Author Topic: Talking Thermodynamics  (Read 154540 times)

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #150 on: July 20, 2017, 01:00:33 PM »
hi ,still following along but as i am more hands on than brain on and i find the all this a bit heavy going, especially as i was brought up on yards feet and inches.!! I am getting the jist of things but am more into the practical applications.........when i have to drink a hot cup of tea in a hurryi always put 3 teaspoons in it much to the amusement of the Baristas !! i then try to explain using words like  Adiabatic Enthalpy etc etc etc.....also were men like Watt, Woolfe, and Corliss really educated in thermodynamics or were they just practical engineers ??

Offline MJM460

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Re: Talking Thermodynamics
« Reply #151 on: July 20, 2017, 01:25:40 PM »
The heat transfer coefficient.

Hi Kim, thanks for following along, I am glad you are finding it interesting.  Cooling problems proceed at a rate proportional to the temperature difference, so it proceeds most quickly when the temperature difference is greatest, and as the heat transfer proceeds the temperature difference reduces so the heat transfer slows.  An arithmetic average only gives the right answer when the process proceeds at an even rate.  When the maths is done in detail, and I have to admit I find it a bit too hard, it comes to integration of a 1/x term, which results in the natural log term, which properly accounts for the change in rate as the temperature difference decreases.  The classic example is the cooling of a cup of coffee.  Cooling proceeds at a rate proportional to the temperature difference between the coffee and the air.  Not totally true with evaporation at a free surface, but not a bad approximation for a good cappacinno with a thick layer of good insulating foam on the surface.  The temperature initially drops very quickly but then the temperature change becomes slower and slower.   The cooling follows an exponential function which also involves that natural log function.  Of course Willy's teaspoons absorb a bit of heat to start the process even quicker, but then with the lower temperature further cooling is slower.  His tea is always a little cooler than if he had not used the teaspoons.  Thanks for that example Willy.  No need for anything too technical, just specific heat of the metal and temperature difference.  But if you really want to get technical, stainless steel ones will work slower, but will have a better cooling effect.  But you don't want hot ones from the dishwasher.  I believe those gentlemen were mostly practical engineers who achieved remarkable results with very little theory and rather crude instruments to guide them.  The theory was only in its infancy at the time.  I will leave it to the historians to say just what order some of the significant events happened, but your historical text will give you some ideas of the status of the technology.  Sorry about the units, I am trying to translate a few key numbers, but please remind me if more would be helpful, or particular ones I miss.

Returning to the discussion on the heat transfer coefficient.

The heat transfer equation would be quite easy to use if U was a constant which we could look up in a book for our particular application.  In some situations it comes pretty close, for example conduction in a solid, where U = conductivity/ thickness.  We can look up the conductivity of the material we are interested in and insert it in the equation.  For example, the conductivity of pure aluminium is 236 W/m.K, while copper is 399.  Alloys tend to lower the conductivity, a few percent of copper in aluminium reduces the conductivity to 164 W/m.K, while brass is 111 W/m.K and bronze is only 26 W/m.K.  A good insulating material such as cork would be 0.042 W/m.K.  When we do the dimensional analysis, we see that the thickness has to be in metres. 

It is worth putting some typical thicknesses for copper and brass, for example say 1 mm ((0.001 m) wall thickness, to see the difference in heat transfer over a square meter for each degree of temperature difference.  Similarly say 2 mm (0.002 m) of cork.  These figures can be helpful in indicating differences in materials for some applications.  The high conductivity means that heat is transferred with not much temperature drop, especially across a thin metal wall. 

However to measure the metal wall temperature introduces difficulties.  If you just place a thermocouple on the metal surface, there will be a contact resistance that will affect the reading, and it is difficult to get really good contact.  In addition, the side of the thermocouple not contacting the metal is in contact with the surrounding air and the wiring to the meter.  The thermocouple will read something in between the metal temperature and the air temperature.

Sometimes an electrical analogy is used to analyse heat transfer problems.  The voltage  difference is the analogy of temperature, and the current the analogy of heat flow.  Resistance is the reciprocal of conductivity which is the analogy of heat conductivity.  Now to measure a voltage accurately, we all know we must have a meter which has very high resistance so it draws minimal current.  Not a problem with digital meters, but a real accuracy issue in the days of analogue meters.  In our temperature measurement the accuracy is reduced by the heat transfer from the metal to the thermocouple and on to the air.  If we cover the thermocouple with some insulating material, we reduce the heat flow, and the thermocouple will then be very close to the metal temperature. 

If we want to measure the steam temperature inside our pipe for example, we can put a thermocouple junction on the pipe and hold it firmly in place with some insulating material, a wrap or two of silicon tape is excellent for the purpose.  Some extra insulating material over the thermocouple wires is also a good idea.  Insulating tube can be purchased from an electronics component supplier.  Almost every reasonable digital voltmeter these days comes with a thermocouple as well as its voltage probes, and is well worth buying if you don't have one.

You might want to use an infrared non contact instrument.  These instruments are not affected by the heat loss but unfortunately are influenced by the radiation characteristic of the surface, known as emissivity.  This varies with surface colour, surface finish and material.  Ok for measuring change of temperature over time or different locations on an essentially identical surface, but not good for small differences, or especially the difference between the temperature of different materials.  Even the difference between shiny and tarnished surfaces will introduce a significant measurement error.  A thermocouple is a better option, though they are useful in some specific cases.

Binding the thermocouple to your steam pipe is not ideal, especially if you want to measure several different points by relocating one thermocouple.  In industry, a device called a thermowell is used.  This is basically a solid rod, with an external thread and screwed into a fitting incorporated into the pipe or even pressure vessel so most of the rod is inside the pressure shell. It is drilled with a blind hole so the thermocouple can be inserted from the outside without causing leakage.  The pipe can be properly insulated and the insulation left in place.  The thermocouple can be either permanently fitted for continuous measurement, or a portable unit used for occasional measurement.  I have made miniature thermowells like the one in the attached photo.  It is a short one for use in an elbow fitting in piping.  I use a long one as the filler plug in my boilers, so the thermocouple is closer to the liquid level.  You can see how it is fitted in the pictures of my engines in the gallery post.  This is probably the best way to measure temperature in the boiler, (which allows you to use steam tables to determine the pressure more accurately than a miniature pressure gauge).  Also probably the most practical way to measure superheater outlet, engine inlet and engine exhaust temperatures.  I make them out of brass not bronze for better conductivity, but probably should try one in copper, or a silver soldered fabrication with a copper blind tube or drilled rod, and bronze screwed part.

Next time a little about heat transfer coefficients in a condenser.

Thanks for dropping in.

MJM460
The more I learn, the more I find that I still have to learn!

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #152 on: July 20, 2017, 02:57:28 PM »
Hi, Another practical question i have is what is the ideal shape  (with no pecuniary limitations) are the cooling fins on air head IC engines ? Parallel, tapered outwards, tapered inwards, Perforated etc etc. Also if the exhaust pipe on a steam engine has more surface area for the same weight of metal is that better, also you mention the difference between brass and bronze as conductors of heat ? what is this as a percentage ? We are advised to use bronze in boilers so as to prevent dezincification !....more good stuff to stir up the grey matter. I have also heard that a matt black surface will absorb heat better ,But, it will also give off heat better ? That is why i have painted my house radiators black, much to the chargrin of the council inspector of my council house !!!

Offline Stuart

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Re: Talking Thermodynamics
« Reply #153 on: July 20, 2017, 03:14:52 PM »
Only if the paint is very thin , the fillers that are in the paint could nullify the benefit.

The main thing to take up on is as MJM said temp difference matters , get the rads hot is you need to get the room warmed up .

Or install fan coil units then the water can be hotter due to the coil being enclosed so safer to people.

Or you can do the job properly and fit a optimiser controller , work out the heat loss though the building structure then control the heating/cooling from an outside temp sensor in a Stevensonís screen

The joys of thermo dynamics  :lolb: :lolb:
My aim is for a accurate part with a good finish

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #154 on: July 20, 2017, 03:22:05 PM »
Hi. Also when i made the electrically heated steam boilers, i made the brass holders for the cartridge heaters with a row of grooves to get quicker and more heat transfer. Would this have been correct thinking or would there have been no advantage ?? Also in the pics are the Pressure switch and the low water gauge that i mentioned in a previous post ! Thanks Stuart for info.......i shall get onto the council about that !!!

Online Kim

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Re: Talking Thermodynamics
« Reply #155 on: July 21, 2017, 03:29:02 AM »
Cooling problems proceed at a rate proportional to the temperature difference, so it proceeds most quickly when the temperature difference is greatest, and as the heat transfer proceeds the temperature difference reduces so the heat transfer slows.  An arithmetic average only gives the right answer when the process proceeds at an even rate.  When the maths is done in detail, and I have to admit I find it a bit too hard, it comes to integration of a 1/x term, which results in the natural log term, which properly accounts for the change in rate as the temperature difference decreases.  The classic example is the cooling of a cup of coffee.  Cooling proceeds at a rate proportional to the temperature difference between the coffee and the air.  Not totally true with evaporation at a free surface, but not a bad approximation for a good cappacinno with a thick layer of good insulating foam on the surface.  The temperature initially drops very quickly but then the temperature change becomes slower and slower.   The cooling follows an exponential function which also involves that natural log function. 

Thank you for the very clear explanation.  It makes perfect sense when you think about it that way!
Kim

Offline MJM460

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Re: Talking Thermodynamics
« Reply #156 on: July 21, 2017, 01:41:41 PM »
Well, quite a few interesting questions there.  I will try and address each one in turn, though some will be more easily answered after the post I had prepared.  So I may defer some until tomorrow, particularly your question on fins, Willy.  The answer will make much more sense after I make some explanation of why we have fins.  But the steam exhaust pipe, I am wondering where you are coming from there.  The exhaust pipe is not basically intended as providing condensing area, although there is no harm in taking every bit of area we can get.  So long as the pipe is sloping down, that is, so the water droplets do not fall back into the engine, or sit around causing corrosion when the engine is not running.  Essentially the flow in the exhaust is sort of steady, I know it is a stream of pulses, but the pipe finds an average temperature.  The weight of metal and its specific heat do tend to stabilise things a bit there, but I am not sure it is any real advantage.  If anything, extra metal will condense more steam when the engine first starts until it gets to temperature, then if the pipe is insulated it makes no difference.  If we are wanting to loose heat from the pipe, less metal so it increases in temperature a bit at each pulse means slightly higher mean temperature difference, but I think it would be a very small difference, at least for practical tube thicknesses.  Perhaps overthinking the issue a little.

The difference between brass and bronze, and I will add stainless steel for your tea coolers, right on topic with that one.  For straight conduction issues, conductivity, k in W/(m.K) is the relevant property.  I have not found how to incorporate a table in a post, so please make yourself a table with these figures.  I have also included the specific heat, Cp in J/(kg.K), which I will come back to.
Copper, k= 399 W/(m.K), Cp=383J/(kg.K)
brass, k=111 W/(m.K), Cp=385 J/(kg.K)
Bronze k=26 W/(m.K), Cp=343 J/(kg.K)
Stainless steel, k=14.4 W/(m.K), Cp=461 J/(kg.K)

You can see there is a large difference between brass and bronze.  Copper has much higher conductivity again.  I feel that it is better not to talk about percentage, as that facilitates overlooking the contact resistance, I discussed yesterday, when thinking about the heat transfer.  In comparison, Bronze is not a great conductor at all, and stainless steel, (SS), is even worse.  Dezincification is a form of corrosion where the zinc content of brass is dissolved out, leaving behind a much weaker material which cannot be relied on to safely contain pressure.  There are many contradictory stories surrounding this issue, and I am not enough of a metallurgist to be able to explain the issue more clearly.  However, if you get dezincification of a boiler bush, you would have to condemn the boiler, or at least do major repairs to replace the bushes.  So the codes require us to make them bronze.  There is not so much emphasis on the plug which screws into the bush.  I guess this is because it is easily removed and inspected, but please don't quote me in a discussion with the boiler inspector.  The safe approach is to make any pressure containing component in bronze. 

Let's consider the impact of this on two quite different components.  First, my little thermowell.  When screwed into the pipe or boiler, this component is surrounded by the fluid being measured, and there is no intentional heat flow unless there is a temperature change.  With no heat flow, there is no temperature drop, so the conductivity does not matter.  When the temperature changes, some heat has to flow until the new stable temperature is reached.  Conductivity will affect the time taken to reach the new temperature, so the material has an influence on the speed of response of the instrument.  Temperature instruments are always slow to respond, but this makes it worse.  Perhaps I should use bronze after all.

Now the bush for your heater element.  Obviously the bush silver soldered into the boiler shell should be bronze.  Now, the well for your heating element is removable, so probably could be made of brass.   However I suspect it is not often inspected, but then, any leakage might be contained within your wiring conduit, perhaps!  Probably better to use bronze.  Heat transfer through the wall thickness of bronze will mean a temperature drop, so your element has to reach a higher temperature to drive the heat through the sleeve into the water.  Here you are wanting really good heat transfer, so your element within the tube does not have to get so hot to transfer enough heat.  In this application, bronze is not an ideal solution.  This leads me to wonder if we could make a bronze part to screw on to the the boiler, with a copper tube silver soldered in to contain the element, and a bronze plug silver soldered in the end.  Even better conductivity, and no dezincification.

I am assuming that your cartridge heater comes with the element insulated and sealed in a sheath which you have to introduce into a pressure tight component, much like a longer version of my thermowell with the hole drilled to accept the heater sheath, and flanged onto the boiler bush.  I addition you have machined grooves on the outside of your pressure tight sleeve.  I am going to leave my comments on these grooves until after I discuss convection, as I hope it will make more sense then.

Then, your household radiators.  First we need to clarify the terminology.  I know that "radiator" is the normal terminology, but it is probably actually a convection heater.  Especially if the heat comes from circulating hot water.  A common arrangement is a thermostat which controls the water flow so when the temperature is too high, the water flow is reduced.  I am not sure if the controlled temperature is the room temperature or the water temperature, though I am inclined to guess the water temperature.  So either a fairly flat panel, or a more complex column arrangement.  This is a typical heat transfer problem where transfer is by all three of conduction, convection and radiation.  Usually however, one of these modes predominates and the others relatively unimportant.  The term radiator suggests the main mode is radiation.  However radiation depends on difference between the fourth power of the absolute temperature of the heater surface and room objects.  I suggest for a hot water system, this is not a very important contributor, but most heat is transferred by heating the air in contact with the metal surface.  The warm air then rises and circulates the air in the room, thus distributing the heat.  This is called convection.  Conduction is only important if objects are in contact with the metal surface, not usually recommended, though sitting on it is very comforting when you first come in from the cold.

I am totally in agreement with Stuart on the paint, especially if the heater really is a radiator.  A very thin black paint can in principle help increase the emissivity of a radiating surface, but getting this right is tricky.   You would need to do some careful experimenting, as the wrong paint does not work so well.  It also, as you say, increases the absorption.  However, for primarily convection heating, while the metal surface detail is important, paint is more likely an insulating layer which means the temperature difference between the water and the room will be greater.  Surface roughness is probably helpful.

Thanks for joining in again, Stuart.  Good to have you on board.  It would be interesting to hear more about your idea for an optimiser for household climate control.  These days with Arduino microprocessors and the means of programming them so readily available a fully automated household climate control system should be an easy project.  However the logic for the optimisation needs to be developed.

I am glad the explanation was clear Kim, any time it is not, please ask again.  Building blocks in a knowledge base are only useful if everyone one can understand them.

My intent was to continue to look at heat transfer coefficients, but I think this post is long enough.  Better to continue next time.  Not sure I have completely answered all those questions yet either.

Thanks for following along

MJM460
The more I learn, the more I find that I still have to learn!

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #157 on: July 21, 2017, 03:33:36 PM »
Thanks for the info ...cool.... i hope i am not hijacking these posts !! just a thought but no questions this time.! this pic is the exhaust arrangement of a small double acting steam engine in the local museum. As you can see the exhaust pipe goes strait up ?!!!! However it was taken apart and reassembled, so they may have got it the wrong way round as it is bolted on. I did make a model of this and used the same configureation . I may have to write a comment in the visitors book !!they also got other parts in the wrong places as well !!! Also the cartridge heaters are designed to fit into reamed holes, and make contact when they heat up.
« Last Edit: July 21, 2017, 03:37:21 PM by steam guy willy »

Offline MJM460

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Re: Talking Thermodynamics
« Reply #158 on: July 22, 2017, 01:07:15 PM »
Hi Willy, I am glad that you are finding the information interesting, and don't worry about hijacking the thread.  It is all about building a knowledge base that is helpful to model engines.  I always have the choice to defer a reply until later.  I am just as happy to look at radiation now as after convection, so I chose to look your heater questions when you asked.  Mostly, I find your questions right on topic, and they help keep me grounded in just what it would be useful to cover, so they are very helpful, thank you. 

That is a beautiful model you have made of an interesting museum model.  Just a bit more about the exhaust, I was thinking particularly in reference to an exhaust pipe connecting the engine to a condenser.  Points in piping which collect liquid cause all sorts of problems, hence my comments about making the piping self draining.  Of course, if there is no condenser, the exhaust steam still has to go somewhere.  In an industrial situation, a horizontal hot exhaust is quite dangerous, downwards not much better, and upwards is probably the best option.  Of course, weather conditions determine whether the steam mixes with air and is carried away, or condenses into a fine fog that is carried away, or condenses into drops which rain down on everything in the area.  On my models, I run the exhaust down to a separator/oil separator, where any water (mostly only on starting) is collected and drained, while the dry steam is discharged straight up.  I suspect that in the period of the model, there were no such niceties, or possibly no cylinder lubrication.  They may have just relied on condensate for lubrication.  So the vertical exhaust on the the museum example and your model is most likely quite ok.

The requirement for a reamed hole for your electric elements is interesting.  Can you ream a blind hole?  By the way an electric element is easier to deal with in experimental work.  You know the power dissipation of the element based on supply voltage and element resistance, and the element just gets hotter until all the heat is lost to the water.  So good contact, and a high conductivity sheath both help to limit the maximum temperature of the element.  Do you also use a smear of heat conducting grease to help even more?  I am not sure if there is anything available that would not cause other problems, such as mess or corrosion.

Yesterday, I mentioned that heat transferred by radiation was proportional to the difference in the fourth power of temperatures.  Mathematically Q = U x A x (T1^4 - T2^4).  The temperatures have to be absolute, K or Rankine if you must.  Radiant heat travels in straight lines like light, but not evenly in all directions.  Think of a car headlight compared with a room light with a translucent diffuser. So A and U have to be modified by a view factor which relates how much of the radiated heat is actually received by the receiving surface, also by directional factors and so on.  But if the water in your heater is say 65 C, the heat transferred by radiation will not be much compared with the heat from a red hot glowing element.  You can get a good idea of whether the main mechanism is radiation or convection by holding your hand facing the heater but say a metre away at the height of the middle of the heater and feeling the warmth.  Then hold your hand above the heater, again about a metre distant but directly above the heater palm facing downward, and feeling the warm air rising.  Which one gives you the most heat?  On the other hand if you have a fireplace, or campfire, or perhaps a one or two bar electric radiator, and hold your hand facing the fire, a metre will be too close for comfort due to radiant heat.

Now let's return to our condenser.  We usually have a metal wall, usually tube, with the condensing steam on one side and perhaps water on the other.  This is when things get difficult and we have to look again at types of heat transfer.

Most of us learnt in school science that heat is transferred by conduction, convection and radiation.  We then usually talk about conduction, possibly mention radiation as heat transfer from the sun to earth through space, and rarely go into convection in any depth.  Now this is not entirely without reason.  Convection is quite complicated.  And radiation not much different in complexity as we saw when looking at your household radiators.  My text book on heat transfer is significantly bigger and heavier going than my book on thermodynamics.  And much of this is due to study of convection.  I don't want to go too deeply into heat transfer, but it is necessary to just peek in and try and understand the main issues.

With convection we find that we have to look at three resistances to heat transfer which are effectively in series, to use an electrical analogy.  We are talking about conductivity which is the reciprocal of resistance.   We have the steam side of the tube, the metal tube wall, and the water side.  Now we can look up the thermal conductivity of steam at 100 deg C, it is about 0.025 W/m.K, and the conductivity of water at say 25 deg C, about 0.6 W/m.K.  Now this is not looking good for our condenser, steam is about as good an insulator as cork and water not much better.  But this is where convection comes in.  The copper tube is a good conductor, and will have only a small temperature drop from one side to the other. 

Now let's look at the water side of the tube, and conduction of heat from the tube to the water.  The water temperature is measured well away from the tube, and if the water is not flowing, perhaps trapped in a porous foam, the temperature will increase as you move the measuring point closer to the tube with a linear temperature gradient as heat flows by conduction, and will match the metal temperature very close to the wall.  However, if the water is free to move, everything changes.  The water against the wall expands as it get hotter, and the hot water rises through the more dense cooler water, and is replaced by cooler water.  This means that the temperature gradient near the wall is very steep, much steeper than if there was no water movement and only conduction.  It is  this high temperature difference across the layer very close to the wall which means much higher heat transfer than the conductivity would imply.  In addition, water has a high specific heat, so the moving water can carry away a lot of heat.  So the water side will carry away heat very well.  If we then use a pump to force the water past the tube the heat transfer will be further increased.  So the heat transfer on the water side is not only proportional to the temperature difference but also to the water velocity, whether it is a forced (pumped) flow, or natural convection flow.

The steam side has a quite different situation.  The steam cooling against the tube condenses and forms a film in the tube.  Of course gravity makes the film flow down and off, and you can see this is quite complicated to analyse.  Just to make it interesting, water is one of few substances which in this situation can form droplets which drop off the tube.  The resulting turbulence further increases the heat transfer.  I assume that now days with computers the maths is doable and coefficients can be calculated.  For most of my working life, approximate coefficients were assumed based on industry experience, and there are books with suggested figures for various situations.  In the end it should be clear that to calculate coefficients from theory is probably not practical for most of us.  I am sorry if this is too heavy going.

Let's just take away the summary that the convection coefficient for a condenser is determined by three individual coefficients, the steam side, the tube wall and the water side.  Usually one of these provides most of the resistance to heat transfer and so determines the overall heat transfer rate.

Next time I will talk about a few things we can learn from this basic understanding of heat transfer.

MJM460
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Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #159 on: July 22, 2017, 03:33:30 PM »
Hi, I have had another look at the Bridewell exhaust pipe and there is a drain cock arrangement at the bottom of it, see pic.and there was a hydrostatic lubricator in the steam line. Also you get two types of basic reamers The Hand type have a longer taper and the morse taper type has a very short taper, about 3-5% and these are to be used on the lathe specifically for blind holes .....And Bronze is approx 88% copper  12%tin   and brass is 65% Cu and 35% Zn...so yes bronze is a much better conductor.

Offline MJM460

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Re: Talking Thermodynamics
« Reply #160 on: July 23, 2017, 01:23:39 PM »
Went for a bike ride this morning.  Disturbed a mob of kangaroos that were grazing by the path.  They all bounded away in that typical flowing motion and were gone.  Not the everyday experience even for for most of us in this country.  All too quick for any chance of a picture unfortunately.

Willy, I am not surprised that there is a drain cock at the bottom of the vertical exhaust of your prototype engine.  There is a lot of condensate to get rid of when the engine starts, and a little more when it is shutdown, the two occasions when it is good to be able to drain condensate.  If you have ever looked at a petroleum refinery or petrochemical plant and seen that mess of piping everywhere, you may be interested to know that every one of those pipes has a drain valve at every low point where liquid would collect, and a vent valve at every high point where air would be trapped.  A little known fact, I believe real rather than alternative fact, is that the equipment count with the best correlation to the total plant cost is the number of high and low point drains and vents.  Unfortunately, when you finally know the number, you know the cost anyway, so not very useful for budgeting.

Thank you for the information about reamers, I have often wondered which I should buy.  One of those puzzles that we all have to deal with as beginners in this hobby.

Now conductivity.  I am not sure whether you are expecting intuitively that more copper is the same as better conductivity, or if you are using a very different text book to mine.  Pure metals such as copper, aluminium, have relatively high conductivity.  Tin and zinc much lower. The conductivity of pure copper 399, and aluminium 236, while zinc is only 121 and tin 67, all in W/(m.K) from the same book.  However, when the elements are melted together to make an alloy, the conductivity is normally less than either of the components.  So brass is 111, which is less than either copper or zinc.  Similarly, bronze is only 26, so again less than copper or tin.  You could also look at Duralumin, an aluminium copper alloy with only 5% copper is only 164, and aluminium bronze, also a copper aluminium alloy but this time 95% copper, 5% aluminium is only 83.  I don't have the facilities to test these, and do not have the opportunity at the moment to check other sources, but I would suggest that while any one of these could be a misprint in one book, the for whole lot to be misprints, all the same direction, I suggest would be unusual.   Interestingly, Carbon in iron to make steel seems to increase conductivity, and chrome or nickel individually in iron have a very different result to the combination in stainless steel.  Definitely an area where intuition does not help much. 

In summary, I suggest brass is actually the better conductor, while bronze is only better than stainless steel.

Getting back to our topic of heat transfer and condensers, I hope you can  see why I am not proposing that we try and calculate a heat transfer coefficient for a new condenser.  However we can do it the other way, if we have a condenser, and we can measure how much steam it is condensing, and the inlet and outlet temperatures, we can calculate an approximate overall coefficient.   If we have a condenser, we can calculate an overall heat transfer coefficient from its performance, and this would be a reasonable guide to a similar condenser with more or less area.

We can also apply the knowledge to other problems such as when to add fins to our surface.  On an internal combustion engine, with air cooling, we can identify a film coefficient for inside the cylinder, conducting heat to the metal cylinder wall, then the conductivity of the metal wall, then the metal to the air surrounding the engine.  In this case the combustion gases are very hot, and provide a large temperature difference to drive heat transfer into the metal, and a smooth cylinder wall is an obvious necessity, so the main variables we can play with are the metal composition and its thickness.  When we look at the transfer coefficient from the metal to the surrounding air we find this is the lowest of the three and basically controls the overall heat transfer.  We can increase the coefficient by forcing a cooling air flow instead of relying on natural convection, and we can increase the metal surface area by adding fins.  Of course adding fins is not quite as simple as we would like.  Basically heat has to travel to the parts of the fin which provide the extra area.  So conductivity along the fin becomes more important.  In travelling to the end of the fin there is a temperature drop which reduces the temperature difference to the air, so the extremities of the fin are less significant as the fin becomes deeper.  In the end, a very deep fin has no heat transfer advantage over one of the "just right" depth.  The "just right" depth depends on the the ratio of the surface coefficient and the conduction coefficient, so again no simple answer, but cast iron fins would have a different ideal depth to aluminium ones.  But you can see some clues to the question on fin shape.  A fin that is thickest further from the cylinder wall is not only tricky to make, but has more metal where it is less useful.  On the other hand, one that is thicker nearer the cylinder is actually more effective than a constant thickness fin, but you will notice that I am summarising the answer rather than trying to include all the maths.

This logic applies generally to problems involving transfer to air.   Transfer from condensing steam to a copper tube wall is very good, conduction through a copper tube wall good while transfer to air from the metal is much lower.  So we see the extended surface approach on our car radiators for example.  Some indication of when fins might be a good idea is provided is given by industrial steam condensers.  A normal water cooled condenser for an engine or steam turbine exhaust is normally built using plain tubes, in very large numbers, I might add.  It is quite unusual to use air cooling for a condenser, partly because water is normally cooler than air and easily achieves a lower condensing temperature, and hence pressure.  However, I do have experience of one quite large air cooled steam condenser.  I can assure you it was very large and had very large fins on the outside of the tubes in addition to large fans to force a high air flow.  So air side film coefficients something between water and air cooling is the indicator for adding fins.

You might also be interested to know a little more about your use of teaspoons to cool your tea.  In addition to just absorbing heat to warm the spoon, thus cooling the tea, the handles of the spoons also act as extended surface area, in addition to the surfaces of the cup, so the spoon handles are fins on your tea cup which increase the cooling rate.  I am serious. The specific example is in my text book!  Also, I assume you sit the cup on two pencils, or more spoons, so air can circulate underneath instead of the bottom being insulated by the saucer.  I think it's time to get out the stop watches and thermometers and do some serious thermodynamics over a few cups of tea.

Next time I will have a look at your electric boiler sheaths for the heating elements.

Thanks for following along

MJM460
The more I learn, the more I find that I still have to learn!

Offline steam guy willy

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Re: Talking Thermodynamics
« Reply #161 on: July 23, 2017, 02:36:45 PM »
Hi MJM,  Wow.OMG. My intuitive expectations are so wildly incorrect i feel i need to go back to school, However as a Baby Boomer we did not really do Science or technology lessons.!! Interesting about conductivity (thermal not electrical) or there might be some correlation, I do not have the text books to hand to look up specific tables. When you have an amalgam of Tin /Lead as in solder the melting point is less than either of the two metals, so i assume this is correct with brass and bronze ? I have always wondered why cast iron melts at about 1100 degrees and steel about 2000  ? I use german or Nickel silver (copper/Nickel) quite a lot in my models so what is the value for this ?  Interesting info about the tea cup cooling, and i will now have to explain why i am now taking 5 teaspoons (M'Lud)!! instead of 3 !! Interesting about the fins on IC engines...On my 1920's Scootamotor the cylinder was steel with lots of very thin fins turned up out the thickness on the billet,.I notice that fins seem to be evenly placed around cylinders rather than longer at the back where there is less and higher temp air flow or are they made from an asthetically pleasing rather than a thermodynamically correct logic.? On Condensers ,The tubes in the boilers are steel where we want maximum heat transfer ,but, incondensers the tubes are invariably brass ,where we also want maximum heat transfer !! This is to do with cost considerations i suppose.....in some of the GWR locomotives the inner fire boxes were made of pure copper !!! .Thanks for all this info, i have always said that if you have all the correct Info about anything, you can make the
correct decisions about how you proceed using that info.

Offline MJM460

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Re: Talking Thermodynamics
« Reply #162 on: July 24, 2017, 11:51:40 AM »
Hi Willy,  intuition is often helpful in forming a hypothesis as a basis for further inquiry.  Like you, I am quite surprised when I come across examples which are not in agreement with intuition.  However, intuition still helped you formulate the question, and when I looked carefully at a few examples of data, together we found useful information.  Data leads us to modify the initial hypothesis to something like "when metals are melted together in an alloy, the thermal conductivity is less than either of the pure metals".  When I then looked at more complex alloys, like steel, or alloys of more than two metals, we have to modify the hypothesis a bit more to be even less positive.  Something like "often less than any of the components" or "may be less".  Not so definitive, but useful none the less.  Then on thinking further, steel may have other trace or significant quantities of other metals, but it also has carbon, which is of course not a metal.  And we know the properties of steel are very sensitive to even very small amounts of carbon.  I believe there is a fairly good correlation between thermal and electrical conductivity, but again, there are some exceptions.  You may have one in your electric heater cartridges where there are conflicting requirements for good electrical insulation and good thermal conductivity.

I don't think it is necessary to go back to school at our age, we already have a life time of knowledge and experience that schools are trying to prepare kids for.  Life is not long enough to learn everything.  We are better to concentrate of filling in the gaps in our knowledge in areas that interest us, a privilege of our age.  Of course we may choose to do this by private reading, discussions or even by taking a class.  I am also a baby boomer.  In high school we had to choose between science or humanities, and each stream only did one light subject from the other side.  The stuff we are talking about here was only introduced at tertiary level, but most of the real learning came from a lifetime of needing to apply these principles in my every day work.

The melting points of alloys vary over a wide range, depending on composition and these are usually described in a phase diagram.  You will also find there are true eutectic alloys that have a simple single melting point, and many other alloy compositions that melt over a temperature range.  Your tin lead solder example is one of these, where the eutectic alloy heats up then suddenly melts, while other (generally cheaper) alloys with less exact composition, start to soften and gradually melt as they get hotter.  The best source for these phase diagrams is a metallurgy text book, which you may be able to find in your local library, particularly if it has a good technical section.  Definitely not my strong subject, and unfortunately my text is not accessible for now.

The shape of the fins on your scooter engine will be determined by a lot of things, not simply thermodynamics.  In fact thermodynamics (of the engine performance) probably would prefer less heat loss for higher engine efficiency.  The main reason for the fins is so nothing melts, and the necessary cooling aims to do it uniformly so the cylinder stays straight.  Also fins might be shorter lower on the cylinder, as the piston limits the time that hot gases are near the bottom end of the cylinder, so there is less heat to be taken from there.  Again well beyond my knowledge.

When you refer to steel tubes in a boiler, I assume you are talking about steel boilers.  Perhaps locomotives, but ships and stationary engines also.  Again, heat transfer is desirable but even in a boiler, not the primary consideration.  The major thing is strength, particularly at temperature.  Copper and its alloys are not strong enough, particularly at high temperatures.  Copper is chosen for model boilers as it is easily worked by people such as us, and readily joined by soldering or brazing.  But copper strength at only 200 deg C is only half that at room temperature.  Better make sure you have plenty of water in the boiler, especially with a good hot coal fire.  Steel is stronger than copper at all temperatures and has useful strength to quite high temperatures.  But steel working (as opposed to machining) and joining by welding to maintain full strength even at temperature, is not for the average hobbyists.  Of course steel is subject to rusting, much to our dismay when we find it.  While copper is very much less so.  Some special stainless steels, known as duplex stainless steels, have been developed to resist corrosion as well as have high strength at temperature.  In fact there are groups working on making model boilers from duplex stainless, but you can safely assume that these people are real expert welders in their working life.  They are not average hobbyists, or even just good welders.  So many more factors than pure thermodynamics are involved in choosing the best material for an application.  It is necessary to have not only correct information, but also to the extent practical, complete information.

 Very few real life problems are single dimensional, most have many factors, and very few real problems are binary.  Despite computer logic, the answer is not often limited to yes or no, black or white.  Rather the answer is mostly maybe, or some shade of grey.  And rarely do we have really complete information.

Today's adventure in the long paddock, a horseman rode out onto the highway, and started walking in small circles in my lane.  Obviously a sign to stop.  Out came about 100 head of cattle, being driven across the road by two drovers on horse back.  They had put out signs to advise the traffic coming towards us, but I think they forgot our direction.  To complete the picture, we came up behind a truck with a rather superfluous "Wide Load" sign on the back.  The road is one lane each way, yes it is a main highway, each lane about 4 meters wide.  The truck was carrying a bulldozer with a cab about 6 meters high, and a blade at least 6 meters wide, protruding well over the centre line.  Even the pilot vehicles for wide loads coming towards us, usually quite pushy about claiming their side of the road and more, moved over for that one.  We had a very sedate peaceful drive behind him for about 50 km before he pulled off into a rest area.  Obviously mining in the area as well as cattle.

I was going to continue the heat transfer discussion by looking at Willy's electric heating elements, but I seem to have been side tracked.  Oh well, life is more than pure thermodynamics.  That will be tomorrow.

Thanks for dropping in,

MJM460
The more I learn, the more I find that I still have to learn!

Offline paul gough

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Re: Talking Thermodynamics
« Reply #163 on: July 25, 2017, 11:33:25 AM »
In post 128 you state, "It is a matter of understanding the energy balance for your engine, knowing exactly where all the heat is going."

Well, this and all the discussion lately has raised a question I have never been able to answer satisfactorily. I would like to optimise the design and material choice for small gauge 1 locomotives with inside cylinders, fixed cut off with dimensions of the order of 8X12 mm, (to a little larger), that operate with methylated spirit fuel, single firing rate and throttle setting, hence mostly more or less stable cylinder conditions. I previously had two locos like this, twin cylindered Aster Lions, (Titfield Thunderbolts). One has a brass block cylinder and the other brass tubes silver soldered into end plates, neither had cylinder lagging. The latter engine seemed to be very slightly superior in run time/distance and a little less condensate out of the chimney, but I had not done any measuring unfortunately and have now donated this engine to a mate some thousands of kilometres to the South so can't do any analysis now.

For future engines of similar type and size I am wondering if moving to bronze cylinders built up from two tubes with end plates silver soldered together and insulated with Kaowool lagging would achieve any superior results than the use of a bronze block for the inside cylinders. I have some intuitive and experiential notions but am not competent enough to work out the thermodynamics of it all. Given that modern loco cylinders were relatively thin walled steel castings I am presuming models with big lumps of heat absorbing and transferring material like solid block brass fabrication or castings are potentially working against us. But to what degree?

So, I beg your indulgence in pondering this issue, and are able to address my specific enquiries by showing us some thermodynamics that might resolve the issue. Thanks for your labours to date, if it be any consolation some of us labour just as intensively trying to absorb your energy output. Regards, Paul Gough. P.S. Operating pressure in my loco is 50 to 60 psi so assume cyl. pressure to be somewhere around 50 or a bit more.
« Last Edit: July 25, 2017, 12:02:14 PM by paul gough »

Offline MJM460

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Re: Talking Thermodynamics
« Reply #164 on: July 25, 2017, 01:23:28 PM »
Heat transfer example - electric boiler heater elements.

Hi Paul, I was just about to post this when I saw your reply.  More very interesting questions.  I will give some thought to those, and will definitely come back with my ideas.  I suspect it will continue to involve taking a little bite at a time and weaving these bites between bits on condensers, but I am heading towards boilers, so a very timely query.  I am sorry it is such heavy going, any suggestions on how to make it easier to follow would be welcome.  Even requests for more explanation on the hardest bits.  Then I can try to come up with some examples that will help.  Always a balance between too many words and not enough explanation.  By the way, is tropical Queensland anywhere near Rocky?

While this subject is perhaps a little out of order, I was talking about condensers after all, but it is the last outstanding part of Willy's question, and it is as good an example as any to round out the heat transfer discussion.

Let's look at the complete heat transfer path from the heating element to the water.  Electrical energy is used to heat a coil of wire. The wire has significant resistance, and ohms law gives us the current as V/R.  I believe the elements are connected to alternating current power supply from the mains, not sure whether it is direct to the mains or perhaps through a transformer.  The wire is probably formed into a coil to fit enough length into a compact space, so may have some inductance.  With AC, inductance causes a phase lag so the current is not in phase with the current, but the heating effect is only due to the resistance.  Electrical power is calculated in Watts as V x I.  Alternatively, a little more manipulation of the equation can give power directly from the voltage and resistance as V^2/R.  Looking at it this way is useful in understanding the impact of reduced voltage on the power output.  You can see that this formula has no components relating to temperature, or thermal conductivity.  But a heat balance on the element tells us that the temperature will get high enough to reject all the heat input from the electrical input.  We might think that ideally, we would put the element directly onto the water.  This would result in the lowest wire temperature, but there would be a real danger of someone getting electrocuted, particularly with mains power (220 - 240 V in UK, Europe and Australia for our US readers).  There is also quite a high probability that some of the electrical current might take an alternative path through the water, producing hydrogen and oxygen.  You don't want any sparks around that combination.  And there is no need, the wire has very high temperature tolerance and is unlikely to melt.  It is safer to surround the wire with an insulating material.  In industry, and even domestic hot water services,  a temperature measuring element is also incorporated into the bundle within the sheath.   This element is to protect the wire from excessive temperature by isolating the power supply when some high temperature limit is reached.  I don't know what specific material is used for the insulation, it may be some sort of ceramic or a magnesium compound.  Willy, do you know what it is?  As I have previously mentioned, there are conflicting requirements for its selection.  It needs to be a good electrical insulator, but ideally have good thermal conductivity.  In the end, there must be no compromise on the electrical insulation properties.  Then the whole lot is placed in a metal sheath so it can be safely sealed up.  The sheath is almost certainly kept thin, perhaps for better heat transfer, but it is probably not rated for significant external pressure.  I assume the manufacturer has some specification for the maximum temperature this sheath should be allowed to achieve.

 In order to use it in a pressure boiler, the user has to produce a second sheath designed to withstand external pressure, and also designed so it can be installed in the boiler without causing leakage.  Willy has produced a brass sheath similar to the thermowells I make for temperature measurement, which he has grooved to increase the surface area for heat transfer to the water. 

If we assume that steam is to be raised at 350 kPa(g), 450 kPa(a), it's temperature will be about 148 deg C.  The heat path from the manufacturers metal sheath to the water involves a contact thermal resistance between the sheath and Willy's boiler fitting, the conductivity of this fitting and finally the film resistance inherent in the convection transfer to the water.  I was interested to learn that the heater elements are designed to be fitted in a reamed hole.  This implies very close contact, possibly even slight interference that compresses the manufacturers sheath, even if just a little to ensure very good contact.  Certainly an air gap would be a real problem, and must be avoided to the extent possible.  I don't know if any heat conductive grease is used, similar to that used in assembling heat sinks on electronic components where there is the same problem.  Willy can choose the material from which to make his well.  As we have already noted brass has better conductivity than bronze which might also be chosen.  The better conductivity of brass means that the element will not get so hot.  Stainless steel could also be used, however stainless steel has even lower conductivity,

Finally, the question of fins.  Now adding fins adds surface area which you would think would always help.  However this is another of those cases where intuition does not always give us the right answer.  So how do we answer the question for this particular case.  The maths for determining the effectiveness of fins is complex.  You will find it in a text book on heat transfer if you want to look in more detail, perhaps in the local library.  My quick summary is that there is a dimensionless ratio called the Biot number, my book uses the symbol Bi, which tells us when fins are likely to be helpful.  The Biot number is defined by Bi = h x d/ k, where h is the convection film coefficient, and k is the conductivity of the fin material, and d is half the fin thickness (please don't ask why the half, it's in the book).  Fins are worth using when Bi is very small, meaning much less than 1, while they actually are counterproductive when Bi is much greater than 1.  As an indication, convection transfer to a gas generally gives a very small Bi due to a very low film coefficient on the air side.  Heating water is on the borderline, while boiling water has a very high film coefficient, especially if the temperature difference is enough to cause vigorous boiling, so fins are counterproductive.  The border between fins helping and not helping with brass fins is somewhere in the region between just gently heating water and vigorous steam production.  Unfortunately I do not know whether your fins are useful or not, so the issue becomes one to devise an experiment which will tell us whether fins help or not.  That sounds like a good spot to pause until tomorrow.

A bit more adventure in the long paddock today.  Came around a bend on the highway, only to find a small herd of cattle, perhaps about 20, standing on the road.  We stopped.  Beautiful healthy looking animals.  Collecting fresh steak for dinner had some appeal, but it tends to do a lot of damage to the car.  So we just tooted.  Half started moving on, the others moved back on the road.  No drovers in sight, so we waited.  Eventually they moved off and we went slowly past.  I reckon somebody left the gate open!

Tomorrow I will try and devise an experiment that will help Willy decide whether or not to continue machining his fins.  Has anyone got any suggestions?

MJM460
« Last Edit: July 25, 2017, 01:35:38 PM by MJM460 »
The more I learn, the more I find that I still have to learn!