turned on and stayed close to this number both while raising the temperature AND while maintaining it. Once the radiant was shut down, it nearly tripled! Outside temp/conditions didn't change too much during this time.
IF you allow me (for argument/simplicity) to say that the room was heated solely by radiation when ONLY the floor was heating, we can assume that the space had a radiant potential of a 23° temperature rise (38° outside, 61° inside) and then:
Again for simplicity, let's say that the "Warm-Heat" oil-immersed electric B/B heated 80% by convection and 20% by radiation. Since the radiant floor was still running, it was providing only a portion of the heat. 71° seems a good average air temp at maintenance level with BOTH running.
The B/B was now providing 10° (or 30%) of the total temperature rise in the space. 2° (20%) of this rise came from radiation so of the total rise in the space (33°), 25° (or 75%) was coming from radiation. This mix of 75% radiation/25% convection resulted in a 5° floor-ceiling temperature differential in a 9' high room.
Now lets try to draw correlations:
1) When the radiant was shut down, the space was heated 80% by convection, 20% by radiation. If 25% convection results in 5° floor-ceiling temp difference, what (by simple ratio) would be the floor-ceiling temp difference? Answer: 16°. Not too far from the actual measured difference of 13.5°. Cooincidence? Fallacy? Real correlation? I truly don't know.
2) This is a BIG assumption, but for argument sake let's say that by virtue of similar proportion of exposure and surrounding conditions that spaces of different size BUT the same ceiling height will have similar floor-ceiling temp differential based on the proportion of convection. If this is the case, the 5° rise correlating to 25% convections jives nicely with my calculated (and assumed correction factor for the nature of an iron rad) in the room with the standing iron rad. Cooincidence? Fallacy? Real correlation?
The ONLY number "pulled out of a hat" in this experiment was the 75% radiation by the rad in my office--it was based both on calculation and an applied guess. The experiment proceeded in "real time" exactly in the manner described. I had ZERO knowledge of what would happen. This was written as the calculations proceeded--I did not make the calculations before writing.
3) WHERE IS CONDUCTION? To me, conduction is the FINAL step in the process but can be considered completely separately from convection/radiation. A convective system heats the air which conducts heat to surfaces; a radiant system heats surfaces which conduct their heat to the air. Both achieve "balance" in a different way, but this explains two well-known phenomenon, "Cold 70" and "Radiant Coziness" depending on which way the conduction is mainly occurring.
4) At the VERY least I believe this definitely shows that radiation results in much less temperature stratification than convection. Of course we all knew that anyway, didn't we? BUT, "conventional" sources STILL insist that radiantly heated rooms are heated about 50-50 radiation/convection. Should this instead be 50-50 radiation/conduction? Or 99%-99% radiation/conduction if you (like me) consider these two DIFFERENT steps in the process? I simply cannot see a significant driving force for convection (FLUID temperature differential) in a radiant system, but I see LOTS of it with BB.
Again, I KNOW I have oversimplified and assumed much by trying to apply thermodynamic theory in simple constructions to the highly complex constructions in the real world. Reliability in such a case comes ONLY from repeatability. Does anyone out there have a similar circumstance to see if similar results are produced? It takes little in the way of equipment and not too much in the way of time if you work on other things in between measurements.
I don't believe that any of the propositions presented break any physical laws, but they could result in a change of the view of how REAL spaces are actually heated.
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To \"Revive\" the post
no message0 -
I remember this!
There was some off The Wall discussion too.
I am with you up to where we have 26.26 Btu/hr/sq.ft of radiation. I made a boo boo on my calculator and got really small values for radiation and I jumped to some conclusions. You did straighten me out there, but then you make the assumption on how much surface area of the radiator actually radiates and base all of your proportions on that assumption. The above calculation applies to an "ideal" radiatior-- a flat plate of known area at uniform temperature. You can't possibly get an accurate guesstimate of the radiating area of a piece of standing iron though. Without a "real" area to use for the calcs it's all meaningless.0 -
\"Real\" area doesn't matter!
What matters is that the radiative percentage CHANGES with temperature. It doesn't matter if a 75 sq.ft. EDR radiator only has 10, 20, 30 or whatever square feet of "real" radiative surface. If it changes, it changes PERIOD.
Trying to find the "real" surface area of a shape as complex is a raditor is extremely difficult--and then it would ONLY be from one "point of view". With all possible "points of view" I could probably fill my 40 gig hard drive with numbers WAY before all the angles were considered.
I can only offer these observations:
The net radiation received by a line in the room is highly related to the number of lines on the rad that can be found tangent to that line.
American Capitol fin-tube rads not only have LOTS of tangents (by way of curvature), they have lines of FOCUS via concave curves, i.e. linear "dishes".
Think of how some recessed iron "convectors" have that strangely undulating exposed surface made of side-by-side concave curves; think of how some modern steel panels have the same sort of shape. Do you REALLY think it's just there for aesthetics?0 -
You lost me.....
I thought lines were tangent to circles.
In your calc at the top of this page, you took the heat loss of the room (2335btuh), the radiation per unit area of cast iron (26.26 btuh/sq.ft), and assumed an area of radiation to arrive at a number for radiated energy. Then you converted that into a proportion based on the heat loss of the room. then you recaculated under different operating conditions. You can't do that. Your percentage only changed because the amount of error in the radiation calc changed for each calc. Since you over estimated the "real" radiation area in both cases your math is fooling you!
94% radiation from standing iron is madness!!!!!!! (so is 84% or 42% for that matter)
No, I don't think maximizing the surface area of heat emmitters is there for asthetics, that is what you do with heat exchangers-- cram as much surface area into as small a volume as possible.
Maybe we should take this off The Wall again. We could share some calculations and formulas......
Eric0 -
Bad nomenclature, I think. Believe this is how a cylinder radiates to an imaginary line on a plane. Now start imagining LOTS of cyclinders (rad tubes). Worse yet if those "cylinders" are in fact composed of four bell curves.
Will dig for the rest of the formulas later. Believe I used my heat loss to try to estimate the temperature of a smaller radiator in the same space at same outside conditions.0 -
I get the geometry now....BUT
I found a good example problem in my heat transfer book. Note that in this example 100% of the "real" area both convects and radiates:0 -
The soloution
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Now change the Delta T
I got roughly 45% radiation at 50*C and 20*C ambient
and when I changed the 50 to 30 I got 42.5% radiation.
You've got the formula right Mike, I just don't think your assumptions are perfect.
Oh, the book is:
Heat Transfer
Seventh Edition
J.P Holman
copyright 1990
To give credit where it's due.
Eric0 -
Also
Lets talk area again.
How much real surface area of a rad convects? 100% It all touches the air.
How much real surface area of a rad radiates? I have no idea, but it is way less than 100%.
Try to paint a rad with the following rules:
Don't bend the bristles on the paint brush and always hold the brush perpendiclar to the surface of the rad. i.e.-- pretend the brush is the radiation line.
How much of the rad gets painted? Not too much!
Eric0 -
Numbers--ONLY RAD HAS CHANGED
Assumptions:
1) The standard formula for radiation from/to a black body when applied to a standing iron radiator in a room will NOT produce ARBITRARY numbers given reasonably accurate numbers and assumptions.
2) A US Capitol radiator will have about 1.5 btu/hr/sq.ft EDR total output for degree of temperature difference between it and the air temp of the space in which it is located.
3) That the average surface temperature (measured top, center) of THIS radiator in THIS space can be accurately predicted based on outdoor temp when MAINTAINING a given indoor temp AND that consequently the surface temperature of a radiator of DIFFERENT size in the same space at the same conditions can be predicted by using 1.5 btu/hr/sqftEDR.
---------------------------------------------
Q = 0.1713 * .85 * 1 ((552/100) ^ 4) - (523/100) ^ 4)
WHERE:
emissivity = .85
rad = 92°; "average" temp of surfaces = 63°
Q = 26 btu/hr per square foot
---------------------------------------
CHANGE ONE NUMBER, the radiator, to 101°
Q = 0.1713 * .85 * 1 ((561/100) ^ 4) - (523/100) ^ 4)
Q = 35 btu/hr per square foot
---------------------------------------
Radiator got hotter so it's putting out more radiation PER SQUARE FOOT. Exactly what is expected, BUT THE RADIATOR GOT SMALLER!!!!!!!!!
In the first calculation it is 75 square feet EDR. In the second calculation it is 50 square feet EDR. This results in the SAME OUTPUT of about 2,335 btu/hr--that required by the space at the SAME CONDITIONS.
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Please bear with me.
I VERY SERIOUSLY DOUBT THAT A RADIATOR OF 75 SQUARE FEET EDR HAS 75 SQUARE FEET OF "REAL" RADIATING AREA.
But, if you can just let me assume that a rad of 50 square feet EDR has about one third less "real" radiating area than one with 75 square feet, you will see what happens.
-------------------------------------
EDR * Radiant Output/sq.ft. = Total Radiant Output
75 * 26 = 1,950 (radiant output IF 75 sq.ft. EDR @ 92°)
50 * 35 = 1,750 (radiant output IF 50 sq.ft. EDR @ 101°)
Heat lost by space remains the SAME at 2,335 btu/hr.
Smaller radiator at higher temperature has a lower proportion of radiant output.
Larger radiatior at lower temperature has a higher proportion of radiant output.
---------------------------------------------------
Now recall than when the OUTSIDE temperature changed, the proportion of radiation changed as well.
Radiation and convection are CONSTANTLY changing in proportion depending on conditions.
You can maximize radiation by:
1) carefully controlling the temperature of the radiator to match the heat loss of the space
2) carefully choosing the position of the radiator
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I REALLY wish I could make even a "guestimate."
Take that little sketch and make 74 more cylinders. Turn those cylinders into shapes like below.
Space those "cylinders" such that what you "see" changes from about 1/2 of the frontal area (looking dead on) to what you are certain is greater than the gross rectilinear dimensions (oblique). Now consider elevation--my fuses BLOW!
It's NOT just about increasing surface area. I don't know if he's the "only" or even the "first" to do so, but Starbuck (the author of some old heating and plumbing "bibles") made a BIG distinction between "prime" and "extended" radiator surfaces, calling prime surfaces the more valuable.
Remember that in his day most of the radiators were column-type and manufacturers were "playing around" by making all sorts of projections from the interior surfaces of the iron.
A "black body" isn't a sphere for no reason. Since radiation leaves at a right angle and spheres have no angles it is considered to come equally from imaginary points. By making the entire thing "imaginary" it becomes ever more simple...
Prime surface: in direct contact with water
Extended surface: "titties", "fingers" and feet0
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