[Bored chemist]

"immersion heaters get fouled and lose efficiency rather rapidly do to the increased insulation due to scale (efficiency/effectiveness)"
Really?
If my 4KW heater is scaled up, where does the energy go?
A very small amount of heat must, initially, go into warming up the scale.
But what can happen to the rest of the energy if it doesn't go into heating the water.
OK, if the tank is poorly lagged there will be greater losses- though only very slightly.

Eventually, the heater will burn out, but are you saying that it will have a shorter life than an induction heater's electronics?


"May i question the value of the heat you are going to collect from my shower water please"
Sure, you can ask the question. If nothing else, you could use it to heat the water feed to the hot water tank.

With a bit more trouble, you could use it and a heat pump to seriously reduce the energy you need to heat water for showering/ bathing.

[SimpleEngineer]

"immersion heaters get fouled and lose efficiency rather rapidly do to the increased insulation due to scale (efficiency/effectiveness)"
Really?
If my 4KW heater is scaled up, where does the energy go?
A very small amount of heat must, initially, go into warming up the scale.
But what can happen to the rest of the energy if it doesn't go into heating the water.
OK, if the tank is poorly lagged there will be greater losses- though only very slightly.

Eventually, the heater will burn out, but are you saying that it will have a shorter life than an induction heater's electronics?


"May i question the value of the heat you are going to collect from my shower water please"
Sure, you can ask the question. If nothing else, you could use it to heat the water feed to the hot water tank.

With a bit more trouble, you could use it and a heat pump to seriously reduce the energy you need to heat water for showering/ bathing.

When you heater gets scaled up you will have lower heat transfer to the water requiring the heater to be on for longer the energy is lost through the heating of the scale that doesnt really want to be heated.. (high heat capacity) the extra time taken will 'wear out' your element quicker, and the increased resistance due to the element having to get hotter to warm the water will threaten your electrical supply, meaning your system will trip more readily and 'wear out' faster.

Direct and indirect losses to efficiency. Can't tell you if it will have a shorter life than inductance as I don't know its lifespan.

I qualified my question with the practicalities of achieving any kind of realistic heat transfer to incoming water from the tepid remnants of my shower.. the temp difference will be very low (probably around 8-10 degrees maximum), so you will need a huge heat exchanger to extract this minimal waste heat from a pretty low volume, atmospheric pressure drain.

   

[Bored chemist]

"When you heater gets scaled up you will have lower heat transfer to the water requiring the heater to be on for longer the energy is lost through the heating of the scale that doesnt really want to be heated"
Nope, the scale ahas a much smaller heat capacity than the water.
If the element is dissipating 3KW then each second it transfers 3KJ of energy to something. The only things available are a little scale and a lot of water, so almost all the energy ends up in the water- just the same as if the scale wan't there.
The surface temperature of the heater (inside the layer of scale) rises until the heat transfer rate from the element to the water is the same as the rate at which heat is provided by the electricity.
Where else could the 3KW go?

Incidentally, the heater's resistance will rise as the temperature rises so the current will fall so slightly less heat will be dissipated. The breaker will be less likely to trip out.

Let's imagine a heat exchanger made by running a 1 inch pipe down the middle of a bigger pipe. We will have the feed water (incoming at, let's say 10 C) run up through the smaller pipe and the outgoing water from the shower (let's say 40 C) run down through the outer pipe.
We can make it 6 feet long and assume it's well lagged.
That's not too big an assumption and there's easily going to be room for it if the shower is upstairs so that's not unreasonable.
So we have a pipe made of copper, if no temperature change in the water took place there would be a temperature difference of about 30C across it. Say the copper is half a millimetre thick.
How fast is heat  transferred?
Well the circumference of the pipe is about 8cm and the length is about 180 cm so that's 1400 cm squared of area.
The conductivity of copper is about 4 watts per centimetre Kelvin.
So the half millimetre  thick pipe wall will transfer 80 watts per square centimetre for each 1 degree temperature difference.
We have about 1400 cm2 so that's 115 KW per degree and we have a 30 degree change in temperature.
In principle, that's enough to transfer 3.5 megawatts of heat.
Now, I realise that I have made some very dodgy assumptions there but even allowing for the temperature change (which roughly halves the temperature gradient) and the serious effect of boundary layers, I think that you might transfer a significant fraction of the heat needed to warm the water in the first place (I think we are talking a few tens of KW to heat the water so, if a thousandth of the heat got transferred it would heat the water for you.

What would be interesting would be if there's someone here who actually knows about heat exchangers who can give us some idea of how much heat you could really recover.

[SimpleEngineer]

I 'really know about' heat exchangers as I design them for a living. A few points

Fouling of any heat exchange surface decreases the rate of heat transfer, the element will get hotter to transfer the same amount of heat to the water. hotter = higher resistance = more power =  more amps = more likely to trip.. you can arrange that however you wish for whichever cause you want to focus on. Scale is an insulator

The heat exchange area as you describe is 0.15m2 the heat transfer coefficient for me came out as 3.34kW.M2.K (1.5 milimeter thick wall typically) with your unrealistic 30 degree temp difference I work out there is only 15kW of heat to be transferred through your exchanger. Using the very same basic (and overly simplistic) equations.

You would need a lot of work to go into the log mean temperature difference and flowrates of the streams. Boundary conditions and fouling issues aside, We are already at a heat exchanger 6 foot long.. and we haven't even begun assessing it. We havent even mentioned that the approach temperature for water is around 10 degrees.. (10 degrees difference that is) which makes the calculations required even more complex.

As the temperature difference gets lower the heat transfer decreases, The water loses heat to air, body and bath tub.. if its coming out of your shower head at 50, the losses on the way down would easily reduce it below 40 before it hits the bathtub or enter the drain. it is more likely to enter the drain at 30. Mains water temp is slightly variable, however most industry estimates take it to be 15degc for calculation purposes. so you actually have around half the temperature difference you guesstimated. Which by the simple calcs show half the energy transfer, but more complex calculations will show it drastically reduces the effectiveness of the heat exchanger.

In all.. you will gain something from doing so.. but it wont be half as much as you think, if you use 100kg of water (for a 15 minute shower) you only lose at most 11kW of energy (2.75kWh - 20p? not sure on this calc)       

[Bored chemist]

"Fouling of any heat exchange surface decreases the rate of heat transfer"
Yes, in a heat exchanger, but not for a heating element.

"the element will get hotter to transfer the same amount of heat to the water."
Yes, as you say, the heat transfer will be the same and the element (inside the scale) will be hotter.

"hotter = higher resistance = more power =  more amps = more likely to trip.."
No
Hotter means more electrical resistance.
So that means less current. Check out Ohm's law.
So it's less likely to trip.
However the temperature coefficient of resistance form most pure metals is about 1/273 per degree C and the alloys used as heating elements like nichrome have (deliberately chosen) even lower coefficients. (about 0.0004 per degree for nichrome)
So if the element heats from 293 K to 393 K (slightly hotter than boiling so it's probably an overestimate.) the resistance will increase by 0.04 and the power will decrease by 0.04 so the 3KW heater becomes 2.88KW. Not a massive change.
If the scale means that the element runs 10 degrees hotter then it only reduces the heating power by 0.4%.
Fluctuations in mains voltage will have a much bigger effect.
In any event, I live in a soft water area.


I measured the wall thickness of some copper pipe. it's 0.88 mm.
I checked the cold water feed temperature it's 11.8C
If I remember, Iwill checkthe outflow temperature next time I have a shower.
You seem to get cheap electricity, mine costs 14.14 pence per KWhr
Two showers a day 350 days a year (to allow for a couple of weeks or so of holidays elsewhere).
£275 a year.
If I could save a quarter of that for an outlay of £100 for some pipes it would pay for itself fairly quickly, rather better than double glazing for example.
I might look into that.
The big problem would be fouling, I might end up spending more on bleach than I save in electricity.





Edit.
Just measured the outgoing water at the drain as 37.8C
So the differential is 26 degrees compared to my initial guess of 30
And the pipe is a bit thicker so the power transfer (if the flow rates were so high that the temperature drops were negligible) is "only" about 1.75 megawatts.
If you accept that the temperature gradient probably averages about half of that you still have nearly a million watts of power to dissipate if the water flow were high enough.
Of course, it isn't, but we know that you only need something like 30KW to heat the water on the fly.


I think that it might still be viable

[SimpleEngineer]

Oh its viable.. I dont contest that.. but like I said a 6ft heat exchanger is a pretty hefty outlay for that £250 a year saving. I would estimate at around £1500 for the bespoke unit, down to about £750 if it were mass produced (could give you drawings if you wished) But my main issue is that with our very basic outline calcs, we would not achieve the potential savings (even half of calculated value seems hard to chew out over 6ft tube) as you mentioned the fouling, difficulty in ensuring entire wetted area etc.

I would suggest using lower shower temperature would save more than you would recover. And of course.. shorter showers.. 15min is a pretty long time for a shower, even if it IS the household average. (Mine rarely last more than 10) each of these would save more energy than you would be able to recover.

YET.. it is a viable option in the goal for a sustainable house.

I am with you with what seems to be an inconsistancy with practical results and ohms law etc. I know that when my heater element gets fouled (which it does, as my water could be used as structural material) I have trips and use more electricity to heat my water. Current MUST drop when the resistance goes up.. Agreed.. Maybe it is the longer duration of power that is required to heat the water up? My breaker trips about once a year (usually to tell me to descale my element, which i do once a year) I would LOVE to know if someone could point out, other than scale build up what causes my element to overload?

And as for heat transfer.. Any hot -> Cold heat transfer is a heat exchanger and follow the same reasoning and limitiations.

Surface area, temperature differential and residence time are the driving forces to say how much energy is exchanged and how fast. Subtle applications exist with convection heaters and radiators but essentially you can boil it down to those three and improving any of them improves effectiveness.

[alancalverd]

   

"Fouling of any heat exchange surface decreases the rate of heat transfer"
Yes, in a heat exchanger, but not for a heating element.

Yes, in a heating element. The fouling has no knowledge of the source or purpose of the heat. The only variable in the integrated heat diffusion equation for a given thickness of infinite diffuser is the temperature difference between the input and output. 

My breaker trips about once a year (usually to tell me to descale my element, which i do once a year) I would LOVE to know if someone could point out, other than scale build up what causes my element to overload? 

Depends on the nature of the breaker and its position in the circuit, and the mode of operation of the thermostat. If an electronic stat adjusts the duty cycle of the heater, it might normally be switching between say 0 and 50% on a 1 second cycle. A Type B breaker will tolerate a 5x overload for 1 second, so you can put a 20A mcb in a circuit with 40A peak current and a 50% /1 second duty cycle. But if the fouling reduces the heat flow such that the thermostat demands 100% duty, the breaker will trip. Seems that you have a pretty well-designed installation.   

[Bored chemist]

Just to simplify things a bit, lets imagine that the electrical resistance of the heater is not affected by temperature. I can do that by putting two resistive elements in series, one with a positive temperature coefficient like nichrome and the other with a negative temperature coefficient like carbon. If I get the resistances right the change in overall resistance with temperature is zero.

OK, so I make this element with a resistance of exactly 19.2 ohms.
I connect it to the mains which delivers exactly 240 volts
The current is 12.5 amps.
And the power is therefore 3KW.

The scale doesn't affect that.
Now I put that heater in some water.
Do you agree that in this case, exactly 3KW of heat gets transferred to the water (neglecting any conducted out through the power cables)? If not, where does it go?

Now I scale up the element.
Its electrical properties remain the same.
It continues to dissipate 3KW.
Where can that power go apart from the water?
Initially, it can heat up the scale, but there's little scale and a lot of water so most of the heat ends up in the water.
In fact, practically all of the heat still ends up in the water- we are talking a few grams of scale and a few tens of Kg of water and water has a higher heat capacity.

What changes in the heat equation is the surface temperature of the element (I think I said that earlier) and eventually, that will cause the element to burn out (I think I said that too.)

So, give or take the few tenths of a percent change in the resistance due to changes in temperature, the power is the same and there's only one place for that power to go- into heating the water.

Any alternative is skating round problems with the conservation of energy.

A heating element designed to draw 3KW will do that. If it overheats because it's scaled up then it will draw less current and hence less power (ohms law applies whether you like it or not).
The thermostat can't make it draw more power.

What might trip the breaker is an inductive surge when the thermostat happens to trip out at the "wrong" part of the mains cycle.
The thermostat may well switch on and off more quickly when the heater is scaled up. If it switches more often then it's more likely to hit the "sweet spot" for tripping the breaker.
Or it could be a thunderstorm miles away.

BTW, re
" it might normally be switching between say 0 and 50% on a 1 second cycle. "
If your thermostat is switching in and out that quickly you need to increase the hysteresis- a lot.

[alancalverd]

" it might normally be switching between say 0 and 50% on a 1 second cycle. "
If your thermostat is switching in and out that quickly you need to increase the hysteresis- a lot.

If the cycle exceeds 5 seconds in a pulse-width-modulated mains water shower, you will scald and freeze alternately. I've built pwm thermostats with millisecond cycle times - though admittedly not for heating domestic water!

Now, back to your 3 kW heater and, say, a conventional bimetal thermostat. If it draws 12.5A for less than 10 seconds at a time, it probably won't trip a 6A type B breaker. If there is no scale on the heater, then the adjacent water will heat quickly and the thermostat will trip before the breaker. As the scale builds up, so it takes longer to get the water to target temperature and the probability of the breaker tripping before the thermostat, increases.

[Bored chemist]

Since I'm talking about a 3 KW heater, I'm clearly not talking about heating water on the fly am I?

Ten seconds is also absurdly fast.
The figues above suggest it needs about 2.75KWHrs of heat to get the water hot.
At 3 KW that's roughly an hour and the rate of change of temperature is of the order of 30C per hour or 0.5C per minute.
So you would need a switching time of ten seconds if you were hoping to get the temperature control to something like a tenth of a degree.
Do you think bimetallic strips are that good?
Also typical switch lifetimes are of the order of 100,000 operations. At 1 operation every ten seconds that's less than two weeks. Even at 1 hour a day it's less than a year.
At best, it seems we are at crossed purposes here.
I'm talking about the old fashioned immersion heater- typically 3KW in a big copper tank, where the "temperature" of the water isn't very well defined because it's a lot hotter at the top than the bottom (deliberately- that's what the Surrey flange is for) so having a thermostat trying to maintain 0.1C would be silly.

Also, you should have breakers rated for the full load current.
If the heater draws 12.5 Amps then it should be connected through a breaker rated for a bit more than 12.5 amps- not less.
So, even if the thermostat tells the heater to run continuously- very cold feed and a high set point- the breaker shouldn't trip.
Not doing so is not good electrical practice.

And, finally, I'm invoking the law of conservation of energy. If the heater element in a "power shower" that heats the water on the fly scales up  (and, according to you, somehow draws more power than ohms law permits) where does the extra energy go?
If you have x litres a minute running through it and it is fed with water at - lets say 15C and produces water at 45 C it has to draw some  defined amount of power.
OK, if the heater scales up and (according to you) it draws more power, where does tthat energy go?
It can't be dissipated within the "box" with the electrical bits in, because that is heated by the outside jacket of the water heater and, since the thermostat maintains the outlet temperature, that is still at the same temperature as before it scaled up.

Where does the extra power go?

[CliffordK]

Microwaves are only useful for heating a small quantity of water to make a hot drink but even then an electric kettle is a better option

I just got an electric kettle.  It is HUGE.  But, if I put in about 1" of water in the bottom, it heats up a bit more than a cup in about the same time as the microwave, and I assume using less electricity.  I try not to empty the pot 100%.  Am I wasting power that the microwave otherwise would be saving by heating up an excess 1/4 cup or so?  No sense in heating a full pot, then just using a little off the top and letting the rest cool down.

It probably wouldn't take much to design a resistance heating element that could efficiently supply boiling hot water (on demand) from the spigot.  I think many that are available today keep the water hot all the time which is a bit wasteful for personal use.

[alancalverd]

And, finally, I'm invoking the law of conservation of energy. If the heater element in a "power shower" that heats the water on the fly scales up  (and, according to you, somehow draws more power than ohms law permits) where does the extra energy go?
If you have x litres a minute running through it and it is fed with water at - lets say 15C and produces water at 45 C it has to draw some  defined amount of power.

The problem is that a power shower isn't a steady state device. You can supply constant power and vary the flow rate to control the outlet temperature, or switch the power at a rate that will give you the required average into a relatively steady flow. Either way, if you put a thermally resistive element (scale) between the heater and the water, you introduce a phase lag that requires a longer duty cycle in the transient after switch-on.  I don't know where you got the idea that it violates Ohm's law - I only used your figures for voltage, current and power!

[Bored chemist]

The bit about Ohm's law comes from this bizarre assertion " hotter = higher resistance = more power =  more amps = more likely to trip..  hotter = higher resistance = more power =  more amps = more likely to trip.. "
The fact remains that if you draw more power from the mains,but only the same amount of power  goes into heating the water, you have to explain where the rest of it goes.
And if the breaker won't take the full rated load of the heating element then the breaker isn't the right one for the job.
The scale will make temperature control more difficult (though a PID controller that "learns" should be able to cope with it).
But, fundamentally, the maximum current is the voltage divided by the resistance, and if the breaker is properly rated it will not trip.
It will take longer for the transient heating to get through the scale- but you are overlooking the fact that the hot scale will provide heat to the water during the "off" part of the duty cycle.
The net average power remains the same.

[alancalverd]

SE has reported an observation. I have suggested a cause, but you have merely stated that it can't happen. I think the ball remains in your court, sir!

[Bored chemist]

If you look carefully, you will see the hole in that.
It has something to do with the fact that I already posted a possible explanation that doesn't involve a breach of the laws of physics.
I didn't "merely state that it can't happen" did I?
So, where does the extra energy go?
and is it good practice to wire a 12 amp heater to a 6 amp breaker?

[alancalverd]

First of all, let's deal with the breaker capacity. A standard cooker circuit may be supplied from a 32A type B breaker, giving a nominal 7.3 kW, but most 60 cm domestic cookers are rated at nearly twice that power. The reason is that random diversity of the thermostats means that although each element can deliver its rated power when commanded, there is very little probability of them all drawing current at the same time (even when all nominally "on, max") and even if they were, a type B breaker will sustain twice its nominal current for a few seconds.

Regarding water heaters, "all the energy" obviously eventually ends up shared between the water, the heating element, the scale on the heating element, and the tank, and if it is well lagged, they all end up at the same temperature.  But the key words are "energy" and "eventually". When you switch the heater on, the power in the transient phase first heats the element, then the element casing temperature starts to rise. Now the element casing is usually metallic, and bolted to the copper tank, so there are two outflow paths, radially to the water and longitudinally to the tank wall. If you put a thermal resistance (scale) round the element, more power is dissipated into the tank wall and less into the water. So it takes longer to heat the water between the element and the thermostat, the transient phase lasts longer, and overall more energy is lost to the atmosphere from the tank hotspot.

I probably wouldn't use a 6A breaker in a 12A nominal water heater circuit precisely because of this, but when we install large motors, x-ray machines, and other stuff with high transient inrush currents (in the 300 amp range - limited by mains wiring impedance only) , we use slow-blow Type C or D breakers that will sustain 5 times the rated running  current for up to 5 seconds but will blow in 0.1 second at 20 times the rated current .   The trick is to determine the difference between starting load and a persistent fault.   

[Bored chemist]

The cooker is irrelevant.
You can turn some bits of it on independently. You can't do that with an immersion heater.

Most immersion heaters I have seen are immersed. (There's a hint in the name)
So they can't heat the side of the tank without heating the water.
If the heaters in "power shower" types are actually heating the tank wall then that's a poor design.
However the tank wall is very well heat sinked by the water so the effect will be minimal anyway.
So, where does the heat go? Don't forget, for the effect to be significant on a power shower you would be needing to dissipate kilowatts of power in a small plastic box with no ventilation.
The loss to air should be pretty much the same since the tank wall will lose heat to the air anyway and you are only looking at the slightly higher temperature of a small part of the tank.

"I probably wouldn't use a 6A breaker in a 12A nominal water heater circuit precisely because of this, but when we install large motors, x-ray machines, and other stuff with high transient inrush currents (in the 300 amp range - limited by mains wiring impedance only) "
There are two issues with that, first it's wrong, and second it's irrelevant.
The inrush current is not just limited by the mains wiring, the resistance of the windings in the coils also plays a part. Additionally, the inductive reactance will limit the current.
Saying " limited by mains wiring impedance only" is just wrong.
But that's a minor point.
Heaters are a very near purely resistive load and, unlike things like light bulbs, their resistance, and hence current, doesn't change much with temperature so they don't have inrush currents to speak of.

So the cookers are irrelevant and the motors and Xray kit are irrelevant, and you still haven't come up with a satisfactory explanation of where the excess heat goes.

[alancalverd]

Oh but I have. You seem to think that immersion heaters are not attached to the tank they are heating. Funny, then that the manufacturers build flanges into the tanks and fit the heaters with screw threads and nuts.

OK, let's accept that on your planet the immersion heaters are fully immersed in the water and not attached to any metal object. So  once again the ball is in your court: why does SE's breaker trip out when the heater needs descaling?

[SimpleEngineer]

btw I have my 3kW element on a 16A breaker as per british standards.

The element is roughly 5-6 years old, when i descale I empty the tank completely (chunks and all), remove the element which i clean up using a descaler solution (viakal) and a plastic scouring pad, I have been known to scrape off bigger lumps with a small screwdriver.

Similar to
http://www.heatrodshop.com/80014atsta-immersion-heater.html

[Bored chemist]

Oh but I have. You seem to think that immersion heaters are not attached to the tank they are heating. Funny, then that the manufacturers build flanges into the tanks and fit the heaters with screw threads and nuts.

OK, let's accept that on your planet the immersion heaters are fully immersed in the water and not attached to any metal object. So  once again the ball is in your court: why does SE's breaker trip out when the heater needs descaling?

On my planet the heating element is entirely surrounded by water apart from the insulators and connecting wires attached to it.
Those are inside a (usually) copper pipe which is in the water.
That pipe extends for an inch or so and then meets the flange.
The losses through the connectors and flange are small. Part of the reason for that is (as I already said) the bit where there is an attachment is well connected thermally to the water.

And, since there's still no way that a 3KW element draws more current when its hot you have actually got two problems to address.
Where does this mythical extra ennergy come from and where does it go to?

Re "So  once again the ball is in your court: why does SE's breaker trip out when the heater needs descaling? "
The ball has not been in my court on that score since post 27.
I pointed that out in Post 34
Is there some reason why you didn't read/ understand it?