Efficient Heat Transfer Device for High Temperature Systems

In summary, the system uses a small device to add energy to a system primarily via radiation. Temperature differential is high—at least 1,500°F. Intermediate heat transfer is via forced convection of a fluid (water) to iron. Energy output is again primarily via radiation. Temperature differential is low—say 20°F. Is it possible for any amount of the transferred energy to pass through the system without appearing as detectable temperature? If not, what law prevents this? Have lots of data from datalogging equipment and spot measurements. Numerous anomolies that are difficult if not impossible to subscribe to "experimental error". Can provide more details if needed.
  • #1
Swampeast Mike
48
1
Please don't beat me up too badly. I ask this in all sincerity.

A very small device adds energy to a system primarily via radiation. Temperature differential is high—at least 1,500°F.

The system itself is rather massive—tons.

Intermediate heat transfer is via forced convection of a fluid (water) to iron.

Energy output is again primarily via radiation. Temperature differential is low—say 20°F.

Is it possible for any amount of the transferred energy to pass through the system without appearing as detectable temperature? If not, what law prevents this?

I have a situation where this [appears] to be happening, but am at a complete loss to explain.

Have lots of data from datalogging equipment and spot measurements. Numerous anomolies that are difficult if not impossible to subscribe to "experimental error". Can provide more details if needed.

Thanks!
 
Science news on Phys.org
  • #2
unless you are working with WMD or something proprietary, a small picture will be useful.
 
  • #3
Nothing so Devious or Exciting

Old home heating system using cast iron radiators and a new boiler of rather unique design. Have attached some photos. One shows the burner in operation. Note that there is no flame in the traditional sense. It is considered a "radiant burner". Next shows the heat exchanger--sort of a hollow slinky. Dimples are made in the hollow rectangular stainless steel as it's coiled to keep the gap through which the flue gasses must pass very small and precise (around .003" I think). One end of the heat exchanger is attached to a water-filled jacket—the burner is "sideways" inside the boiler--not upright as in the photo. The entire combustion chamber is sealed with combustion air arriving through a concentric vent to the outdoors.

Last photo shows the style of the radiators. The profile of these is unique. Look at the shadow. The individual "tubes" are in fact composed of four intersecting "bell curves".

The boiler also varies its level of fire depending on the real-time heating load of the system. All of the radiators are fitted with devices that proportionally vary the flow rate to maintain space temperature with very high accuracy (thermostatic radiator valves or TRVs). System itself benefits from high mass and volume (tons of iron and hundreds of gallons of water). Everything about the system is as proportional to the real-time load as you can get in the real world. The boiler varies its flame and temperature as a function of outdoor temperature. The pump varies its rotational speed. The TRVs vary the flow at each individual radiator.

Have connected multiple data-logging temperature sensors to the system. Verified them against a known accurate thermometer and to each other. Accuracy to ±1°F absolute and ±½°F among the devices.

(In the situations below am ONLY referring to conditions where the system is as close to stasis as possible--burner running continually, TRVs maintaining the same room temp setting for days if not weeks.)

One anomoly is flue gas temperature (measured about 2" away from the heat exchanger) that is significantly lower than the maximum water temp being produced inside the boiler. That's not supposed to happen, but others report similar measurements.

Another strange thing is the supply temperature. The boiler itself measures this temperature just as the water exits the heat exchanger with the sensing element immersed in the water. I also measure the temperature on the surface of iron pipe about 3' away from the boiler. The difference seems WAY too high (as much as 15°) to be accounted for by the differing measurement methods. I can however get a surface temperature measurement only about 4° lower (very understandable) by manipulating controls and thus throwing the system out of stasis.

What I find most difficult to explain is the extremely low temperature of the radiators themselves. I know the amount of energy being consumed by the boiler and can reasonably calculate the small amount of heat being lost through the flue. The net energy gain to the system compares very closely with the expected output. The problem is that the radiators are too cool to give off the amount of heat that they must be liberating. Output data for iron radiators at low temperatures is hard to find, but the numbers are well beyond what can be reasonably expected.

Have taken similar measurements with the old boiler (conventional type where the flame extends through a cast iron heat exchanger). I used to be able to predict the temperature of radiators with a very high degree of accuracy given only indoor/outdoor temps and adjustment for heavy wind. The only change made to the system was the boiler, but the radiators are now significantly cooler for the same indoor/outdoor conditions.

To make matters even stranger, if I intentionally reduce the maximum temperature of the boiler at all outdoor temperatures to the bare minimum to maintain stasis, the spaces start to feel chilly even though the numerous indoor temp dataloggers report no reduction in space temperature.

Again, is it possible for some of the radiant energy to be passing through the system without appearing as measurable temperature?
 

Attachments

  • Viessmann Radiant Burner.jpg
    Viessmann Radiant Burner.jpg
    25.7 KB · Views: 402
  • Inox Radial HX.jpg
    Inox Radial HX.jpg
    4.8 KB · Views: 437
  • Max Radiant Iron (small).jpg
    Max Radiant Iron (small).jpg
    21.2 KB · Views: 426
Last edited:
  • #4
It seems you need to look for troubleshooting manual. What I would do is to check the water flow first, because you claim that the water temperature near the boiler is significantly smaller then the temperature of the tube slightly outside. Again, I would first to check specifications for that or similar system, may be that is a reasonable number.
 
  • #5
Am 100% positive that the flow rate is well within the specifications of the boiler at all times.

Documentation with the boiler is not the best. It comes from Germany and things get lost in the translation. The TRVs aren't particularly common in the US (but required by law in Germany) and the English language documentation is concerned mainly with systems using traditional, digital wall thermostat(s).

Absolutely nothing in this system is "on-or-off" any time the load exceeds the minimum possible input.

Am writing here because as of yet nobody can explain the magnitude of the anomolies.
 
  • #6
Supply Temp Sensor Location was Carefully Selected

Could easily have placed it inside the combustion chamber very near the boiler's sensor.

Wanted to get an estimate of the "buffer effect" of a heat exchanger of comparatively tiny volume and surface area driving a system with high volume and high direct radiation surface.

Boiler itself uses 3/4" connections. The "near boiler" piping where my supply sensor is attached is 1". About 3' after that the 1" pipe splits to supply two 3" pipes.
 
  • #7
A couple of quick thoughts/questions...

By the sounds of things, I don't doubt your intrumentation set up. It sounds like you have a good handle on things there. Also, by the term "stasis" I am assuming the meaning is "equilibrium."

Is there an appreciable run of piping between the radiator and the boiler's outlet? Do you have a good estimate of the heat loss from this run of piping?

Is there any possibility that the radiator itself could have a large, trapped air bubble in it? Are you measuring the flow rate going into the radiator?

The radiation from the burner, I suppose, could be being reflected by the coil you have for the heat exchanger so it's going to the atmosphere in stead of the water. The coil does look nice and shiny which will help in that respect.

Russ would be the expert in this area.

Give me a bit more time to digest your system. Sorry about all of the questions.
 
  • #8
Thanks Fred. No problem with questions. Hope the answers are decent.

One meaning of "stasis" is "state of static balance or equilibrium" so we're talking the same thing. The stasis I'm referring to is the balance between energy entering the system via the boiler and energy leaving the house via heat loss.

Length of flow path to individual radiators varies from about 12' to 70'. The vast majority of the main and branch piping is well-insulated. Do have a reasonable estimate for the heat lost during transmission. System originally worked under "gravity" circulation--the differing density of hot vs. cold water. VERY slight motive force this way so the piping is enormous by modern standards. Essentially zero friction loss in the piping and water velocity is extremely low. Flow varies from about 1.3 to 4 gallons per minute with that amount of flow shared between two separate two-pipe (supply and return) circuits each with a maximum diameter of 3". As the mains wind around the basement, they decrease in size as branchs are taken off for radiators.

The thermostatic radiator valves (TRVs) are proportional devices that modulate on room air temperature. They provide the flow restriction that keeps flow and velocity low. Without the TRVs, such a system typically has a circulating pump that moves 30+ gallons per minute.

In unused rooms with shades pulled, the temperature will vary less than 1° for days. In occupied rooms with south and/or west exposure where shades are used daily, temp variance is about ±2° and follows both the occupancy and solar cycles with extreme regularity. Temp variance in occupied rooms with primarily north and/or east exposures is a bit less.

No trapped air. Devices are installed to both remove any air in the system and to prevent the migration of air in the compression tank back to the system.

Unfortunately I do not have any flow sensors installed. The less expensive ones are problematic and inaccurate. The long-lived accurate ones are extremely expensive. For flow estimates, I use the time-honored equation: gpm = Btuh / (500 * temperature drop). (The 500 constant isn't really a constant as it varies very slightly with the temperature of the water--when splitting hairs will recalcuate based on average temp in the system but the difference is slight at best.) Because I know the amount of energy being consumed by the boiler and can get a good estimate of the small amount being lost through the flue, the system-wide flow estimates are quite accurate. Flow estimates for individual radiators are not as precise, as it's difficult to get a highly accurate estimate of either Btuh being given off by the radiator or Btuh being lost in the room.

The unexpectedly low radiator temperatures occur system-wide in any space where temperature is being maintained. There are 15 radiators with combined total of about 1,050 square feet of surface area. There are also four baths heated via copper tubing inserted in heavy, close-fitting aluminum extrusions and attached to the bottom of the floor. These baths have no form of flow or temperature control and maintain space temperature that "floats" right at 4° above the average temp of the spaces surrounding. Another curiosity in the system is the way that the baths all produce the same relative temp difference despite wildly varying heat loss from a fully internal room to ones with exposed walls and windows.

Exceptionally little heat loss from the boiler itself. The highest recorded flue gas temperature over the past winter (at about 2°F outside) was 129°F with a reported boiler temperature of 142° and supply temp I could measure of 124°. Water was returning to the boiler at 97°. While I never measured the temperature of the boiler case, my hand tells me that it's at ambient with the basement—never even warm.
 
  • #9
I must admit, I am a bit stumped on this one. That energy has to be going somewhere. The big problem I have is that I can't see the entire system. The addition of the baths is a good example.

However, back to your original question, I can not think of any way that energy can pass through without resulting in a temperature increase, especially the radiant energy. It can get reflected, but it's going to go somewhere. I would expect it to go right up the flue, but you have accounted for that. The next thing I would suspect is a leak to some sort of structure that could be acting like a sink. Again, my lack of knowledge on the installation is killing me here.



Can you describe the baths in more detail?
 
  • #10
Here's a photo of the heat transfer mechanism used for three of the bath floors. 2nd sketch is what is used in a large shower (the "Martha Stewart" notation was part of an inside joke).

Last attachment is a .pdf of radiator temperatures measured throughout the house one evening.

Two of the baths have ¾" plywood, cement board and ceramic tile for the floor. These two connect to small common supply/return tubes in such a way that flow through both is identical. (Exact same amount of tube is used for both and even the same number of bends in the pipe.) The third bath has two layers of normal lumber plus the cement board and tile. It has three of the plates per joist bay instead of two.

All of these were carefully engineered to achieve a specific surface temperature in the tile. No data was available for the copper in the fins (PEX plastic tube us normally used) or the copper slipped through garden hose, so had to make some educated guesses. Temps came out within 1° of the prediction.

All just connect into the main piping with simple "set-and-forget" valves used for a one-time setup adjustment. Any time that the boiler circulator is running—generally all times that the outside temp is below 55°F—these radiant floors receive circulation of heated water. The temp at the connection to these baths (one is at least 30' down the mains) is within just a few tenths of a degree of the temp I measure 3' from the boiler.

---------------------------------------------------------------------

Don't believe that significant energy is being lost in/near the boiler. Fuel consumption dropped 43% based on degree days.

What utterly baffles me is the lower temp in the radiators at the same indoor/outdoor conditions.

I do use an average when measuring the temp of the radiator. Measure at top center. Have verified multiple times (with both boilers) that this is indeed the average of the temps when measured right at the supply and return connections. Near freezing outside, I'm heating rooms to 68° with only

There's very little convection associated with these radiators:

First, they're quite low in temperature--most are well below 90° until the outside temp drops into the teens, and even then some are still well below 90°. Radiator temps are running 3°-5°F below what they did with the old boiler, and the boiler was the only thing that changed in the system.

Second, most have unusual (for the time period, c. 1922) placement in the rooms. Instead of being located under/near windows or on outside walls, most are against interior walls with great "views" of the outside walls and windows. (Modern studies are finding that with decent air infiltration control, such is actually a better placement as it reduces convection while enhancing radiation.) The long-dead men who designed the system actually increased the size of these radiators due to what they believed less-than-ideal placement.

-------------------------------------------------------------------

Sorry for the crash course in both modern and archaic hydronics, but here's some background that might help.

Radiators were and still are measured in Equivalance of Direct Radition (EDR). This measure goes WAY back to the original radiators that looked rather like an old mattress with ticking "buttons". It also refers primarily to steam at low pressure producing a radiator temp of 215°F in a 70° room. One square foot EDR is capable of liberating 1.66 btu/hr per degree (F) of temp difference between the radiator and the surrounding air. Some radiator designs and placements resulted in slightly more or less output, but differences are rather slight and that measure has been successfully used for over a century.

It was quite easy to determine output with steam as you only had to know the pressure of the entering steam and measure the weight and temp of the condensate produced. With water it was (and still is) much more difficult to determine exact output.

All of the old references show that output of iron radiators drops off when water below the boiling point is used. At 150°F surface temp, all of the old tables show output dropping to 1.375 btu/hr per degree (F) of temp difference. At 95° these tables show output drops to 0.

The few modern references for old radiators come from Europe. There, output of radiators at lower temperatures is generally considered to be 1.5 btu/hr per degree (F) of temp difference. That's the number I used with the old boiler and I could predict radiator temp with extreme accuracy. Now, in most cases I must be getting 2-3 btu/hr—possibly even more.

Large, flat radiant panels like floors or ceilings are generally accepted to give off 2.5 btu/hr per degree of temp difference.
 

Attachments

  • Shared Bath Radiant.jpg
    Shared Bath Radiant.jpg
    32.1 KB · Views: 444
  • Shower Radiant Detail.jpg
    Shower Radiant Detail.jpg
    42.4 KB · Views: 407
  • Radiator Temps.pdf
    84.3 KB · Views: 308
Last edited:
  • #11
Fred:

You said, "back to your original question, I can not think of any way that energy can pass through without resulting in a temperature increase, especially the radiant energy".

Radiation is always a "handshake" between objects with both receiving and both giving despite their lack of physical contact. It acts like either a thing or a no-thing (particle or wave) depending on your state. If you're real (a thing) it seems to behave like a particle; if you're imaginary (a no-thing) it seems to behave like a wave. If you imagine yourself as both objects at the same time, you find a connection of some no-thing.

Before I continue, is this a reasonable explanation of energy transfer via radiation?
 
  • #12
Well, one slight modification to your statement would be in the "thing" - "non-thing" area. Energy transfer via radiation is a transport directly due to matter. The radiation is the result of movement in electrons which make up matter. So, for something to radiate, it must be made of matter and therefore a "thing". The actual transmission of radiation (once it has been manifested) does not rely on matter.

I hope I at least answered that question. You've presented a tough scenario. I constantly keep bringing myself back to the flow through the system. A very nice piece of information to have would be the flow at the radiators versus the temperature. I'm sorry I can't be much more of a help to you. It is an interesting problem.

I have now added your heating system to my top 2 list of things to solve. Your problem and that darned NotPron game are keeping me up at night!
 
  • #13
FredGarvin said:
Russ would be the expert in this area.
Thanks, but with only 2.5 years in the industry, I've learned a lot about airflow but have a long way to go with hydronic systems. However, I have several ideas (and will also need some time to digest the problem)...

-Surface temperatures of uninsulated pipes are significantly lower than the temperature of the water inside. Is the pipe with the surface temp anomaly insulated? If not, it should be - even if its only temporary, for the purpose of the investigation.

-The supply temperature seems low and the delta-T seems high, though that is based on what we design for modern systems: 180F, 10F dT. That implies to me a capacity problem - either that you're not getting what you think out of the boiler (unlikely for a new boiler) or you're losing more than you think somewhere in the system (with a crappy, old system, possible - but difficult to find/verify) ------ or a flow problem: flow too low means the water spends longer in the boiler (and in the radiators) and the delta-T goes way up.

-Related to that, I'm concerned about this "gravity circulation" - I'm not real familiar with it, but it seems to me that it might require a high delta-T. You imply that that isn't how it is now circulated - how is it circulated now?

-And related to that, calculating flow instead of measuring it makes me nervous - isn't there any way to measure it via pressure taps? It can be a pain, but if there aren't any, a drill and a raincoat may be needed...

-Re: the flue gas temp, based on what do you say it's too low? Did you get a spec on that? A well set-up heat exchanger will do that: the exit temp of the exhaust gas should be lower than the exit temp of the water if it's doing its job. This seems counterintuitive, except that the flows are opposite each other, maintaining a relatively constant delta-T throughout the heat exchanger. Though its possible I misunderstand this particular application...

This rings a bell for me:
The boiler also varies its level of fire depending on the real-time heating load of the system.
With the high thermal inertia, doesn't that create an enormous lag in system-response? Why doesn't the boiler control just maintain constant supply temp and allow the radiators to separately control room temp? I could see lowering the supply temp as the outside temp increases, but not too much - with a well-insulated system, you don't gain much at all in system efficiency by lowering supply temp.

Have you tried overriding the controls and manually screwing with the boiler temps to see if it improves things? - or just to see how it affects the system?

Anyway, I need to chew on this a little more. I may have been way off-base with my questions... Be back tomorrow...
 
Last edited:
  • #14
Russ:

Can either you or Fred display a 1600 x 1200 {please excuse original with 1600 x 800} screen resolution? If so, can send you raw data and the program I wrote for monitoring. Let me know.

The sensor where I'm measuring supply temp is installed in a dab of heat conductive paste and has good insulation wrapped around. It's horizontal and edges sealed so no chance of air moving through. Again, I could have placed the sensor inside the combustion chamber but chose to measure a few feet away—but still before it connects to the huge piping.

Old radiators are typically oversized by modern standards and they're massively oversized in this house due to insulation and weatherization. This new boiler thrives on low temperatures and high delta-t. Unless some physical law has been shattered, maintenance flow is always within the specs of the boiler—it varies from about 1.3 gpm to 3.8 gpm with increasing flow as weather gets colder.

No, the system no longer uses gravity circulation. The boiler has a built-in variable speed circulator. The only thing mentioned in the manuals regarding how the boiler varies the speed is that it is "weather responsive."

No specs regarding flue temp. Numerous people with a LOT more hydronic experience than me insist that flue temps below the supply temp are impossible.

I recently found a flow meter of good quality that's accurate, long-lived and "just" expensive. Will try to install for the next heating season as I'm not very happy with the way I have to estimate flow either. Believe it has a data-logging option, so that would be great as I could graph along with temps.

Despite the high mass of the system, response is very fast. Opening even a single TRV results in an immediate increase in burner output. I conducted numerous response tests and can see the results perfectly. An extraordinarly rapid increase in outdoor temp does result in a bit of overshoot, but that happens with any heating system.

The boiler does maintain a constant supply temperature, but that temperature varies with weather. Every condensing/modulating boiler on the market uses some form of reset. The reset curve is set by the user. The general shape is very slightly non-linear, but you cannot change the shape of the curve, only the slope and shift.

I did do some experimenting with the reset curve--mainly lowering the supply temps. That's when I found the strange situation where the space started to feel cool even though the indoor temp showed no real change. With outdoor temps in the high 20s to mid 30s was able to heat the house to setpoint (for two days) with a measured supply temp in the low 80s! But, I felt a creeping chill. Lots of large original windows. Better-than-new condition with good permanent weatherstripping and good storms, but just plain glass. My guess is that the interior glass surfaces were cooling with the lower supply temps. Again, most of my radiators are on interior walls in full view of windows.

The only thing connected to the boiler is the outdoor temperature sensor. There are no wall thermostats--in fact the boiler does not have connections for such. In systems without the TRVs, the boiler is usually hydraulically "uncoupled" from the system via a device called a "low-loss header". When the low-loss header is used, traditional thermostats can be installed to controllers on the system-side of the header, but not to the boiler itself.

Really no way to override the controls on this system. There is a test mode used when measuring flue gas that locks the burner into full output, but on this system it will just start "boucing" off of the internal high-limit. There is a way via external connection to operate the boiler with a fixed supply temp and fixed pump rotation speed, but the burner still modulates to achieve that temperature.

Not sure if I've said, but the boiler is a Vitodens by Viessmann. They manufacture nearly everything themselves and this boiler is HIGHLY proprietary. It uses an operational data store to collect information and modify its operation based on the system to which it is connected. ZERO information is provided on just what the ODS collects or does. Hydronic heat is nearly universal in Europe (as are TRVs) and competition there is fierce. Despite the high cost of Viessmann equipment they maintain a high market share and they certainly don't share any of their secrets. The air/fuel mix device uses a "self-adapting, pneumatic, non-mechanical, proportional link" and is supposedly the envy of the industry. It even adapts to high wind in the flue that would cause other boilers to become unstable and shut down.
 
Last edited:
  • #15
Fred:

Reason I went into the radiation explanation is because of a possible (remotely I'm sure) explanation.

Energy is both entering and leaving the system with a very high degree of radiation. Even though the water is moving, if I imagine the entire system as a single object accepting radiation from the burner and liberating it to the house, is it possible that some of the characteristics from the "hot end" (the boiler) appear in the "cold portions" (the radiators) without being detectable in the object itself?
 
  • #16
Sorry to butt in here, but. If most if not all of your system is so old(1922), have you considered that it just might need a good clean out? Rust, scale etc do cause weird things to happen. Also newer additions to the system could be causing problems in flow, both fluid and heat. Another factor could be whether it is a two pipe or one pipe system. If it was originally designed as one pipe but the new furnace was designed for two, see the problem?
 
  • #17
No problem whatsoever stepping in.

Rust/scale is not a problem and it is and always has been a two-pipe system. One-pipe gravity systems were quite rare.

System had frozen and burst when I purchased. Have disassembled over 90% of it. Found significant scaling in only two pipes. Both were galvanized (not original) with the rest black iron. Replaced them. All the rest have very little scaling.

Installed a wye strainer in the return line to the new boiler. Opened it a few days ago and it looks utterly new. Not a single piece of debris found.

No performance or comfort problems with the new boiler. I just cannot understand how it is heating the place at such low temperatures.

Half the reason I changed the boiler was to experiment. Only changes were the boiler and circulator. Piping, basic control strategy and even the boiler temperature curve stayed the same.

To my knowledge I was the first to experiment this way. The results have surprised me and others.
 
  • #18
Sheeesh! Thats some nice clean water you have there. Where I'm at it's a wonder that the pipes don't clog up in a day, Haaard water. A while back I had to replace a line off the cross, supplying the pressurtrols and pressure gauge, at work. Plugged solid with scale etc.

Any road, I can't understand what's going on with your system. It simply doesn't make sense to me. Outflow from the boiler has to be hotter than the returns unless you're adding heat somewhere after the boiler. Waait a minute! You said the rads were on the walls opposite the windows? Hows your insolation? Maybe?
 
  • #19
I agree Kleinjahr. It's like there is a heat sink somewhere in the system that is unaccounted for.
 
  • #20
Am working on a reply that might explain the "missing" heat sink. GREAT way to put the problem by the way!

Find it exceptionally difficult to write a clear, concise response.

----------------------------------------------------------------

Can the "desire" of an object to change temperature influence the flow of radiation?
 

1. What is an efficient heat transfer device?

An efficient heat transfer device is a device that can transfer heat from one system to another with minimal energy loss or waste. It is designed to maximize the rate of heat transfer and minimize the temperature difference between the two systems.

2. How does a heat transfer device work?

A heat transfer device works by utilizing a medium, such as a fluid or solid material, to transfer heat from a high temperature system to a lower temperature system. The medium absorbs heat from the high temperature system and releases it to the lower temperature system, thereby equalizing the temperatures between the two systems.

3. What makes a heat transfer device efficient for high temperature systems?

A heat transfer device is considered efficient for high temperature systems if it can withstand and operate at high temperatures without degrading or losing its ability to transfer heat. It should also have a high thermal conductivity and low thermal resistance to ensure efficient heat transfer.

4. What are the benefits of using an efficient heat transfer device for high temperature systems?

Using an efficient heat transfer device for high temperature systems can result in improved energy efficiency, reduced operating costs, and increased system performance and reliability. It can also extend the lifespan of the systems and reduce maintenance requirements.

5. How do you choose the right heat transfer device for a high temperature system?

The right heat transfer device for a high temperature system should be selected based on the specific requirements and conditions of the system, such as the temperature range, heat transfer rate, and type of medium being used. Factors such as material compatibility, cost, and maintenance requirements should also be considered when choosing the most suitable heat transfer device.

Similar threads

  • Thermodynamics
Replies
2
Views
1K
  • Thermodynamics
Replies
3
Views
1K
Replies
3
Views
1K
  • Mechanical Engineering
Replies
34
Views
4K
Replies
10
Views
2K
  • Thermodynamics
2
Replies
43
Views
6K
Replies
8
Views
994
  • Thermodynamics
Replies
6
Views
2K
Replies
5
Views
2K
Replies
9
Views
731
Back
Top