Challenge Questions

This is not only a heat transfer problem but a pumping system problem. As Panel B has more bends it has a higher friction loss through the panel. As friction losses are cumulative, pump first through panel B (13 loops) then through panel A (9 loops). As the temperature of the water increase the friction losses will decrease, hot water is less dense than cold water, therefore as the water heats up the friction losses in the pipe will be lower.

When I think of these rooftop (or wherever) solar heating systems, I wonder why not just use gravity to draw water through the system and let that be the given flow rate. Just make a reservoir of some sort up top that can be filled with a relatively small pump (or two in parallel if you want redundency and lower the duty cycle of each) that can fill the reservoir as fast as it would ever drain. The lower operating pressure would make the rest of the system last longer. This

Anyone see a problem with this? Seems kind of funny to spend money on powerful pumps and electricity to draw water through a pipe when the goal is to reduce the amount of "purchased energy", whether that cost be in $$ or in environmental factors. I'd like to see a good gravity fed one designed so the flow rate would at least match what is needed for a shower and see what kind of a pump would be needed or it.

Any 'indirect' system circulates the fluid through a loop to indierectly heat the water in the cylinder which the user actually uses.

Any loop must effectively start and finish at the same level, therefore a gravity system can't be used.

A direct system or batch heater type system for a shower can work on gravity...but someone still has to provide the energy to pump the water to the top in the first place! (Usually the utility company)...unless of course you harvest rainwater, in which case the good old current bun (sun, thought I should inject some Cockney Rhyming slang) does the job as well as heating it!

Any loop must effectively start and finish at the same level, therefore a gravity system can't be used.

Well said! And in the closed loop the power is only needed to overcome friction not to lift the fluid from the tank to the roof.

The problem with roof-mounted solar panels is that the hottest point is usually near the top, so there is no head of hot water to drive the convection. Essentially, convection can only work if the heater (solar panel) is below the cooler (storage tank).

You gor it! Spent $$ should be a criterion.

But what about required: Output Temp @ cubic meters of water (demand)? To have a nice shower for two.

One reason for having the storage tank separate from the heating is that it is not very practical to insulate the solar receptors to the extent that they can retain the heat in the absence of sunlight. This requirement is met by separating the solar receptor from the storage, and stopping the water flow whenever the solar receptor is cooler than the stored water. Once you do that, it makes sense to place the hot water storage where it is sheltered from the elements, and therefore relatively cheap to insulate.

A secondary reason is that solar panels are generally placed on roofs, where the sunlight is least likely to be obscured. They will either be set at an angle on a flat roof (except in the tropics), or placed on a sloping roof. As natural convection would require the storage tank to be higher than the solar panel, the issue of support for the storage tank becomes... problematic??

Fyz

Warning: Friction produces heat! So more energy delivered by pumping more will add to heat from Sun

So sorry Guest , I should read all before I post.

Assuming both panels receive the same solar load, the tubing in panel A will carry away less of the heat so therefore it should be hotter than panel B. Therefore the water should be pumped from B to A. B will initially heat the water and A will raise the temperature still higher.

Remember to think about steady state and where the energy is coming from and going to.

If each panel is the same size, made from the same materials and oriented the same way (and no heat is lost to convection or radiation), both coils of tubing will have to carry away the same amount of energy.

Having had solar water heating panels for eight years, I can assure you that the only time when there is a steady state is at night after they have cooled down.

Del the cat asked a real life question, not one asking for an equation that is true for a single microsecond.

Cool...I'll drop the theoretical stuff then and reread your posts. I'd like to set something up to heat my pool but can't decide what sort of system to use. I like the sound of the original post (pipes on black metal behind glass) since I have an old patio door and a 3'x7' window (neither are the new thermal or low-e glass) that I could use for the tops of the boxes. I'll have to go look at some good diagrams on the web and see what'll work be for me.

If the panels are in series, then A (the shorter tube) should be first in the flow stream as it will be more efficient at the higher Delta-T due to the higher thermal resistance form the absorber plate to the fluid in the tube.

Ben Barnett

The first pannel you run through will have the advantage of having an higher temp difference. Each pannel has an potential to give the same energy if the water moved real slow. I would pump it through A first so I could counter the efficency of having fewer pipes with a higher temp difference and go to B second where its higher efficency can still transfer energy efectivly with higher input temps.

total E = [deltaT(A) x efficency(A) + deltaT(B) x efficency(B)] x constant

Like speeds, increasing the slow one helps the average the most. You could use some defferential math to prove.

For my money (although this is a free site) that's the most elegant description so far...

I'm assuming a continuously pumped recirculating system.

If the loss from the panel to the environment depended linearly on the temperature difference, the order of the panels would not matter - at least so far as the solar heating effect is concerned.

There would be a second-order effect on pump power (or on water flow rate) as mentioned in post 60: water viscosity reduces with increasing temperature, so the pump has to work less hard if the water is hotter. Passing the water through A first will heat it in a shorter length of pipe*, so the pump will work less hard with A first.
*This is the reverse order to that suggested in post 60 - that post noted that the water was hotter when it left panel B, but omitted that it went through a longer path to get to that temperature.)

However, although the incoming radiation to the panels doesn't depend on the temperature of the panels, re-emission to the environment does. Radiation increases supra-linearly with increasing temperature, and convection increases supra-linearly with temperature difference. As a result, there will be less re-radiation loss from the two panels if the panels are at similar temperatures - which means that more of the heat remains available for transfer to the water. Cooler water entering the first panel will reduce its temperature more effectively than the preheated water entering the second. So, to equalise the temperatures of the panels, we need to place A first in line, then B.

Thus, on either criterion it is best to pass the water through panel A first (that's quite unusual - mostly different parameters require opposite compromises)

Fyz

I couldn't agree more :D (see post #52). This is one of the most elegant problems I've seen in years.

Eon
South Africa

Fine so far as it goes - but perhaps we should be answering a different question... To minimise water resistance and pumping speed for a given heat transfer efficiency, we should really operate them in parallel and choke the flow through panel A to obtain an optimum. So the different question is "operating in parallel, what is the optimum relationship between the flow rates through A and B". It's soluble if you assume a square-law provides adequate fit for local heat loss - so I'll leave it here for the ambitious
But I'd rather not try to set that up without instrumentation.

Fyz

The panel with 13 zigs should be first.

Why? The additional zigs imply longer tube length. Therefore, this panel has more tube surface area in contact with the aluminum collector than the other panel with fewer zigs in the tube.

By placing this panel first, you get the coldest water (influent into the collector array) in the system in contact with the hottest heat source for the greated amount of time. DIfference in temperature drives heat flow (like voltage drives current), so the combination of heat flow rate and time that this heat flow continued by using the longer tubed collector first.

Water exiting the first collector will be at a higher temperature before entering the smaller collector ( must assume that the same heat flux being collected by each 1-meter-squared aluminum collector), so the temperature difference between the collector panel and the heat sink (the water in the tubes) will be less and less heat will transfer in this heat exchanger/collector. The water will spend less time in this heat exchanger too due to the shorter tube length.

"By placing this panel first, you get the coldest water (influent into the collector array) in the system in contact with the hottest heat source".

In principle, that wouldn't matter either way if the system was linear - but unfortunately it is not even correct. By placing panel B first, you ensure that it is the cooler panel, as it is losing more heat to the water... so you have the water in contact with the cooler panel for longest.

Electrical analogy may only apply in first /rough approximation because heat /temperature /thermal resistance as a functional relation are not LINEAR as electrical ones!

Why are Electrical types so fond of √-1 ?

Mostly because phase is best handled mathematically using complex numbers, and relatively few people are sufficiently sophisticated to handle complex numbers more abstractly - which makes this the least-bad means of communication. (You can blame god if you like)

I have a nice little routine to solve cubic equations . It will churn out non-real roots quite merrily , though I have no use for them myself. I put them in the structure just for the heck of it (as much use to me as a chocolate teapot , but one day I may fall into that Alice in wonderland place of phase.). 'Least-bad' makes my fur crawl ! what a dilema the real world is - that probably explains why my knowledge of Electrics stops ar Radio Shak .

OK, I'll present it all in 3D complex tensors if you prefer. That is as complete as you can go at the present time, compact, and entirely impenetrable for engineering purposes.

Whoops1 - it allows a bit more freedom in numbers of constants than we have data to cope with, but we can find a work around for now

Whoops2 - oh dear, exp(A + B.t + 2.pi.j.F.t) still drops out as soon as we want numerical output, so we still haven't escaped the dreaded imaginaries

Fyz

Save yourself Fyz (and me) . I prefer tangible things I can hit with a hammer (but not Scmidt) or make holes in.

I am good at burying my head in the sand when people start talking imaginary , and will leave it to those who enjoy such.

If you place the 13 panel first, the water will extract more heat from it than from the second panel, both because the water starts colder and because it has a greater length of tubing. As it is receiving the same heat input from the sun, that will make it the cooler heat source.

You will have marginally impoved the transfer from an already good transferer, and degraded the transferer from a poor one.

That is the thermal equivalent of increasing the speed over the half of a route where you can go fast, and slowing down by the same MPH on the slower half - which nearly everyone knows makes the journey take longer.

Sorry, but you've got it upside down. Your analogy is based on the journey time being the important factor and the speed being related to the reciprocal of the time.

What we have here is a system where the transfer fluid spends 13 time units in B and 9 time units in A, irrespective of the temperature (ignoring second order quantities). What we want to do is to maximise heat transfer (heat loss to the environment will be greater if we choose the less efficient set-up). A will always be hotter than B while the system is working (unless you put A in front of B and empty and refill the tank in the middle of the day so that you send some really cold water through A first so that it reduces A's temperature by more than the temperature differential between A and B). The transfer fluid heats up as it passes through the system. The rate of heat transfer to the fluid is proportional to the temperatutre differential between the panel and the fluid. It follows that you will optimise by putting the water through the cooler panel first

For goodness sake try it with simplified equations if you can't handle the full exponential decay. You will find that, in the quasi-steady-state situation being considered, the results are independent of the order - until you include temperture-dependent losses to the environment. Although not stated explicitly, guest indicated that the result depended on a nonlinearity; this is not identical to the inversion nonlinearity in the journey time, but the analogy is good, and guest did correctly show the fallacy of the type of argument used in #75 and repeated in your #162. You have even made the opposing statement to number 75, with indistinguishable logic, and yet you have given the same answer. I know that last time we discussed this, you claimed that the simplified conditions considered by theory didn't correspond to reality, so it didn't matter - but that in no way means that incorrect "theoretical" statements can in any way be helpful.

It's not that you can draw the opposite conclusion from the information you present - it's simply that it is not possible to draw a conclusion either way on the basis of what you present.

As an indication of what you need to do to make a serious argument (simplified, of course, so you don't have to handle the decay part)

Power into A = Poower into B
=> Power out of A = Power out of B
The only question is where it goes. Some goes to the water, and some to the Environment. An indication as to what you need to do:
PEA = (TAin/2+TAout/2-TE)*KE(TA)
PEB = (TBin/2+TBout/2)-TE)*KE(TB)
PWB = (TB-TW)*KWB
PWA = (TA-TW)*KWA
Tout-Tin = PWB*HW + PWA*HW
Now you just need to try both orders of setting and solve for each. You will find the answers are the same provided that KE is independent of temperature. Now put in KE increasing with panel temperature, and you will see why a simple model will show that panel B should go second.

Pump from 'A` to 'B`. Since the water from 'A` is pre-heated at 'B`

there is a benefit in the longer heat transfer time being in the second

stage where the differential temp. is lower.

Since this is a real life situation, I can tell you that your panels are: a) not built right, and b) not plumbed right.

For a) - the copper pipes will eventually break away, if they haven't already, from the aluminum panel. I'm willing to bet that the panels are all copper - if not, then the efficiency is going to be far less than all copper, or all aluminum. I built a set of panels with dissimilar metals (back in the 70's), and, as the tubing pinged off, the efficiency dropped a bunch (80% to 50%).

For b) - the efficiency is greatest where the temperature gradiant is greatest - that is, from the tank of cold water to the first panel. ( It's a Δ^Τ4 thing). In the author's house, the water is heated up in the first panel, and then is passed to the second panel. The temperature rise, and hence the efficiency will be far less in the second panel, no matter which panel is used. It is far better to connect the two panels in parallel with the tank - most solar water controllers shut down the circulation after the tank temperature reaches 120 dgrF (to prevent scalding). What you really want is to heat up the water to a usable temperature as quick as possible (around 100 dgrF, unless you want to burn yourself in the shower), and be able to use the hot water as soon as possible. You won't get as the water as hot, but the water will be heated to a comfortable temperature much sooner. (My current house had panels hooked in series - I switched them to parallel as soon as I could - it does make a difference.)

Don't forget to heavily insulate the pipes and the water tank, plus ensure that you've done something for freezing conditions, such as using drain back or antifreeze with a heat exchanger - you have a lot invested and need this to work for a long time for payback.

Much of what you say is sensible, though you can in principle make a successful system using copper and aluminium if you use appropriate construction (and keep water away from the joins).

However, the law for loss is nothing like deltaT^4 - not even Twater^4-Tambient^4 (T in Kelvin). Assuming that the spacing to the glass is as large as possible without convection, the transfer of heat to the glass sheet will be a mix of thermal conduction through gas (roughly proportional to deltaT*Taverage^1.5), and radiation (the fourth power law - but not of temperature difference). Then there is the loss from the surface of the glass - mainly forced convection, which is more or less linear.

Parallel connection should, as you state, be best for identical panels - but that seems less likely if (as here) the water paths through the panels are very different..

You have lost your bet!

The panels are aluminium, the pipes are copper, both are painted matt black, the pipe is attached with loops of plastic coated galvanised wire twisted tightly at the back of the panel every 4" or so.

I don't have a lot invested as I built and plumbed it all myself as a winter project using scrap timber and glass.

Maybe it is plumbed 'incorrectly' if you want to throw money at it! But it is plumbed 'right' in terms of cost. It is Tee'd into the indirect hot water circuit with some check valves to prevent the central heating warming Essex. The hot water sensor for the central heating is mounted fairly high up the hot water cylinder and to a relatively low temperature, so as to provide some hot water on dull days.

And as for your assertion about cold water entering the panel...a common missconception. The pump starts when there is an 8deg C differential between the output of the panels and the hot water cylinder. So what you tend to get is a pseudo-steady state where the input output differential is relatively constant but the water temperature is slowly rising.

And before you comment about the 'down loop' between the panels, it can be flipped up for ease of draining. And yes, I know the net curtains could do with replacing!

I maybe daft...but I am not stupid.

Looks fine to me - even if parallel connection with equal piping lengths would be marginally superior in theory. I was expecting a tin roof, or at least a Reliant Robin, but you can't have everything. There should be lots of scrap material to be found if what I hear about the deconstruction on the trading estates around Harlow is correct. (At least it doesn't look as if you have one of Sir Fred's much admired flat roofs).

Fyz

Brilliant Del ! I hereby proclaim my Essex roots , that I may bask in your reflected genious .

Del,

Sorry if this is a little off-thread. Take a look at the 2 pics below. Was wondering about this kinda solar heater system...if anyone out there has experience with them. Considering one for the house but not sure...how stacks up against the bigger (pool heater) type units. Also concerned about wind resistance. In some ways it seems it could be more efficient, even with no metal and far smaller "pipes" than the big units we've been talking about.

Anyone?

Hi CowAnon , I think it looks great. What else can I say - it's neat. Not as much fun as self-build from scratch , but it looks like a good solution all the same . Plenty of people would like this solution I'd have thought. Kris

Del,

NIce pic, and may I compliment your handiwork! Just wondering about the glass panes on the, uh, er...shadow boxes. Seems to me that the glass panes could be both beneficial (solar magnification) as well as detrimental (reflective when transmissibility [spelling?] is most needed). Any thoughts? (I'm imagining how, in places like yours where sun stays quite southward, those boxes might be mounted on a, uh, er...capstan, or turntable...and rotated by a timer motor [in particular, a mains-frequency regulated timer] to keep sun and solar receiver at normal incidence angle. The scant mains power consumed might be less that the increased savings heating water?)

Also, is that a single ply roof the units are sitting on? Do you anticipate any problems down the road (or lane ) from the support blocks pressing down, or rain water pooling under, the boxes?

Cheers!

The glass is pretty vital to help prevent re-radiation. Maybe that twinwall polycarbonate sheeting would be better than glass? It would pressumably re-radiate less, and it's certinly lighter and less fragile. (Fortunately I had some old glass from a greenhouse...specially as I broke one pane...D'oh)

I pretty much got the 'recipe' off the web.

If I was doing it again I'd maybe try different things. Mainly I'd get the zig zags the same! And plumb parallel. I'd certainly do it better if I was doing it from scratch...it was very much a 'cheap as possible/ make do with what I've got' project, I only paid for Ali' sheet copper tube, pump and pipe work. A two coil cylinder would be the best so that I could totally isolate the central heating/hot water circuit from the solar one.....but I didn't want an 'n year' payback.

I was thinking about solar tracking. Another simple, cheap idea would be a pop up reflector panel which helps catch the morning sun, by reflecting it back down onto the panels. This would need to drop back after midday to avoid shading the panels.(Windage would be the major problem)

They actually face slightly East of due south and are slightly too vertical, this is a) because the house faces that way! b) To help Spring/Autumn efficiency.

They actually work fine a 'summer only' panels, and got upto a new record of 65C yesterday. Where I am we'd need something much more efficient to get much gain over winter, or when the sun isn't out.

I think that is the main problem with a diy panel compared to those vacuum tube ones. Bottom line with this sort of panel...you can't gett any hotter than the panel!

The flat roof is thick ply covered in EPDM (done last year), the blocks have two layers of lose EPDM sheet between them and the roof to take up any movement, the bocks themselves are not actually attached to the panels, they just have a groove to locate them and prevent them 'walking' out, the load is pretty light and there isn't any pooling there...there is some slight elswhere as the roof has a few slight dips, but it dries v quick. That black EPDM gets v hot, you'd think there would be a way of capturing that heat, however it's not very conductive.

Del.

Thanks for posting the pixs - you do nice work!

I was the person who stated the parallel configuration is superior for hot water, and I stick by my statement. Look, what happens is that, in the early morning, if you used the hot water last night, then the water in the tank is room temperature ~ 65-70 degrF. (Most people with solar tanks use a backup system to provide heated water at night.) In the early morning, if you tried to shower just with the water in the tank, well, you wouldn't. (The saying is - passive solar - active owner - you have to accomodate the sun.) A parallel panel system would warm up that water much faster, since the temperature gradient is greater, and your system is much more efficient converting cool water into warm, useful water. (I built a solar waterbed heater way back in college, and measured all these efficiencies for a solar engineering class.) Remember that the maximum energy from solar is 1000 watts/meter² - it's all downhill from there - a typical electric water heater is areound 4000 watts - you should have a long time to wait before your first shower.

But the main problem is that the tubes are not brazed or welded to the aluminum - that really limits your conductive heat transfer to almost nothing - you are really picking up only convective and radiant heat transfer energy. And, those plastic straps are going to rot in the sun, and the copper tubing will pop off the panels. Anyway, without conductive heating, you're not going to get much heat from these panels, but they'll work better at low temperatures. My present panels were made by Gruman Aircraft in the early 80's - all copper, double circulating, almost 6 meter^s of collector - lots of hot water, except in the early morning.

Ta Guest (go on join, and have a name) good post!

Couple of points/questions.

1. My straps are not plastic they are galavanised steel wire which is plastic coated (got it from a gardening shop) which gives a pretty tight connection as the copper/ali' expands more than the steel...but obviously still a poorish thermal contact.

2. My real question... the serial/parallel agument may be is ok for several panels in series, but surely it's it's more a question of matching the water flow to the panels?

After all, theory states that maximum heat transfer is with maximum flow (and therefore max temperature differential), so if you pump water through the series panels at the right speed you still maintain a high temperature gradient!

It's a bit like one of the posts which said the time the water has got through one panel it will be so hot that it will then be cooling down when it goes through the next!!! If that is the case then turn up the pump speed.

However if you actually MEASURED it back in college (as opposed to being told) I'll take your word for it!

Like all these apparently simple things...there are soooo many variables...I did try taking some measurements, but short of permanently attached sensors and a data logger it is nigh on impossible (especially with the English climate...damn the sun's gone in again)

Derek (the cat)

It's a bit like one of the posts which said the time the water has got through one panel it will be so hot that it will then be cooling down when it goes through the next!!! If that is the case then turn up the pump speed.

I was assuming that your sensor cut in at roughly the same differential as mine (3C), and looking at the position when the panels are cooling in the late afternoon although it could apply if you had heavy cloud after a bright start to the morning.

A has lower thermal capacity than B - I don't know by how much, but to simplify the arithmetic I shall use 20% (and ignore the difference between (302^4/300^4) and 1). So its temperature will rise 10C for each 8C that B rises before the pump starts. It passes onto the water 70% as much heat as B for every 1C temperature difference. When the pump starts A transfers 87.5% as much heat as B, so its net heat gain is greater, so it heats up, initially even faster. [There is no steady state, but if there was A and B would settle when (T(B) -T(W)) was 70% of (T(A) - T(W))]. At peak temperatures, (well before steady state) A and B are noticeable greater than 60C, so T(A)-T(B) would be more than 18C if differential heat loss to the environment had not already started to apply. As T(B) and T(W) approach each other in the afternoon, the ratio of heat transferred from A and B to the water will increase and will exceed unity, so A will cool faster, but it will remain significantly hotter - it will only cool as fast when T(B)-T(W) is 70% or less of T(A)-T(W); if your pump cuts off when (T(B)-T(W))<8C, you'll miss out, if it cuts off when (T(A)-T(W))<8C, then you could have T(A)>T(W)>T(B). There are just too many unknown variables to be positive about this, but with a 3C cut-out it would be difficult to avoid by chance.

At a 3C cut-in/cut-out, with panels colder overnight and a well-lagged tank you could also find that water started circulating when T(A)>T(W)>T(B). Start with T(A)=T(B)=6C overnight and T(W)=20 and T(A)=23 gives T(B) =19.6.

Demonstrates I should not make assumptions.

The argument about pumping through B first to maximise the integral along the length of pipe of [T(B)-T(W)] and [T(A)-T(W)] remains valid.

Ta John,

I have many hours of happy tinkering ahead of me!

Changing the temperature differential is easy (well it should be as I designed it!) I borrowed an old repaired board from a central heating condensate pump that just happens to kick in at about 8 deg C. I shall have a go with that, and maybe turn the pump up a speed! I also need to turn the central heating contribution down to a bare minimum.

Are your panels the evacuated tube type?

It's been a good discussion all round.

Del

Hmm - some good ideas and data, but somehow this doesn't quite get it right:

First, about losing heat to the second panel. If there is no heat loss to the water, the second panel must lose more of its heat to the ambient - which means it must be hotter than the first - so there seems to be no way that it could cool the water, regardless of pump speed - assuming the panels are in similar environments, that is.

Second, the argument about putting B first remains incorrect. If you could join the panels so they were at the same temperature, the order wouldn't matter. If the cooling to ambient was linear, separating them would make no difference to the outgoing temperature. But the heat loss increases faster as the temperature rises - so you will get best results if you can run the panels as near the same temperature as possible. That means putting the colder water into panel A.

Unfortunately, you will find measurements to demonstrate this rather difficult under British conditions

Fyz

There is no steady state while the system is operating (that includes the period between sunrise and the time the pump starts).

As far as I can see, the only time that you get hotter water from placing A second is in the initial phase after the system is first warming up and no water has been flowing. Under those conditions, I agree that you will extract the stored heat quicker if you place A second - and B second could cool the water coming from A. However, that would suggest that the temperature differential between plate and water is quite small, so quasi-equilibrium would be asserted rather rapidly.

So, if you need to warm the water in your storage tank by more than the initial 3-degree differential, you will have to wait long enough that quasi-equilibrium conditions dominate - in which case, pump from top to bottom through the panels and place the "hotter" one first (better still, if you can control the flow rates, place them in parallel and throttle A to ensure adequate flow through B).

I am assuming that heat transfer is proportional to the temperature difference between the copper tube and the transfer fluid and that the heat loss to the environment is an increasing function of the difference between panel temperature and ambient temperature, and that the effect on the change in the viscosity of transfer fluid for a small rise in temperature on the rate of heat transfer is a second-order quantity.

On those assumptions, which do not appear to me to be controversial, heat transfer will be proportional to the integral of T(A)-T(W) and T(B)-T(W) along the length of the pipe. T(W) is not a constant. T(W) increases as the transfer fluid flows across the heat exchanger: if you maximise the initial temperature differential and minimise the final temperature differential, you reduce the average temperature differential. So heat transfer will be maximised by passing the water through the cooler panel first. By maximising the heat transfer to the water, you reduce the average temperature of the panels compared to passing transfer fluid through A first.

You cannot have A cooler than B while the system is operating unless the water in the tank and the transfer fluid are so much hotter than the ambient temperature that the lower thermal capacity of A leads to it cooling faster than B due to losses to the environment while it is transferring 70% or less heat to the transfer fluid than B. Normally this does not occur until after the two panels have stopped heating the water.

After the transfer fluid starts flowing the temperature difference between A and B will increase until 9 times T(A)-T(W) = 13 times T(B) -T(W) or until A starts to cool because the loss of heat to the environment plus the heat transferred to transfer fluid exceeds heat received from the sun.

The example of T(A) being 23 and T(B) being 19.6 is trivial and was just to illustrate a point.

If the system is working, A is hotter than B. Since the transfer fluid heats up as it passes through the panels, the total amount of heat transferred will be a function of the average temperature of the fluid as well as that of the panels and the water in the tank. The average temperature differential will be greater if the fluid passes through B before A, so the heat transferred to the water will be greater and that subsequently lost to the environment will be less.

I cannot see a flaw in that logic: if there is one, what is it?

There will also be a point each afternoon when T(A)>T(W)>T(B), but with an 8C cut-off the system may have switched itself off by then

Incidentally, when I was young "counter-current" heat exchangers meant that the hot and cold liquids were coming in from opposite ends so that the coldest fluid met some that had been cooled and the hottest liquid met some that had already been warmed. Computer simulations supported the common-sense conclusion that these were more efficient that "co-current" heat exchangers, where the coldest fluid met the hottest at a common inlet. So, even apart from his treating the two panels as having insignificant differences, I have to differ from RAMConsult.

John

Some of the time it is clear that you are describing a quasi steady-state condition with continuous flow. This is the state I will address here. I will also assume that both A and B receive equal input radiation, and have the same losses at the same temperatures. I suspect that some of my disagreements are because I don't know what conditions you are describing at any time. What I will assert - categorically - is that whenever the panels are near a steady state (everything warming up gently on a continuous basis, with the pump running), it is better for the water to flow through A before it flows through B. If you agree with that, we have no basis for disagreement.

In case of disagreement, here is a single issue for starters:

You say: "Heat transfer will be maximised by passing water through the cooler panel first".
In the case of a linear system under quasi continuous conditions (i.e. where we can ignore the heat capacity of the plates and of the pipes etc - but not of the water), the total heat transfer is independent of the order of the plates.

the total heat transfer is independent of the order of the plates.

This is clearly a, or the, main point at issue.

The transfer fluid temperature increases as it passes across the panels (otherwise we are all wasting our time installing the panels). So the heat transfer is not solely a function of the input temperature: it is a function of the temperature differential at all points along the flow path which a simple-minded mathematician would express as the integral of T1-T2. A is always hotter than B while the system is working but will approach its nightly low temperature more quickly than B.

we can ignore the heat capacity of the plates and of the pipes etc

I do not. The differential heat capacity is the reason why A heats up faster than B. if you had a hundredweight of aluminium and six ounces of copper tube, it would not matter. However, the question specified aluminium sheet and scrap, hence substantial, copper tube. If I argued about the water/transfer fluid residing in the panel before the pump started , I could claim that A would heat up more than 20% faster than B until the pump started.

When you say "same losses at same temperatures" I assume you mean BTU or Joules, rather than degrees C

If we are to get anywhere, we both need know what set of conditions we are discussing at any one time. If we can totally restrict our view to quasi-continuous conditions first, that gives us a hope of at least talking the same language. Under these conditions, the thermal capacity of the plates and of the pipes is irrelevant. This, and linearity of loss to the environment, are the conditions under which my assertion that order is unimportant becomes relevant. Do you agree that - under the constraints as stated my assertions are correct?

{If possible, I would prefer to avoid posting the maths - because, although it is trivial, it is also uncommonly cumbersome - mainly because of the number of definitions}

I should have said - for steady state analytic purposes, losses are in Watts or B.Th.U/aeon or whatever (yuck). In the transient condition, losses tend to be relatively independent of the order of flow, because most of them occur before the flow starts - unless the flow starts relatively early, in which case they are a "standard" transient excursion on the way to the final average condition - which tends to look a bit like a rise to a limit, with error decaying roughly exponentially to a final value (one exponential time per plate)


Fyz

As I said in 68

Having had solar water heating panels for eight years, I can assure you that the only time when there is a steady state is at night after they have cooled down.

Del the cat asked a real life question, not one asking for an equation that is true for a single microsecond.

I am quite willing to believe that under the conditions that you state, your assertion is correct (i.e. you know more than me about it and I can't see anything wrong with it, only I don't know enough about quasi-continuous physics to produce a proof to support it, although you presumably can).

I did assume, as it was pretty obvious, that you meant losses were in Watts or B.Th.U - just wanted to avoid any risk of further misunderstanding

The trouble is that I don't believe in the steady state or quasi-continuous conditions. The temperatures in my panels tank follow a daily cycle, but differ from day to day.

If the panels were at the same temperature and had the same thermal capacity, then it should not make any difference - but they are not, which is why Del the cat asked the question, and all my analysis starts from there

Of course you don't have absolutely steady-state conditions. That would require unvarying insolation and a continuous steady use of the water.

What I expect is quasi-steady state - where differences in heat flows (Watts) due to the input and output energy of heat (Joules) stored in the thermal capacity of the plate and the copper are small compared with the total heat input (insolation - also Watts).

The whole point of modelling is to fit the real world. For complex problems, you often work up to that by starting with a simplified model and then seeing how much difference the differences between the practical situation and the modelled situation are likely to make. You can't justify assertions simply by saying that none of the models fit. Ideally, you can start with two models that fit at apposite extreme conditions, and modify each and come up with the same results from each version - that is what I would do professionally, but it takes more time than I can devote to an area outside my professional areas of interest.

You say "the situation varies from day to day and from hour to hour". That is what I would expect. I understand you turn the pump on when the temperature difference is 3-degrees. Can you tell me - what is the maximum temperature differential you see for water flowing through the set of panels while the pump is running? If you can also tell me the difference between the temperature of the panel and the temperature of the water (again, while the pump is running), I could at least assess whether you have something approaching the quasi-continuous conditions (according to my simplest model), or how much dynamic variation I would need to include. (For what it is worth, it would also give an idea as to whether the non-linear dependence of losses on the pumping were worth worrying about)

Fyz

If you can also tell me the difference between the temperature of the panel and the temperature of the water (again, while the pump is running),

I just looked at the dials which say, at ten o'clock in the morning, it is 23C. I can't remember the maximum temperature difference I've seen but I am fairly confident that it was between 30C and 40C. The difference between the panels and the water at the bottom of the tank will, of course, be greater.

That is a very substantial difference. I'm not clear which temperature differences you are reporting, however.

If it is the difference between the output water from the second panel and the panel temperature, and the water temperature is rising less than 10-degrees in each passage, the effect of the order on losses to the environment will be quite small.

If it is the rise in the water temperature flowing through the panels, and the difference between output temperature and panel temperature is less than ten degrees, the system is operating under quasi-stationary conditions, and you should definitely place panel A first.

I would comment that, if you base your judgement on the temperature of the water reaching the tank when the sun first reappears, you will always get the impression that it is better to put A second. But, in the absence of heat loss to the environment this would soon balance out. Indeed, if the sun goes in again, the initial difference will be made up as the residual heat is extracted from the panels. If we add in the effect of losses to the environment, putting A second will result in the temperature difference between A and B being greater at all times as compared with putting B second - which means the losses will increase. However, this will not show up as a large change in temperature - it is a continuous small change.

Essentially, the reason that observations can be misleading unless they are adequately detailed and correlated** is that they tend to be weighted towards the peak; but it is the average over time that is important, and in this nonlinear situation the two will inevitably go in opposite directions

**Or they can be carried out on total through the day under similar circumstances - not likely in any part of the UK unless you have cooperative a neighbour with a very similar set-up so you can try alternate reversals.

Fyz

That is a very substantial difference. I'm not clear which temperature differences you are reporting, however.

They are probably not the ones you want to know for designing your model, but it's the data they thought we needed - the temperature of the panel and the temperature at the top of the hot water tank (they also give us the temperature at the bottom of the tank, but not the middle which would be useful if we want to know of there is enough hot water left). I don't have a sensor telling me the temperature of the circulating fluid at entry to and exit from the panel but I presume that it will be little hotter than the water in the middle of the tank at entry and is clearly hotter than the top of the tank at exit: that suggests to me that on a cloudy day when things warm up slowly the temperature rise across the panels is only a few degrees but on a bright sunny morning it is more than 10C.

Thanks. That temperature would probably be what they need to know when to start the pump.

If you are correct about the various temperatures, that would mean the effect of different orders of pumping would be small - but I'd still favour B before A. The other thing it highlights is that you believe that the thermal resistance between pipe and tank-water is vastly lower than between pipe and copper plate, in spite of the (presumably) much greater length of piping in the plates. If that really is true of your professionally constructed system, it raises the question as to whether it would have made sense to include some additional thermally conductive material around the pipes.

Fyz

The other thing it highlights is that you believe that the thermal resistance between pipe and tank-water is vastly lower than between pipe and copper plate, in spite of the (presumably) much greater length of piping in the plates. If that really is true of your professionally constructed system, it raises the question as to whether it would have made sense to include some additional thermally conductive material around the pipes.

Er, no I don't. What I do believe is that the heat-exchanger at my tank starts near the top and exits further down (the reverse would create unwanted turbulence) and that the heating up of the water at the top of the tank is because the transfer fluid is hotter than the water and that the transfer fluid cools down but passes some more heat to the water lower down the tank before flowing back to the panels to gather more heat. I do not know what length of pipe is in the heat exchanger in the tank and what length is in the panels, nor whether the heat exchanger in the tank continues all the way to the bottom but the bottom of the tank does get hotter while never being as hot as the top and the only plausible explanation is that the transfer fluid enters a heat exchanger at the top of the tank when it is hottest and leaves near the bottom when it is coolest. So I expect the transfer fluid to be a bit hotter than the water lower down the tank when it flows back to the panels.

"bit" is horribly vague because I have no means of measuring it. To suppose that the difference between the temperature at the top of the tank and that at the bottom represented the temperature gain across the panels would require some unreasonable assumptions.

"To suppose that the difference between the temperature at the top of the tank and that at the bottom represented the temperature gain across the panels would require some unreasonable assumptions." If you are referring to the temperatures of the water in the tank, I'd be inclined to agree. Once running, the temperature change of the water running through the pipe should be (approximately) equal and opposite, however.

On the other hand, it would be overkill* to pump so fast that the recirculating water barely changes temperature on the way through the panels (or the tank - those temperature differences should be similar).

*In case of this overkill, the order of flow makes practically no difference anyway...

Fyz

The relative rate of heat extraction can be deduced from the temperatures of the steel plates. If the panels are identical, and you maintain the same total flow rate, then parallel connection will result in identical plate temperatures, and give an advantage. You also have marginally lower resistance for the pump to work against.

The situation with non-matching panels is not as simple - you would need some means to to throttle the flow through panel A - otherwise the reduced flow through panel B would result in the otherwise more efficient panel B becoming starved. If you can adjust the relative flow to its optimum (more through B than through A)**, then parallel connection can always be more efficient than series. Apart from issues of adjustment, if you have adequate flow in the present configuration I doubt it would make much difference. Having said that, if it really made much difference swapping the order of the panels, you might still see some advantage.

**Although the optimum ratio will depend on the non-linearity of the cooling, I suspect that it will be reasonably constant, as a local fit of linear-plus-square law is likely to be good enough for practical purposes

Fyz

Hello Del de Gato -

Sorry, I posted my note before re-reading your posting about the wire - the vinyl will eventually rot, and your tubing will loosen a bit, but not much. I know that copper is pricey, but if you could find some thin copper and braze the tubing to the plate, your system would last far longer, and give you more heat. (I'm sure there are some economic considerations that you factored in - that's the point of experimenting/engineering.)

One additional bonus of parallel pumbing is that the pump will work more efficiently with the larger (and less resistive) effective tubing diameter. (I mean, the point of this experiment is to save money, right? - why use extra electricity to pump water?)

For testing the system efficiency, you might want to shut down the system for a couple of days and let the tank match the ambient temperature of wherever it's stored, then turn it on during a clear day, and see how long the water takes to arrive at certain temperatures (don't use the water for that day, just measure the temperature - take a shower at a friend's house or whatever.) Knowing the delta temperatures, and the volume of water, you should be able to determine the energy that your system acquires. It'd be interesting to see how much time it takes to heat the water up for the first ten dgrF, then the second, then the third, etc....

Lastly, if you do keep the aluminum (it's built and already working), you might think about connecting some air ductwork and heating a room or two during the winter. I have a wall of windows on my house, facing due south, and, with air temperatures of <40 dgrF, my living room temperature approaches 75 dgrF ( We live in New Mexico, so we get lots of sunshine.)

Good luck on your project, and I'll sign up sometime today! Thanks!

When I worked for a company that had a plant in Harlow, we referred to it as "sunny Harlow". This was intended to be ironic, because it seemed to rain (or worse) whenever we visited. That is not quite what the climate tables indicate, but maybe the management had a pact with the weather-god to keep provincials away

In the early morning, if you tried to shower just with the water in the tank, well, you wouldn't.

My wife does so. Despite my son (or sons - depending whether the elder is at home or college) having their baths at night. [My bath-time varies - if I go on a run it's likely to be the middle of the day]. After two baths were run last night, the tank thermometer showed 51C (124F) this morning - just as well we have a mixer shower.

In late spring/summer/early autumn we have the gas boiler switched off (the rest of the year we have it on part of the time to boost water temperature from that achieved by the panels to bathing/washing up temperature). My panels are smaller than Del the cat's.

In the early morning, if you tried to shower just with the water in the tank, well, you wouldn't.

My wife does so.... After two baths were run last night, the tank thermometer showed 51C (124F) this morning - just as well we have a mixer shower.

Okay, it takes 4.186 Joules to raise 1 gram of water 1 dgrC. Assuming 20 dgrC (70 F) inlet water, and a 150 L (40 gallon) tank, with final temperature of 51 C (124 F), how long would a 2 meter**2 solar collector to reach that temperature, and beyond that temperature for morning use?

So, if my math is right, for the water just to reach 51 C, then 150L * 1000g/ml * 4.186 J * 31 C = 19.5 e6 joules. 1 watt = J/sec. The maximum energy of the sun is 1000w/m**2, so the maximum output of the collector is 2000 Watts (but it is much less than this). With a perfect system, the amount of time it would take to collect this much energy is 19.5 e6 J / 2000 J/sec = 9732 seconds, or 2.7 hours. Let's apply some losses - say the system is 60% efficient - then it would take 4.5 hours.

So, you're claiming that you have two teenagers taking baths (at night!), plus maybe a wife and maybe yourself taking a bath during the day, doing laundry, etc.. . and the water temperature is still 51C. Let's make some assumptions - your sons use 20% of the hot water per bath, so now you have to add 40% more energy to the water before sundown, plus make up for whatever you used during the day - let's say, another 60%. Your collector would need to run, perfectly, 2.0 * 4.5 hours = 9.0 hours, but the angle of the sun changes through the day, but I'm not taking that into account.

The final temperature of the tank at sundown would have to be 51 + 0.4* 31 = 64 C, which is scalding hot. Most solar controllers shut off at 120 F to prevent scalding, which is close to what you stated (51C = 124 F). You might want to check the temperature of the tank at sundown - some safety mechanism might be defeated. But if the temperature doesn't drop much from the early evening to early morning, then you might have what I had when I bought my house - a broken controller. (It used two pumps - one for the collector, and one for the water tank - that one was broken, and the hot water heater was in series, so I never knew. Another disclosure by the previous owner - not!)

Please read 17, which was timed at 2.02 pm

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

We mix hot and cold water in our baths, showers and even washing up. The washing machine takes in cold water direct from the mains and heats it up. I do not get actually scalded washing up but the water is painfully hot if I do not add some cold on a hot summer's day. So your arithmetic may be fine but your assumptions are not because we use less 64C water than we would 51C water in a bath and mix it with cold.

The temperature of 51C (top of the tank - it was 17C at the bottom) in the morning was 12C below that at sunset (which was a bit below the peak level in the afternoon).

The maximum number of hours sunshine varies according to the time of year but if we say 15 then you are saying it would need to be 60% efficient for 60% of the time, based on your (intended to be reasonable but actually excessive) estimates of our use of hot water.

I wasn't told of any automatic cut-off if the water got too hot: I think that heat losses from the panels balance out the inflow of energy from the sun when they get really hot so somewhere around 70C is probably the maximum attainable. There is a switch I can use to stop the circulation, but I have never had to use it The panels were designed and installed by a firm in the North of England where it is cooler and less sunny than the USA (same latitude as Labrador). They install a circulating liquid that doesn't freeze - if they were working in Florida, they might design them differently.

The quotation above was on a bright sunny day. It doesn't get that hot on cloudy or rainy days so the morning after a rainy day my wife might need to heat the water. In the winter we use a gas boiler to bring the water temperature up from the level provided by the solar panels to a comfortable temperature for washing up.

In a solar panel there are at least two heat transfers, solar to panel and panel to fluid. The solar to panel for these nearly identical panels should be identical which implies that the shorter coil panel will attain a higher equilibrium temperature.

The heat transferred to the working fluid will be so nearly identical A,B = B,A that this difference would be difficult to measure, however since the collector efficiency is improved by a higher output temperature the system should function better plumbed B to A.

I think - That is the beauty of science you apply reason and understanding to predict the "right" answer and then you test and experiment to find out if your "right" or "not" often being not right contributes more to the growth of your understanding so I will be interested to learn from your actual experience.

Tony

Mr. Gee,

Greetings from the Island of Stone Money.

I admire your approach very much. You deserved my respect.

The beauty of science and reasoning is that you use your knowledge so far to make a prediction and check it against observations. That is how people learn, and how science and technology progress. Passive bystanders who make no predictions learn little, and contribute less.

In case you find this condescending: if it hadn't been for the contribution of your Yap supporter, this would not have been written

As an engineer for an electric utility back in the 70's, our Solar Energy Task Force designed, installed and instrumented a number of solar water heating systems that were put on customers' homes. Here it is 30+/- years later and the same arguments, discussions, etc. are resurfacing regarding topics that were hot (sorry) back then.

The correct answer is that the panels should be plumbed in parallel with balancing valves, but of course that is not the situation that we are dealing with here which involves series panels.

There are a lot of assumptions being made by the posters, and a bunch that aren't stated, but the biggest one is that the temperature differential across the collector panel and inside the collector enclosure is a constant, neither of which is true, except under very unusual operating conditions.

When we instrumented our collectors and the domestic hot water systems that they were installed in, we found that all things being equal (same panels, same insolation, same plumbing, same useage profile, etc.) the flow rate of the fluid through the panels had the greatest effect on efficiency of collection. If the flow rate was too low then the fluid temperature approached the temperature of the collector plate at some point in the tube other than the outlet, thereby leaving thermal energy in the collector enclosure that will utlimately be reradiated out through the cover glass or lost to the outside air via convection.

With that as a basis, the posters who suggested that the series connection of two 1sq.m panels was no different than considering them as in one 2sq.m enclosure were on the right trail, but that ignored a crucial piece of information. What's missing (aside from the flow rate) is the orientation of the straight runs of the collector pipe, horizontal or vertical, and whether the inlet is at the top or bottom, similarly for the outlet.

So the answer is...it depends upon the above factors, but the maximum amount of energy will be collected if the panels are arranged as follows:

1. The long runs are horizontal (so that the fluid is exposed to the lowest gradient as it traverses horizontally),

2. the inlets are at the top (so that the coolest fluid is exposed to the highest temperatures first, also known as a counterflow heat exchanger),

3. the flow rate is adjusted so that the outlet fluid temperature of the second panel is at or near the hottest point on the surface of the second collector (the fluid cannot get hotter than that point or more energy is being extracted than is coming in from the sun).

Oh, and what is the order of the panels? A then B. Why? Because in the limit as the number of tubes is increased so that the entire surface of the collector 'plate' is now made up of tightly packed tubes, the thermal resistance between the plate, tube and heat transfer fluid is minimized. Therefore more tubes in a fixed area absorb more energy for a given flow rate.

...and we didn't even get into a discusion about selective coatings on the plates, anti-reflective coatings on the cover glass, proportional motor controllers, how to transfer heat into the storage tank, freeze protection, etc., etc.

first of it should be understood that solar radiation available to both the collectors are same,as the area and time of radiation available is same. So the collector having nine tubes will have say 2.0 liters of water in tubes where as the other with 13 tubes will have assume 3.0 liters of water. As the radiation and time and area is same the water in the collector having nine tubes will have assume 55.0deg. C and the other collector with 13 tube will have assume 50 Deg. C. temp.

Now if the collectors if connected in series will have no differnce but columative out put temp will have mean temperature out put and assume it is 52.5 Deg. C.

If the collectors are connected in parrale then both collectors has different out lets and if the collected in common container then the total hot water availabel will be 2.0 + 3.) + 5 liters but the temperature also will be same as inseries means 52.5 Deg. C. This is with the experience I am giving my reply. I am yet ready for further disccussion. Manoj Pandya

STEELHACKS INDUSTRIES.

MANUFACTURING SOLAR WATER HEATERS SINCE 1982.

Do you people really use the hot water direct from the solar collectors? That wouldn't work in the UK or in most of N. America, as you need quite a lot of water, and you cannot get sufficient heat transfer for continuous use*. Also, we like to have hot water available after sundown. When solar heat is available, we transfer it to a storage tank.

* Even for direct heating, the configuration does make a difference - but perhaps it doesn't matter if you have lots of spare heat available.

No, we use a heat exchanger to transfer the heat from the transfer fluid, that absorbs heat from the solar panel, to the water in the hot water tank.

When did you move to India? (Poster of # 114)

This is becomong an interesting thread Del . I shall shamelessly scavange ideas for a home project in a few months. Nice one.

Ta,

Just hope I don't get pilloried when the 'correct' answer is published!

We seem to have about a 1/3, 1/3, 1/3 split between A>B, B>A, Doesn't matter.

So I s'pose 2/3 will be after my blood! I shall hide under my desk!

Del

Hi Del

Yes, it's a good thread.

It looks as if it depends on the system.

If the system has spare capacity to provide the heat you need from the heat stored in the panels during initial warming, then you might want B first, then A.

If you need the system to be running for quite a while so that losses to ambient are important, then you want A then B. And, if the pipe and tank insulation are decent and you start the pump at the optimum time, it's always A then B (unless the pump is overspecified and consumes too much power - in which case quasi-continuous pumping would be best thermally - and undesirable from the aspect of pump life etc.).

Better still, place the panels in parallel, and throttle A to match you requirements (you could even bypass the throttle at start-up and get the best of both worlds).

Fyz

Why doesn't someone just make a scaled down model and test the darn thing....nothing like some empirical evidence!

Great - a volunteer. Lampbulb heater for repeatability, or two equivalent devices run at the same time for comparison?

Fyz

Del,

I am a member of the 1/3 group in favor of A then B, and have followed this thread and its posts since the beginning. My original post (#34) was poorly worded in its second half, but I believe the reasoning is sound. Regardless of which panel is first, the majority of the total heat gain in the system will be from the first panel, because in that panel the circulating fluid has the greatest temperature difference from the panel's surface temperature. Thus, the average temperature of the panel surface will be lower for the first panel than for the second one.

However, the panel which has the best ability to conduct its collected temperature to the tube and its circulating fluid is the one which should be placed second, because it will be more effective in getting that last "little bit" of energy to the fluid, and will thus be able to reach a higher overall system output temperature. That is the reasoning which has me place A ahead of B (where A has less tubing length and less bends than B, although I thoroughly enjoyed the comments about the technical writers' propensity to edit the letters so A is always the first one). Panel B, with its greater number of "zig-zags" has the lower average distance for the heat to be conducted from a unit of panel surface to the nearest tube, and so there will be a lower temperature differential between the surface and the fluid.

I completely agree with your defense that "steady-state" is not a reality in this system, for all the various reasons cited. In reality, I don't believe that "steady-state" is a reality in any system, although some may achieve the slowly-changing state of relatively constant insolation and only a slowly-changing fluid temperature (reflecting the slowly-changing storage tank temperature).

Those who talk about heat losses raise valid points. The second panel, with its somewhat higher average surface temperature, will have a higher heat loss than the first--regardless of panel order. The suggested use of surface coatings with selective emissivity (a lower e value at the comparatively lower black-body panel surface temperature leads to less heat loss if the same coating has a substantially higher e value at the comparatively higher black-body temperature of the incident solar radiation, since emissivity and absorptivity are closely related to each other) is a good idea, and would probably result in greater overall efficiency gains than any shuffling of the panel order A-B vs. B-A. Likewise, the use of surface glazing with low-iron glass has a modest but measurable benefit. Similarly, the non-mentioned use of a different fill gas, such as argon, would cut the convective losses from the system.

All these academic questions are worth reviewing and discussing as we have been doing so. However, I believe you chose the most important step--actually going out and doing something. Anyone who does something, even if it is not the theoretical or ideal "best" needs to be applauded, because there are far too many who are sitting around waiting for the proof of the "best" approach, or for some other form of the "sky is falling" before they do anything.

Keep up your tinkering and doing. I doff my hat to you.

John Mueller

Lots of scientific babble.

The article gives no reference to any intended desire, from any beginning, any GPM, or that even the copper tubes were different lengths, just two panels of about the same shape with copper tubes in them with different amount of bends.

Regardless of which way they are connected, ( as one unit) they have 22 bends, they have the same amount of resistance and flow, the same amount of heat being transfered into them (total).

Being that the sun projects about 1000 watt per sq. meter at the equator, one can't even assume that the input temp. is less than what the sun can generate on the panels. Who knows with this example, too little information, it in fact it might radiate the temperature to a cooler state if the input temp is 400 deg. F.

Hi, I agree that maybe there is some 'overthink', but it is a surprisingly difficult question.

But there is enough info' for this question as long as you take it at face value and don't look at it as a 'trick question'.

No intended desire?????? Yes there is, max efficiency regarding order of panels.

Look at the pics in earlier my post if you are serious, you can just see the zig zags are the same length therefore panel A has a shorter tube than B.

10mm copper tube if you really want to know this.

Pump starts running when there in an 8 deg C differential between water storage cylinder and panel output.

Location England so 400 F is unlikely! I get an output of about 60C on a good sunny day.

Good luck!

The difficulty in the question isn't surprising do to the lack of info. I didn't read all 149 other responces and wasn't asked too.

The answer to the original question ( being that I didn't run across any update of the 20 or so I read) is that it doesn't matter which way based on the info.

I didn't look at it as a trick question, just one with a lack of info for a more accurate answer.

Your pictures don't help me a bit with out measurements etc. and I don't remember it being pumped with anything in the original question.

Your 400 degree is exactly unlikely, but just shows what assumtion you won't except from my answers. How can I except yours or any others. At 400 degrees, it will disipate heat, not aquire any, basic thermodynamic laws, so this would not be a solar heater, but a cooler for the guest that appears anonymously.

I get lucky once in a while.

I don't often write caustic replies, but in my view you are well deserving of one. Your post # 151 implies that Del the cat was the originator of the 400 degree figure - when it appeared in your earlier posting. If your English was less casual, I would have put it down as a language problem, but I feel that would be overly kind in this case. When the question clearly says a SOLAR panel, it is in no way an "assumption" to work on the basis that solar heating is the behaviour you should be considering; my objection here is to your palpable intellectual dishonesty - and that in addition you refer to the generality of the other replies in an insulting manner - as being "lots of scientific babble".

If you prefer insulting the community to attempting to provide an answer based on a reasoned interpretation of the question, guest was probably wise to withhold his/her identity.

If perchance the issue is that you find it difficult to carry implications from one phrase to the next, please accept my sympathy and apologies.

Fyz

Oh Fyz,

Never have I seen 'caustic' so apologetically conveyed. Bravo! My only suggestion would be to empathise, rather than sympathise,

Davo

Ouch! I didn't know my failings in that area were so obvious.

BTW, did you spot the source of the illusion (changing input temperature) in Del the Cat's analysis? (Extra hint - he fixes the average temperature in the input panel, regardless of heating effect)

Fyz

You have made 2 other posts on CR4.

A. windmills : you gave the first respone - 'I know the answer but can't back it up.'

B. glass stuck to glass: your post at #96 copied #1

I couldn't be bothered to quote you fully , I wasn't asked.

Why not give yourself a break - go to the begining of this thread and read all the way through.

There is enough information in the original question to determine the answer, which is not the exact number of joules transferred at midday when the temperature is 69F in the shade, but in which order the water/transfer fluid should pass through two solar panels with unequal lengths of copper tube but otherwise as identical as practicable.

All solar heating systems use pumps, so that does not need to be separately specified once the problem is stated to concern solar panels. It is stated that the reason why the panels have different number of bends is that the questioner misjudged the length of copper tube.

If you are incapable of understanding the question and providing a reasonable, and civil, answer then the fault is yours, not Del the cat's. If I can do it with nothing closer to techno-babble than the word "integral", then it is clearly not that difficult.

"If the input temperature is 400 deg. F". It was described as a solar panel, not a cooling system for a steam engine. Babble indeed!

You should also take some note of Del the cat's inputs, as he was the acknowledged source of the question.

I'm anticipating that 2/3 of you guys will be after my blood.

My 'answer' is doubtess rather simplified.

My original gut feel was A then B....and it was much to my chagrin that when pressed by the management! (Thanks Chris!) I did some maths with great reluctance and came to the opposite conclusion.

Out of interest they are actually plumbed A the B, and I can't be bothered to clamber onto the roof and reverse them, as the piping wouldn't fit (they are 'handed') and it would be a pain. The arguments have encouraged me to make some other changes though!

I'm sure some will argue with my assumption.

"Let the mean surface temperature of panels=k"

Which says that both panels have the same surface temperature. (Which is probably near the truth but is debatable).

However if we say instead :-

"Let the energy falling on each panel=k"

Then the maths still follows pretty much the same, although I'll be acused of swapping units of heat enery and temperature willy nilly....

Thanks for all the input, it was a pretty good discussion.

Del the Cat

Wow, lots of discussion, and interest. Kudos to you Del for your economic panels. My answer would have been B then A, without picking up my pencil or thinking for 2 seconds, only because my second job as a mech. eng. back in 1983 was design of industrial solar heating systems. All the science behind the answer was already discussed so I won't bore you with more. I actually would pipe in parallel, with controls, to modulate flow, so I could shut down flow one panel if the system is getting too hot. (I could do this with spare parts from my husband's controls business, but for most homeowners it is not an option.) This doesn't appear to be a problem for you, your panels max. out at 60C but the industrial systems can reach 100C on a hot day so we had to design for that. Also, it worries me a bit that I did not see a safety relief valve on the outlet of your second panel. We had them on every panel but your system is small so this would be overkill. Maybe you have one, and I did not see it. Although the risk is low, SRV's are really cheap, and also probably a good idea for house insurance reasons ( i.e if you are away, the unit blows, water damage to roof....).

The company I was working for in 1983 went bankrupt in '84, solar energy was just not commercially attractive back then, but sure is experiencing a resurgence now. We built 16 ft by 32 ft wide panels, and linked together in series or parallel depending on the demand, in fields of up to 48 panels. Pretty nifty.

Ta for your kind reply.

No SRV... not necessary (I hope!) as it is vented to the atmosphere at the header tank which feeds the central heating system. My panels just T into hot water circuit with check valves to avoid heating Essex, and as you point out mine don't get too hot.

A few holes have been picked in the assumptions of my answer but it's nice to know that with your real experience you agree...whew that's a relief!

(Someone didn't like my T and T+4 assumption...but it could be T+3 or T+5...don't s'pose it matters too much if there's only 8C between in and out!)

Nice post

Ta

Del

Now that the answer has been revealed/published I'm convinced? my analysis is/was correct!

OTOH it may have been a lucky guess.

Why do you assume the relationship T : (T+4) survives the establishment of
a new, (pumped), flow rate??

Fair question...but read #165 #171

The +4C is fairly arbitary just to all ow me to do some maths...the debate is still rumbling on inconclusively in some quarters....

Maths isn't my strong suit...

I reserve the right to be wrong...sue me, but I aint going up on that roof again.

(But I may wear sack cloth and ashes for a few pico seconds)

That's all folks!

Del (loony tunes) the cat

This does not make sense to me. Even though the second panel creates more heat doesn't it also have more water to heat up? Isn't it easier to heat up a smaller volume of water than a larger one? It appears to me that both panels create the same amount of heat per square inch as the other. I see no difference.

A is less efficient. Temperature increase of water is not linear. If the coolest water is run through A first it will supply a higher inlet temperature to the more efficient "B" collector. This should allow a higher potential oulet temperature from that unit. B will have a lower energy potential per unit of water flow because it has the same energy input (area) but a larger absorption surface (coils).

The assumption that the temperature in the second panel is T + 4 is not correct.

It would be correct if both panels are equal. it should de delta T and the delta is different for each panel since they have different lengths.

Actually, the assumption of unchanging temperature difference between the averages of the water temperatures in the panels* is correct for the assumption of constant panel temperature, because as one panel transfers more heat the other transfers less and this compensates exactly. However, the sums don't apparently show this and you are on exactly the right tack to find out why. The false assumption is that average temperature of the first panel doesn't change - and this means that the heat flow is being analysed with different input water temperatures for the two cases. Clearly, if you start with cooler water and the same panel temperature, more heat will be transferred. I did the sums - it corresponds exactly to the difference given in the official solutions for the two cases. Factor that in and the order of the panels becomes completely irrelevant (but only because the system is analysed as if all heat flows are linearly dependent on temperature difference).

*I'm taking average to be the average of the input and output temperatures, which is not strictly correct, but corresponds to the adequate approximations of flows made here

Fyz

Del

you are to be applauded for actually building your system. Like some others on here, I do not have the formal education that places a comma then two or three letters after my name. What I do have is 3+ decades of hands-on experience as a millwright/ mechanic. I subscribe to this and other sites to learn; something I hope to never stop doing. Perhaps it is simply over my head why, but it seems to me that engineer types delight in over-thinking things and complicating them to the extent that I have on occasion asked one if he was a RUBE GOLDBERG wanna-be.

That your system works is the important thing. Could it be BETTER? Of course! IMHO if it does what you wanted it to do, the what-ifs and whys are pointless now. The time for them was before you started building it. That was also the time to employ the old adage "measure twice, cut once" regarding your tubing.

Just my2centsworth.

Lol....Thanks,

Too right!

(But in by defense it's a bit tricky to handle a 25m coil of soft copper tube in my garage which is full of junk on a cold winter's night!)

I agree, theory and maths are tools to get you into the right starting place, but you still have to build it and see..then tweak it a bit.

The example I use ...

Has anyone made a longbow or boomerang starting from theory?

In electronics I say hardware seldom works right first time...software never does.

Del