Challenge Questions

The water should be pumped from A to B. Heat always travels from higher to lower. As B has a longer pipe, it will collect more heat energy and therefore will produce hotter water than A. Pumping water from B to A will probably result in heat loss instead of heat gain.

Definitely no loss thru "b" assuming the flow and entry temp is sufficient to take advantage of the cross-sectional area of both panels. This I believe from my experience is purely a question of DIFFERENTIAL.

R.G.C.

I am torn. Ideally, assuming the temperature inside each collector will rise to the point required to achieve thermal equilibrium, and both collectors have equal energy input, then it shouldn't matter in what order they are connected. However, the system being not idea, I would think there may be some efficiency advantage in having panel A after panel B since it will have to rise to a higher temperature to achieve equilibrium, given that they both collect an equal amount of energy input. Having the higher temperature device last would reduce the amount of time that the water is at a higher temperature (loss proportional to delta t) before exiting to the rest of the system.

It makes no difference.

It makes sense to pump from A to B as there is a chance for cooler water in A to become hotter as it passes though B.

I agree it makes no difference heat pick up is cumulative which ever way you go.

I disagree, it takes more energy to heat from cold then maintain it, go through B first.

Very concise...! My first instinct was the same; after all, the only real purpose of "coiling" a heat exchange tube is to maximize length (of tubing), and thereby transfer surface. That is, connecting the two exchangers in series would be essentially no different than laying out two such, connected tubes, without bends, over two proportionately sized rectangles of black material laid end to end (if space availed). However, in this circumstance one must consider the net non-equivalence of the surface areas of the black heat absorbtion-convection panels that are immediately available (for imparting of heating) to the different-length, differently-arrayed overlying exchange tubes. On the one hand, it could be said that the shorter tube will transfer less heat, both because it is shorter and presents less surface, and because more incoming, converted heat escapes skyward, un-utilized, due to its relatively less concentrated arrangement over its black panel. Opposing this..., would be that the longer tube's shadow area on its underlying black panel would be proportionately greater..., to the effect that it would block more sunlight from reaching that black panel, as a consequence of which it would receive less convective heating from below. But, does this really matter?

This might be answered by taking the (provisional) assumption that it does: that heat will be transferred in greater quantity in one exchanger than the other. Then it might be supposed that if either exchanger transfered heat to water more rapidly and in greater quantity, then the result would be that water is accelerated in that exchanger to a greater degree and extent than in the other. And if it was the case that the "system" was open-ended, then the question would devolve to that of whether it was better to place the "impeding" (the slower-accelerating) exchanger in the upstream or in the downstream position. ...which, in turn, further devolves to the question of whether 'tis better to push against a load or pull--something akin to the question as to whether there is any advantage as between two cars accelerated to x MPH by driving wheels in the front or rear.

However, the water circulation system is not open ended, so there is a convenient way to set aside the push or pull question and say that it doesn't make any difference. No matter what the serial orientation of the two solar exchangers was chosen to be, the net affect on circulation--the end objective strived for--remains unchanged. If the slower accelerating exchanger (whichever that is) has the effect of imposing a resistance to the (pushing of) upstream exchanger (thereby tending to decelerate flow), than the pulling of the upstream exchanger will (increasingly) counteract by lowering resistance at the output of the (otherwise impeding) downstream exchanger; thus lowering its resistance and accelerating its throughput....

And if we agree that it makes no difference to the water, or the water consumer, whether the water is pushed or pulled through the closed loop, then the converse--placing the slower-accelerating exchanger upstream--should achieve the exact same stable flow rate; one needs only to reverse directionalities and exchange the words push and pull in the first instance described above; or simply think of system throughput flowing the opposite direction.

So, with a wink and a nod, I am compelled to stand with you on your solution to the challenge.

An awfully long wink and nod. And in common with most such, utterly devoid of meaningful technical content.

Why not have a think about the temperatures of the plates, and that the loss to ambient increases faster as surface temperature rises...

...seem to have made an argument without a premise. The loss to ambient was "discussed." If you want to make a counterpoint, other than to cordiality, please feel free to do so. If it is true that ordering one plate upstream of the other confers an advantage what do you suppose that advantage (in terms of outcome) to be? Or would it be the case that only one arrangement would work at all? This is the technicality which seems to be lost...in many such...

I really thought that your original comment was satirical. Now I'm not so sure.

You talk about acceleration through the exchangers - if the pipes are of equal diameter, the water velocity will be equal through both exchangers. If you mean accelerating (convective) force, that cannot be relevant, as the general premise is that the system has to be pumped (for reasons explained elsewhere in this thread).

That means that the significant difference between the order of the panels is which order results in lower thermal losses from the plates to the environment - which I can't see mentioned at all in ##3 or 95, let alone discussed

Guest

I wrote a reply, after thinking about your comments about heat losses, but decided to bring up something else instead.

You speak of comparative heat losses from the two pipes, and how that would affect the preferred direction of artificial pumping through the series. Seems to me--and we're speaking, if you permit, of a system designed for maximum overall net efficiency--that under any such conditions in which there could be losses--in which the heat collector/transfer pipes could act as as emitters (such conditions as: greatly reduced insolation [clouds, lowering sky, or nighttime], or frigid weather)--would also be times in which there would/could be no pumping (and the checking of any passive pumping), and consequently no flow, at all, through the pipes. The end user would be compelled to rely on stored hot water and other energy inputs as needed...since it would make no sense (at such times) to pump and transfer heat out of the domestic hot water reserve. I would assume that most sytems incorporate sensors & valving to ensure that pumping & and solar driven circulation only occurs when there is a net surplus of insolation and ambient/captured heat, sufficient to maintain "positive" heat transfer, thereby rendering immaterial any issue of heat losses as it affects pipe series arrangement.

If this is the case, seems to me then that the challenge begs us to focus solely on the mechanical properties (all solar and ambient inputs being equal) of the two pipes. The longer pipe will (up to the limit dictated by surroundings) transfer a greater quantity of heat, but will resist flow of the heated fluid at a rough ratio of 13/9 (its number of turns) when compared to the companion pipe. The pipe in Panel A, on the other hand, will transfer less heat, but will resist flow within it at a ratio of 9/13 compared to Panel B. So the calculation needed, it would seem, it to determine how this interaction would operate in a largely undefined, artificially pumped system.

I am inclined to think that no arrangement would be better than the other--and, to an extent, for the same rationales mentioned before in respect of a passively-pumped system (where, because the solar exchange unit is (might be) situated lower than the domestic water-heating exchanger, the system if "pumped" by the sun as well as by water consumer's utility-main or domestic-well-reserve head. Intuitively, if compelled to make a selection between Panel A and Panel B, I might conclude that the more productive heat transferer, Panel B with its 13 longer-pipe bends, should be closer (up stream of) to the domestic water tank--this in spite of the reduction in velocity; the easier flowing, Panel A pipe serving, in a staging arrangement if you will, to provided relatively unimpeded, preheated flow into Panel B pipe. But then, if output from Panel B to the in-house water reserve is relatively slower flowing (than its input from A), there would be more heat loss enroute to the water tank's heat exchanger input. Okay, so you say, that pipe could be insulated. Then what about this?

Nowhere is it stated whether the artificial pumping is to be from the solar exchangers (by suction, say) or to the solar exchangers (by impelling, say). Given all this, I remain unconvinced--as much as I would like to be--that any overall advantage, of flow or heat exchange, would be realized by a particular ordering to the pipe sections. Since the sytem is pumped, the pump will govern.

If this is incorrect, I would expect that any distinction between the two possible panel arrangements will occur only at the margins at which one panel's pipe might begin to lose effectiveness, relative to the other, at "avoiding" negative heat transfer. But, as said initially, couldn't the pumping operation be calibrated to avoid any such marginal situation?

What do you think?

And, while I'm here, I do not disagree with other posters points about hands-on and theoretical experience. So the intended insult is well taken.

When storing heat, you want to minimise the losses. In order for solar panels to work, they have to have large area and reasonable radiative efficiency (=black paint). Even multiple glass layers do not totally stop infra-red radiation, so the solar panels have large areas that is poorly insulated - the last place you'd wish to put the heat if you want to store it. The result is that (in principle) the pump is only turned on when the sun has heated the water in the panels by enough to make up for the cooler water in the interconnecting pipes, and is switched off whenever the water entering the tank is no longer hotter than the water in the tank. In reality, systems generally allow some margin beyond these theoretical limits.

Assuming you are looking to reduce heat loss from the stored water by "diluting" the heat, you need all the storage areas to be at least as well insulated as your tank, and maximise the ratio of volume to surface area. So far as I can see, the closest you'd get to that is to mix the water within the storage tank (because at least you are not increasing the horizontal component of the surface area). But I don't know of any system that does this.

I'm probably agreeing with you here - this is for clarification only: changing the order of the resistances to flow makes no difference to the total resistance. However, from that aspect, the viscosity of water does reduce with increasing temperature, so you would want to have the water hot as early as possible. Whether this effect is significant is open to doubt; this is another area where running the panels in parallel is clearly preferable.

Assuming reasonable insulation for the connecting pipes, it is better to transfer as much of the heat in the panels to the water as is practical - even though this increases the losses from the piping. The reason is that even with minimal lagging on the pipes, we cannot make the panels nearly as well insulated as the pipes - so cooling the panel gives more benefit than not-heating the pipes.

I can't see a basic importance in the location of the pump in the circulatory system - it sets the flow rate and direction. It obviously has secondary effects, but these are both small and uncertain. The pump has a relatively large surface area, and so will be thermally lossy; from that aspect, you would want to put it in the coolest place, before the solar panels. On the other hand, pumps are not 100% efficient, so it will generate heat - and you don't want to start losing that from the panels. That makes this impossible to decide; as it was not part of the question, we can ignored it - all the questioner is concerned with is the order of the flow through the panels.

It seems to me that the only way to analyse this is on the basis of the losses to the environment. The radiant heat from the sun must go somewhere - it either ends up in the tank or in the general environment. On that basis, what we need to do is minimise the losses - and because the loss grows supralinearly with increasing temperature, losses are lower if the temperatures are kept close together. That corresponds to putting panel A first - which also reduces the pumping resistance.

Having said that, the thermal effect is entirely marginal - a decently designed panel contributes more than half its heat to the water. However, for the case described by Del the Cat, the temperature difference between the panel and the water is very large compared with the temperature difference between the panels. So the thermal flow to the water will only change relatively slowly as you change the temperature of the water - and so will the temperature of the panel, which determines the losses. If it is more than 0.1%, I'd be most surprised.

Engineering prowess aside, you certainly get top score for elegant English. What a good read!

You write like a politician, longwinded & saying nothing. I am not a "Engineer" but a mechanic, pipe welder, pipe fitter, millwright, instrument fitter etc. at the supertendant level. I have 40 or more years experence in the field, and what I have read on this question of the panels only reinforces my opinion of "Engineers", which is that they should never be allowed to put pen on paper without 5 or more years experience in the field. Sorry guys, but a lot of my time in the field has been argueing with "Engineers" I use the term loosely, trying to convince them that what they have drawn & what will actually work is very different.

My experence has been with power plants, both fossel fuel & nuclear, chemical plants, clean plants such as for IC's etc.

That said, I would put the "A" panel before "B". It seems logical to me that the more heating area there is, the hotter the water. Besides, in the early 80's when the Gov. was giving a tax credit of $5,000.00 for installing solor panels, I owned a company that did just, installed solor panels & whole house hot water heat. This question never came up, but when I had different size panels, the larger ones alwas went on the down stream end.

Poundkatt

Hi Poundkatt ,

I've got huge respect for hands on people , but I'm puzzled by the last paragraph - You go from 'It seems logical to me...' to ' ...the larger one always went on the down stream end'. I may have missed something , but do you know this is the solution by having plumbed in a system both ways around to see ? I've been chewing my tongue off to hear from somebody who has done so . Some time later this year I intend to build a similar system. I am tempted to make it such that I can turn round 2 panels in order to quantify the difference - I suspect it will not be much , but curiosity is probably going to compel me to do it this way now.

Kris

Why not do it the best way in the first place, and plumb the panels in parallel? You'll want balancing valves to optimise the flow. At worst, you'll need less pumping force. And unless the flow rate is far more than is needed, you'll also improve the heat extraction.

I'll be considering all options , but this problem has made me want to know as fact it's answer. Even with a dirt cheap fun setup this particular question could be tested (so I can observe any lessons before making a serious system). Look back here in 6 months !

Given the nonrepeatability of the environment, I'm curious as to how you will be abe to make comparisons between the different arrangements. (Especially given that initial effects are often in the reverse direction to longer term ones)

Fyz

______________

Caveat experimentor

I'm going to run a test rig when we have reasonably stable weather (it happens occasionally). The thing will get rotated 180⁰ each day. It won't be plumbed into a central heating system , just through some kind of hot storage tank. I'll flush and run it from 'cold' each day. I think I can take reasonable heat averages over 10 days. I'm not looking for exactitude (I don't think there's any significant difference with 2 panels such as Del has). I simply have a compulsion to see by experiment ! I may make a number of panels so I can experiment with different configurations. With appropriate construction I can utilize them in a final working design.

If you are enjoying a quiet summer you could do some calculations (just scavenge loads of 'typical' values off the web ). How long does a system take to pay for itself . What is the carbon cost of building a system , and how long is the payback time for carbon compared to carbon emissions for a house heated by electricity or gas. To simplify things , ignore the financial and carbon cost of pumping water through the mains to my house. There are an awful lot of variables involved I know , but it may be an entertaining exercise. I will look back here for the analysis and it's updates every month starting , oh , I don't know , sometime next year .

Relax Fyz , I'm just being my normal silly self !. I shall probably come running for your help when some anomaly baffles me.

Hey , I just noticed the math evaluation ! No matter , I'm still going to check. 2 % could mount up.

Really! The best way? Where the pumped flow will take the path of least resistance? Where, depending on the unbalanced resistance as between the two zig-zagged pipes, the output of the least resistance will impede output (and heat transfer contribution) from the more resistant? Where, in principal, it is possible to almost totally lose any outflow from, and heat input to the water tank by, the "locked out" pipe?

So much for hands-on, wouldn't you agree?

No! parallel is more plumbing, and a balancing valve...and how do I conveniently tell when the flows are equalised?

But please see my post #165.

thanks

Del

Thanks for response, Del. And even with "balancing" valve, seems to me the effect would be much the same...at the cost of moving parts, lower reliability...etc. And the net result less than the inherent "balancing" to be achieved simply by series connection. Anyway, about your derivation...

"Let average temperature of water in the 1^st panel = T

"Let the average temperature of water in the 2^nd panel = T+4

"Efficiency is proportional to number of copper tube zigzags"

How did you decide on T + 4 for the second assumption? And what means, "average" temperature in a particular panel (tube)? Average over time...absolute or only while motor runs? Median between extremes...from pump start to pump cutoff? Can you clarify?

How are you defining efficiency (in what context or sense) in the application? The zig-zag numbers seem most related to bend counts, hence to flow resistance in the pipes. Flow rate being equal, except to the degree of cumulative resistance imposed at any bends, in the otherwise equally flowing tubes. Does this mean that overall net system efficiency is dictated--at least for the most part--by net velocity (i.e., average throughput velocity) of the flow? If this is so, would it be correct to say that the best overall efficiency is by the tube/plate arrangement that maximizes pump output to a point approaching its design capacity? Hope this makes the sense intended. Or, couldn't system efficiency optimization instead be gained by a flow rate, less than maximum, that minimizes pump starts and stops?

Another thing I find myself wondering: if heating degree day statistics, for a particular locale, could be incorporated into your derivation (the generalized parts) to come up with a formula for predicting (say) the return that could be realized by installing solar heating in various locations. For example, by using solar-degree-day historical averages to determine the k factor to be substituted? Just curious. Thanks for a thought- (and humiliation- ) provoking challenge submission.

Cheers,

I'll try and reply!

I tend to use simplicity as a watchword in design, so forgive if I over simplify, but I prefer this to 'overthink' !

The T+4 is, I admit just plain wrong...but it is an assumption to allow me to do some maths without having another wretched variable (damn those pesky variables) I think that if we assume T+3 or T+5 we will get the same result.(And the temperature between the 2 panels will be somewhere between T and T+8 unless I have a stupidly low flow rate or there is a local suspension of the laws of physics...maybe a small cloud over panel B?)

The basic point is the first panel will have a greater differential temperature between it's water and panel surface, and that is what makes the difference, and that is why we want the most efficient panel first to reap the benefit of this fact.

On the zig zag theme, It is just a convenient way of describing the tube layout, each hrizontal(ish) run is about the same length and the bends are similar radius. (maybe zag-zigs would be better than zig zags? lol), so I think there is some overthink there. OK the resistance in B is more than A but the overall resistance is always the same regardless of their order!

Again...the efficiency...it's just self evident that the efficiency of heat transfer will be in some way proportional to the length of tube (eg number of zigzags). As long as we don't go to outrageous limits.... eg 1 zigzag compared with 35 !

The whole steady state arguments discussed by John77 & Physicist...well let's just not go there too far, lol!

I did try and take measurements but as I said before you'd need at least 3 temperature sensors and a data logger! But I do believe that on a perfectly clear day, as soon as the output was 8degrees above the inpuput, the two would slowly rise together in a pseudo-steady state., again with the usual disclaimer about a sensible flow rate. * (Please tell me when this clear day is due and I'll go and play golf).

It would be fun to data log it and have an experiment (as Kriss is planning)...but the next project looms (and the decorating D'oh!).

Meanwhile I shall enjoy a free hot shower when the sun is out!

Bear in mind I don't like maths..I prefer the emipirical...I see maths a a usefull tool for getting you into the right order of magnitude! So I reserve the right to be wrong!

Anyone care to try the maths of a longbow or boomerang? (I thought not!)

* I think this illustrates that any system needs tuning to optimum performance, or pu another way, poor adjustment can render the best system inefficent!?

Blimey Guv' enough for now.

Regards

Del

My brain hurts..

I just re-read your (excellent) post...

Flow rate:-

The pump has 3 speeds, (just a regular central heating pump) I adjusted it for a reasonable steady pump on/off cycle consitent with minimum current consumption. So I've erred towards slow without too many stop/starts. Theoretically I believe maximum mass flow rate gives maximum energy transfer...but hey who takes any notice of theory?

I shall have my life's work cut out now re-reading all these posts....or maybe I should get back to my work (whoops!)

Del

Del,

Thanks for the clarifications. I have a rejoinder which you might find useful but let's wait a while to give your brain some rest time--mine, too. Okay? Okay. ...later.

You have beautifully described the reason for a balancing valve to slow the flow through the shorter pipe. You wouldn't need a valve for the longer one, so the total resistance to flow will be lower.

Point well taken. Possibly, balance valve is an inapt, and somewhat misleading, nomenclature; a better one might be counterbalance valve (at the [exchanger] system level) or, compensator or counter-compensator valve (at the subsystem] level...for the flow control valve (at component level). So guest's point is valid, provided that system &or practical constraints (exchanger "module" availability, space & fit considerations) dictate the use of an intermediating valve. Others would be equally correct that, absent such constraints, or where retrofit would impose undue burden, the simpler, more reliable flowpath would avoid the use of valving (itself also imposing negative flow resistance trade-off) where practicable. And both together (I venture to say) would probably agree that the "best way" would design match a single exchanger unit to the demand and avoid the joining of dissimilar exchanger modules altogether(?).

Thanks, guest, for the counterpoint (I think) reply.

Hi Kris,

I've often wondered if anyone ever actually reads what I write, & you've answered that question. Thanks.

I said logical because that is what is life is when you only have a 9th grade education. You use logic instead of books. Some times you're right, a lot of the times you're wrong, but logic is based on experence, and believe me when I say I have had experence in a lot of different trades. Once I learn a trade I've always moved on to something new. Thats what life is, a learning experence.

OK, now to answer your why downstream question. The best I can recall, it was because the manufacturer recommended it. It's called CYA, if it screws up its his fault for recommending it be installed that way.

Until next time. Have a good Day!

Poundkatt

Hi again Pounkatt.

That's all totally cool . Some of the best stuff I've ever read is by people who haven't gone OTT in the educational mincer. The system can leave a person with their head shoved up their own **** ! The best graduate engineers are the ones who keep a really hands on approach. A mate once described education from 5 to 21 years old thus : 'We start off knowing nothing about a lot , and end up knowing a lot about nothing' (expletives altered !) . You seem to have the practical knowledge which everybody should aim for . There's little point in learning masses of theory if you don't know your way around a tool box. Sadly Universities don't give much time to this , and don't give students much free time to learn the practical skills. The majority of CR4 users are practical people , which is what makes it such a good site.

Kris

In case you didn't know, politicians don't write. Others write for them.

Spoken like a true politician, pass the buck, I didn't say that, etc.

Poundkatt

i think you're right.

These two systems are in serial type. What ever you do (a-b or b-a), the result will be always the same. The fact is the lengh of the copper tube.

Ok, I hate heat transfer but I'm a sucker for a challenge so here goes.

Assumption 1:

The tube is installed inside a vacuum within the frame. iow-no convection

Assumption 2:

Both pipes are installed from the start.

For the first case we also assume the tube walls to be of negligible thickness. iow- no conduction exchange through the metal and also no additional resistance to heat transfer.

With the sun being as far as it is, both panels will be radiated with an even amount of energy per unit area. However, because panel B has a larger area, more energy will be transferred to it than Panel A.

In a steady state heat transfer situation it wouldn't matter which way round A and B are because there arent any real losses. The energy added from raadiation should be additive throughout the entire pipe and therefore shouldn't differ one way or the other.

If however, we have real thick copper tubing (left over from some 1930's plumming job done in the house) we have to include conduction losses in energy. Again assuming that a fixed amount of energy is being transferred from the sun to the pipes via radiation, we have an area of high temperature on the black surface. Where the cold water enters, the gradient is high and the heat transfer fast and efficient. As the water heats, the gradient gets smaller and therefore also the resistance to the heat transfer gets higher. This happens until no more heat can be added and equilibrium is reached. This equilibrium will be reached after a set distance through the pipes and with the piping being in series, it doesn't really matter in which panel equilibrium is reached or whether it is reached at all, the exit temperature should be the same.

Ok that was my reasoning... for anybody who doesn't want to read my rambling I think I've concluded that it doesn't matter (all that for nothing eh??).

Note. I assumed convection to be negligible but If it isn't, the airflow in ambient conditions should be at a lower temperature than the water flowing through the pipes which would lower the outside pipe temperature and also the temperature gradient through the pipe diameter. This would propably just cause equilibrium to be reached sooner and at a lower temperature.

Now while were on the subject of heat... can somebody send some down to South-Africa? Because we're freezing down here.

Did I miss something, or are you adding things like a vacum!!! where did they say it was inside a vacum am I going blind ?

A first, then B. This way you have higher differential temperatures in the A aluminium (sorry UK English) panel.

Del, Is this more efficient than an 11/11 split?

Randall,

Why on earth are you apologising for using "UK" English. UK English is the only English, everything else is a dialect.

Apologies for the off topic comment!

Al

B first then A. B has more piping which will extract more heat thus the inside cabinet temp will be lower. A's temp will remain higher so it will be able to raise the temp higher. Some what like a high pressure piston compressor, the larger cylinder feeds the smaller which results in high pressure.

68torino

I concur with this concept. The panel with the lowest heat loss (smaller amount of coils) will be hottest inside and should be last in line so the exit water will be hottest if this is the desired result.

I agree (#7), in a gravity system it's necessary.

Maximum heat extraction is the desired result - which means minimum loss to ambient. You get hotter water initially (when the pump starts) with A second - but not if the pump is running for any time.

Finally someone with a simple answer that put my thoughts into words perfectly! After 20+ years working in the engineering field with little more than an associates degree (which I now deeply regret) Ive developed a creative ability much greater than most, but I certainly lack the "numbers side".

But frankly if I had to choose between being very creative verses "book learned" (sorry I just couldn't help it) I'd definitely choose the creative side. I've just met way to many college educated engineers who couldn't design their way out of a wet paper box no matter how much time you gave them. Plus I can always have those types double check my creative designs verses the other way around.

But man what I could have been had I learned even more in college.

Jim T

STL, MO

Finally? Post #7. Intuitively nice, but unfortunately that doesn't make it right. Oh, and before you say "damned theoreticians" you are almost certainly using at least one of my designs (or rather, its successors) at this very moment. (Probably as well as another design I would have killed at birth had I the power)

Since the area of the two panels is identical it is also considered that they are exposed to the same amount of heat. The copper tubing in Panel A has less zigzag and therefore shorter than the tubing in panel B. With the same heat energy in both panels the lesser water in panel A will heat up faster than the water in panel B. The sequence I can see from the process is from cold water, to warm water, to hot water. I will therefore pump the water to flow through panel B and then panel A for the water will gain more heat from the system.

The two panels will receive the same amount of light energy from the sun, passing through the glass and being absorbed by the black paint. So one might think that they will transfer the same amount of heat to the water and it makes no difference.

Panel B has more copper tubing so it will be more efficient at transferring heat to the water, consequently if all the water is at the same temperature it will heat up more slowly or cool down faster than Panel A. Unless very cold water is being pumped through A first, A will be hotter than B while the system is operating.

Since the amount of heat transferred is proportional to the temperature difference [t(p)-t(w)], integrated over the length of the pipe, and as, for a given water temperature, heat transfer per inch of pipe will be greater in A than B, it is better to start with B as the average temperature difference over the whole pipe will be greater.

At high panel temperatures this will make little difference (and if you want to gently warm the swimming pool in your basement using two solar panels, then integrating the function over time will produce a different answer).

The noticeable difference comes when the panel B temperature and the water temperature are close to each other (which happens at least twice every day except on cloudy days in the depths of winter). Then pumping through B first followed by A collects heat from both of them whereas pumping through A first draws no heat from B as the temperature difference is nil or negligible. So pumping through B first is better.

The panels, as it has been said, will reach an equilibrium temperature where the heat gained from the sun equals the sum of the heat transferred to the water and the heat losses from the panels. Since B panel has more tubing contact it more efficiently transfers heat to the water than does the A panel - i.e. A panel needs a higher differential temperature between the water and the panel for the same heat transfer to occur. A panel will be more effective in transferring the heat to the water as opposed to its surroundings if it is receiving cooler water. (I doubt we are talking about a vacuum insulated system here.) My vote would be A first, B second. The real key though, I think, is to pump the water through quickly enough to minimize the temperature rise per pass through the panels for the heat gain available regardless of A first or B first.

Pumping the water through quickly enough to minimise the temperature gain per pass would increase the rate of heat transferred from the panels to the water but would defeat the primary object of using the panels, which is to reduce the waste and expense caused by using fossil fuel to heat domestic water. The pump would be doing so much work that (given the lousy efficiency ratings of the average power station in converting heat into electric power and the transmission losses) the total energy consumed would be greater than if you just used an efficient gas boiler.

The panels do lose heat to their surroundings, mostly through heat conducted to air by the glass and then convected away, but the choice of whether to pump through A first or B first will have very little impact on this (the more efficient system which transfers more heat to the water will reduce the average temperature and so the heat loss to surroundings, but the difference is pretty small).

(the more efficient system which transfers more heat to the water...

You kinda got the notion here... If the co-efficient of heat transfer, for this particular Panel design, is more efficient at 39° then it is at 40° {I'm guessing yes based on a greater density of water at the lower Temperature} then the Panel with greater efficiency [13z-z?] should be inline first to maximize the non-linearily 'better' efforts it is capable of at the lower temperature. [I have a team of nerds, err, ahh, engineers working of this question as we speak...]

However, this is wrong too. The original question is whether Panel A will precede Panel B. Of Course it will! But not based on fact or science but rather on the Rules of Technical Writing; for, the Technical Writer will ensure that it is so. To see proof, RTFM! The label 'Panel A' will always precede the label 'Panel B'. Should any engineers show "better if B 1st"; then the Writer will exercise his prerogative to rename the panels.

=-==

Dang I'm good, two correct answers in one!

=-==
Such certainty; such folly. I feel sorry for your nerds - if they get this right they will probably be fired for disagreeing with the boss.

Who cares, the difference has to be minimal? Just get them installed as fast as possible to start reducing fossil fuel consumption ASAP. Then put detailed plans on the internet using readily obtainable materials so that others can duplicate your noble efforts.

Thanks!...but

I got the design off the internet in the first place, modified slightly to use scrap materials which were to hand !

And I did plumb them up ASAP....they work fine...solar hot water feels so much nicer in the shower than the regular expensive stuff!

I was just intrigued by the question in case I was wasting some potential extra efficiency!

solar hot water feels so much nicer in the shower than the regular expensive stuff!

Just remember to check the water temperature and adjust the mixer before standing under the shower - mine's up to 64C already!

I agree with some of the responses. Here is my way of looking at it without the math.

1. Both panels side by side with the same flow (and temperature) in will heat the water to different outlet temperatures.
2. If you repeat this at a two temperatures, one "cool case" and "one hot case" the results would suggest the higher the temperature on incoming water ( the closer to the heating temp) the bigger the spread between the two collectors inlet and outlet.

To take advantage of the "spread" the longer collector would be last.

This would imply that by putting A (small) collector first is better by the spread.

Not to confuse things but The same would apply if the tubes were the same length and the second has more turns, the extra turbulance would provide better heat transfer at certain flow regimes and product the same effect.

Sorry for the spelling errors, and for repeating what others have said with more math.

Hi folks,

Here's a simple approach and I'm counting on the following to be true:

1. Both panels receive the same amount of sun energy (1 m square panels).

2. The water flowing through A is at the same rate as flowing through B (series).

3. It is not a closed system (shower).

3. It is just that the water flowing through B is exposed to the sun's energy 4/13 longer (hotter).

I liken this to having a 9 volt battery and a 13 volt battery in series; in which case it shouldn't matter whether A before B or B before A if one is interested in the total produced of 22 volts (or of 22 zigzags).

Unless:

Someone wants to consider that if A placed before B the hotter water in B will experience greater expansion to an open end and create a lower pressure on A assisting in the flow and the heat transfer. Also, shouldn't it help that A's water preheats B's water from an efficiency standpoint?

I've ventured way passed my capabilities, so, my conclusion: Doesn't matter . . . unless . . .

In a steady-state environment, the two graphs of water temperature would asymptotically converge, but it does matter because we in the UK are never in a steady state as regards weather.

You have to think in terms of multi-dimensional vector spaces if you want to do the maths (and it is boring as well). There is a minor advantage in that the water heats up quicker if you pump it through B before A, but the significant difference is that about 4 or 5 o'clock (depending on season) one option fails to collect any heat from panel B.

I spent a couple of Fall weeks in Swansea, Wales some 15 years ago and the weather was fairly predictable. Blustery and gray. Not much sun. There was no "steady state at Heathrow either. Hope to return to UK for pleasure next year as a tourist.

I normally try not to think "in terms of multi-dimensional vector spaces" - not even to impress at the bar/pub.

That just would not impress in a bar/pub full stop. Not in West Yorkshire anyway

Al

Hi Al,

Ah so, a man with experience! I agree so what does, then?

Shorinji

That surely depends on the company your in.

Wouldn't know - I've never tried it!

I normally try not to think "in terms of multi-dimensional vector spaces" - not even to impress at the bar/pub.

Sorry - on re-reading that sounds horribly pretentious: rest assured that I do my best not to talk maths in the pub - it would drive away the unfortunate landlord's regular customers. Actually, if you strike lucky on the vision, they are a lot easier than the alternatives, e.g. the formulae for electromagnetism include the square root of -1 which is "at right angles to reality": I just couldn't cope with that in the sixth form.

I agree with this conclusion based on the statement in the problem "the panels are plumbed in series". It makes no difference. They both contribute to the end result. Qout = Qa + Qb = Qb + Qa = Qout. This is about as interesting as it gets. Make the discussion interesting and set them in parallel feeding different loads. Should A supply the kitchen or bathroom sink or the shower/bath...

uh, look at the time . . . gotta go . . . chat with ya'll later!

Shorinji

I don't believe it makes any difference. Although the solar collector is physically two units, it dosen't act any differently than one solar collector with 22 loops with the exception of the slight amount of heat loss (if any) occuring when the water travels between the two collectors.

I think this is a matter of transit time of the water over each panel. Heat flows faster when there is a greater temperature differential. So, you would want the longer transit time on the panel with the greatest temperature differential and the shorter transit time on the panel with the lesser temperature differential. That would indicate that cold water flow through B, then A would give the greatest end temp and the greatest calorie absorption. Of course, I am assuming that the water flow is sufficiently slow that the aluminum (American dialect) panels remain at approximately the same temp.

Dave Meador

Maximum heat gain will be acheived if the average input to output temperature is held to a minimum by the arrangement of the piping and the flow rate.

The aluminum backplates will tend to minimize this differential. Keeping both backplates as close as possible in temperature will also keep the input to output temp differential lower. I would therefore put the shorter zig-zag first as it will contribute the least amount of heat gain. The longer tube wll then have a longer time period to acheive the highest heat gain.

The two panels are separate, so heat is not conducted directly between panels by the aluminium backplates. The question states that each panel is contained in a hardwood frame.

Your suggestion might work if a conductor, well-insulated from the environment, was added to connect the two aluminium backplates; however the benefits might be outweighed by the loss of heat to the environment.

To improve efficiency a heat exchanger could be installed between input and output also parallel piping the two sections would keep the average input/output temperature lower. A wind powered pump/heater could be added but these are not part of the question.

I have a question based on this series of actions;

1. The frames are placed close up (tightly) to each other.

2. A hole is drilled between the 2 frames.

3. The hole is enlarged to a slot.

4. the slot is enlarged to create 1 big frame.

At what point do the 2 separate frames behave differently to 1 single frame ?

The tube diameter is not given , so we don't know if one frame has a closely zigzagged tube. The only question is do you want to pre-heat 9 zigs or 13.

I've no idea , but I will re-instate my continuing Kelvin quotes .

It makes no difference as long as both the pipes in A and B are both in equal sunlight, same ambient temp and of the same I.D. If one has a larger I.D., hence cross sectional area, that one should go first to minimize head loss due to friction thereby reducing pump size required.

A then B. With equal rates of insolation, the average distance heat has to move from a spot on the panel's surface to the tube is lower on panel B. Therefore, the thermal gradient can be lower for an equal rate of heat transfer. The incoming fluid has the greatest delta-T, which drops as it picks up heat. You may get a net larger amount of thermal energy from panel A with it being first, but the final fluid temperature will be higher with panel B last.

Assuming that both panels are within their capability; that is, neither the 9 nor the 13 zigzags can exhaust the heat supply of their respective panels, then, joined together, we could assume them to be as one panel; admittedly with the 13 zigzags of panel B capable of extracting more heat with its extra contact than the 9 in panel A.

That is, there could be a greater heat extraction from B then A. However, as we pre-determined they are both acting within their heating capability, and as acting as "one" panel for the flow of water, it should make no difference to the final temperature of the water which ever was placed first, before the other.

( I know nothing about plumbing or heat extraction and this is simply a "guess" on my part. - but I enjoyed the question, thank you.) jt@swopzone.com

It's better to run them parallel, and run the dual tubing into a mnifold tubing of the same cross sectional area, equal to that of the combined two. This will minimize heat loss, and utilize more efficiency from the pump.

I suspect there's a lot of people out there who shouldn't shop for best value in solar panels....
The efficiency of the collector is related to ( among other things ) thermal losses in collector plate. When light hits the plate it is absorbed, and heats the plate. The plate has to transfer this heat through to the pipe. The further the heat has to travel to the pipe the greater the heat losses. Panel 'B' has more pipe on the collector, so will be more efficient at transfering the heat. The amount of heat absorbed is dependant on the temperature DIFFERENCE between the water and the panel. The best gain will come from having the best panel fed with the coldest water... so 'B' first. The 'A' panel will still collect more usefull heat, but because the pipe is shorter will radiate less heat from between the pipes. Go 'B' then'A'
That's a perspective from a New Zealander, and here in Napier there are 2245 hours of bright sunshine a year.

"I spel like I tipe - fast with a lot of misktaes."

Doesn't matter - for all the "if you bolt them together they become one panel" reasons. The parallel results would be interesting (longer one should get hotter, assuming heat input is high enough & weather reasonable stable)

<how the **** is Blaine going to use a solar water heater?!>

Think about this: The heat loss or tranference is directly proportional to the surface area, inversely to the volume. The larger manifold tube will have the same volume per inch of length as the smaller two combined, yet a smaller surface area of tubing for transference of heat, smaller heat loss.

2 - 1/4 inch tubes A=1.57 square inch cross section, surface area = 1.57 sq.in. per in. lenth, to obtain the same cross section, one would need a .35 inch tube, has the same volume, as the two, yet only 70%, of the surface area of tubing at 1.1sq.in. per in. in legth, thereby less heat loss.

English Rose,

Glad to see that you went back to using a blue rose as your avatar.

Can we connect our brains in series to get more philosophy output?

OK. Assuming (first approximation) the linear transfer of the heat from he sun radiation (the same energy on the both panels) and neglected change in water (medium) density there is no difference how we connect panels: A > B or B > A.

But.....

If we start to count on non-linearities..... do another Ph D

Let go to traditional engineering way: test first connection > measure output note efficiency factor (out/in) then reverse connection > measure.. note efficiency > compare and ....voila, the winner is: ..............

Surely It's as simple as Temperture Rise equals Energy input divided by flow. This would mean that it matter not a jot which comes first.

"Surely It's as simple as Temperture Rise equals Energy input divided by flow."

Ah So, you forgot delta-tee.

Panel B will preheat the water to the extent allowable by the inlet temperature, flow rate, solar input to the panel etc.

Panel A will absorb almost as much solar energy as the first but it will reach a higher temperature due to less heat transfer area to the water flow, and output temperature from the two panels will be higher than if the flow were through A to B to output.

B then A to take advantage of the greater pressure drop first and then the slower water should heat up more going through A because it will have greater apportunity to pick up heat..

"B then A to take advantage of the greater pressure drop first and then the slower water should heat up more going through A because it will have greater apportunity to pick up heat.."

The piping being in series the rate of flow is the same in both panels.

The flow rate for both panels connected in series is the same measured in grams per second but not in cubic meters per second because of different temperatures in each panels. Question: Is temperature linear function of the distance from the inlet? Can we mathematically integrate this function (if it is unknown)?

Temperature @ inlet of first panel (cold water) = T1, temp @ outlet of first panel = temp @ inlet of second panel (assumption # 2) = T2, temp @ the outlet of the second panel (the one we are interested of, or a heat accumulated?) = T3

Any of two connections (if assuming linearity = assume.#1) will vary only in value of T2.

Isn't density change a little bit pedantic here ? Still it's a fun addition to the problem. All Challenge Questions should be analysed ruthlessly - I have been puzzling over pressure loss due to friction in the frame with more zigzags.

As I sit here reading all the responces, it makes me think of a saying a company I had worked for in the past has. K.I.S.S. keep it simple stupid.

now for the question. Keep in mind about the incoming water temp. if you go to "A" first, to have it as a preheater. With only 9 zigzags, you will not gain max heat exchange within the box. less overall surface for the water to be able to gain the max temp gain. So now with warmer water going into box "B", you will have a higher max heat exchange with 13 zigzags, more surface that the water is in contact within the box.

I've seen the same idea done with the hot water tanks in a large house. Worked out cheaper to get the end product (hot water). tank 1 would preheat the very cold water, so when it got to tank 2 it did not have to work as hard to recover faster when the hot water was pulled from it. Also, less shock on the heating elements in tank 2 from not having cold water hitting them, and not having to work as hard. Tank 1 is only having to raise the water temp to low warm, thus less temp shock to the entire system. this was done in a all electric home. But, the K.I.S.S. was still in play.

don't read more into a simple question. kiss

I for the most part, just read the comments, but this is one I felt a need to jump in on. now all we have to do is wait for the answer so we can say, I knew it. Good luck to all. tim v sorry for any bad spelling

I agree...

First B then A. B will gather more heat energy as it exposes more mass, and takes time to raise its temperature. Flowing then to A will help to raise the temperature. Analogy is a metal plate and huge rock under the sun. Metal plate raises its temperature higher than Rock but heat stored in roack is higher than plate.

-Kuna

From Bangalore, India

Colder water will absorb greater heat and so will make the shorter coil more efficient when placed first.

The amount of energy collected by each panel is identical. So A->B or B->A makes no difference. The really smart move would be to reconnect them to be in parallel and let them sort out the relatively minor differences in heat transfer rates to the water. The flow through each would be adjusted by the temperature differential between the top and the bottom. The higher the differential the faster the flow. But the total coolant available to heat up is constant. So the if the flow through A increases Bs flow must reduce, Bs coolant will get hotter and its flow will increase and vice versa producing some kind of oscillation which I bet has its own really interesting characteristics.

John

"The amount of energy collected by each panel is identical"

Let's say that each panel is exposed to the same sun energy. I'm not ready toagree that each panel accepts identical energy.

And when in parallel are you saying that flow rates will oscillate between parallel paths? Do we have to worry about damaging harmonics, too?

Let us assume guest meant that the amount of input solar power input is equal for the two panels - that would be correct. On the other hand, the losses to ambient (power not going into the water) will depend on the temperatures of the panels.

The remainder of the description doesn't make sense to me. But the idea of connecting the panels in parallel remains worth investigating. Assuming that we are not relying on turbulence to help with heat flow, it would be the preferred connection if the panels were identical - the water is in contact with the inside of the panels for identical lengths of time (half the distance and half the speed), so the efficiency of heat transfer to the water is unchanged, and this puts the panels at equal temperatures - which should reduce the heat loss to ambient.

As the panels are different, the above description does not apply exactly. Clearly the shorter path through panel A will increase the proportion that flows through A, and reduce the proportion that flows through B. That will improve the heat transfer through A and degrade the transfer through B.

So we have some clear cases - if the lengths were equal, parallel connection would be best.
If they were very different (i.e. very short through A), parallel connection would give very poor performance (small transfer through A because the path is short, poor transfer through B because the exit temperature of the water is high).

A=9:B=13 is probably sufficiently dissimilar that parallel connection would not be a good option - but showing where the limit lies looks to be far more of a challenge than the original question (I suspect we don't actually have sufficient information...)

Volunteers?

Fyz

Thermal energy in the panels is lost through conduction, convection and thermal radiation. The total rate of loss of energy is minimized when the two alluminium panels are kept at the same temperature.

For example according to the Stefan-Boltzmann law the rate of temperature (energy) loss due to black body radiation is proportional to the temperature (in Kelvins) raised to the fourth power. Heat loss due to thermal radiation will thus be minimized when the two panels are kept at the same temperature because (for a fixed average temperature (x+y)/2) x^4 + y^4 is smallest for the case when x = y.

Assumption 1) Over an infinitesimal slice of pipe we assume heat conduction from the alluminium plate through the copper to the water is proportional to the difference in temperature between the water and the alluminum plate (which we assume has almost uniform temperature because alluminium is a very good thermal conductor). Thus, the colder the water flowing through the pipe, the higher the rate of absobtion of heat.

Assumption 2) More zigzaggs over a panel means more heat gets conducted from the alluminium plate to the water.

In order to keep the temperatures of the two panels roughly the same we want to balance out the total heat conduction from the two panels. From the two assumptions above this works best when water flows first through A (bigger temperature difference between cold water and plate but less zigzaggs) and then through B (smaller temperature difference between warm water and plate but more zigzaggs).

I fully agree. Allow me to put it in simpler words:

The collected energy is the same on A >> B or B >> A. So the result differs only by efficiency or: The lowest loss wins.

The lost energy is higher for as higher the temperature is. On A >> B the second panel has a lower temperature as in case B >> A. Therefore A >> B means less loss.

A >> B is the winner.

Does this not lower the efficiency of the second collector by the same amount it raises that of the first?

It does lower the TEMPERATURE by the same amount, so before taking into account the losses the average temperature of the two alluminium panels would be the same regardless of the order.

But the ENERGY LOSS will not balance out the same way because the loss is not merely linearly proportional to temperature (in the thermal radiation case it's proportional to T^4).

Therefore, taking into account thermal radiation and other losses (such as conduction to air or objects other than the copper pipes) in the B >> A configuration the reduced loss in the first panel will not make up for the more dramatically increased loss in the second panel.

Eon
South Africa

Well done Eon! ;)

What is x, y? No description

Sorry about that. x and y are the temperatures of the two respective panels.

Something else to keep in mind that I want to add is this: if you had only one panel which had no losses other than conduction to the water (which is impossible, but consider it for a while), it would make no difference how many zigzaggs you have or how warm the water is that enters on the one side. Given that rate of heat transfer is proportional to difference in temperature (between the panel and the water at any point) changing these parameters only makes a difference to the temperature at which the panel stabalizes.

Once equilibrium is reached the energy would be conducted away from the panel at the same rate at which it is received from the sun (or else the temperature would still either rise or fall). That is why, in the absence of any losses, order wouldn't matter.

Dropping the assumption of no losses the problem is thus reduced to minimizing the losses as discussed in post #52.

Eon
South Africa

When I first looked at it I thought the amount of square feet (and the proportional amount of sun energy collected) per loop would be the biggest indicator of what's going on.

It's true that overall the two panels have the same area (and thus collect the same total amount of energy) but Panel A has to transfer this energy to the water in a shorter period of time (assuming steady state) so the temp would be higher and thus be the better choice to come after Panel B.