It varies depending on the rated flow rate, temperature rise and design. The energy density / heat flux is simply the rated KW divided by the surface area. Are you inquiring about information concerning the one in the pictures? If so, the electrical diagram, specifications, flow diagram would be helpful along with the exact information you are seeking to determine.

i am trying to find out what is considered acceptable for an instant electric shower's heating element

the power range is 7 - 10.5 kW

the flow rates are between 3-6 lpm - higher in summer and lower in winter - all depending on the temperature of the incoming cold feed.

I do not know the surface area of the heating element which is why i am asking

the manufacturers do not publish data: https://www.mirashowers.co.uk/p/parts-and-accessor...

Understood. This may be difficult without further information because the design is an important factor. The two designs I am thinking about are a one pass type and slip stream or mixing type. The one pass has a thermostat for set point and simply the water enters, passes over the heating element and exits, with a thermostat switches the element on and off depending on the thermostatic set point. Downside is when flow rate and incoming water temp changes, you may not have a consistent water outlet temp. Then there is the slip stream type, where water is heated much higher than usage temp and a thermostatically controlled mixing valve mixes the incoming cold water with the very hot water, so the outlet water is at the desired temperature. This allows for a buffering effect, so the unit can adjust to changes in incoming flow rate and outlet temperature requirements better than the one pass. Overall KW of both systems may be the same but one heating element may have a higher heat flux than the other depending on the requirements of the system.

these heating elements are sold by the millions for these types of instant electric showers.

i have ordered an electric shower to disassemble so i can work out the surface area of the heating element

someone must know what is the acceptable range of energy densities for these widely available products

A quick google found a 220V 9kW shower heating element, 8.5mm diam, 29cm long.

Actually on further review I think that's the length of the elements and there are 6 of them.

So in W/cm2 that's 116 w/cm2 or maybe (probably) 20W/cm2. that seems to equate better with a max for water of 140W/in^2 listed in a few online guides. 20 W/cm2 is 130W/in^2

Why do you want to know?



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Chomalox and Watlow are two major manufacturers of sheath heating elements. Look in their catalogs. They make several different standard Watt densities and sheath materials. The highest density is for water. lower densities are for oil or air.

they are spiral inside

at that density they will be destroyed with limestone very quickly

this is our current heating element which is 27W/cm2 (3600W/135cm2=27W/cm2) - this is after 6 weeks in a hard water area!



with this design we get to 8w/cm2 ( 3.14*10*1360mm = 427.04cm². 3.5 kW / 427 = 8.19)

Heaviside, I suspect the design pictured is the third of the two types you describe. A variant of your one-pass design.

There's no thermostat, only the safety thermal cutout on the top of the element. A flow switch (top right-hand) turns the element on (coarse control comes from selecting whether you energise one element, the other, or both). Once switched on, the element delivers the selected power level continuously. Fine temperature control is achieved by adjusting the set point of the constant flow valve in the middle right of the unit(which guards against fluctuations in inlet pressure) and by assuming that the inlet temperature will stay essentially constant for the duration of your shower. Overall on/off control comes from the solenoid valve in the bottom right hand corner.

A.

Quote (LittleInch)

So in W/cm2 that's 116 w/cm2 or maybe (probably) 20W/cm2. that seems to equate better with a max for water of 140W/in^2 listed in a few online guides. 20 W/cm2 is 130W/in^2

can you share the links to the guidelines that you found

https://blog.belilove.com/2016/02/suggested-watt-d...

Others say up to 300 w/in2, or <60 w/in2

The shower ones are probably higher because they need to be small, but mainly because they have forced flowing water running past them.

Immersion heaters which your picture seems to show rely on convection currents.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

the one in my picture is from our version of an instant water heater - so water flowing past the heating element

Still not sure why you need to know though??

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

I need to know what energy density to target when I redesigned my heating element for our instant electric shower. Heating element is 3.5 kW, approximately 20 cm in length.

We can’t have this limescale problem

Lime scale is from plating out the lime due to the temperature increase causing a decrease in solubility. It's the temperature change that is the cause, not the energy density.

Depending on the energy density, will depend on the temperature of the water that is right next to the heating element. This will depend on different things such as the starting temperature of the water and the flow rate.

If the water that touches the heating element raises above 60 or 65° C, you start to have the buildup of limescale

As long as we can avoid reaching these temperatures, we shouldn’t have an issue with limescale

From my experience operating evaporators you need to keep heat transfer surface temperatures below 170°F as at higher temperatures scale formation can become a severe issue.

TugboatEng - I agree

I don’t know how to do the calculation to work out the maximum energy density we can have based on:
- the flow rate and
- surface area and
- inlet water temperature

OP,
I wish you had started with this last post. You now have one design constraint, being the water temperature cannot exceed 60-65 C. What is the max flow, max outlet temp and minimum inlet temp?

Sorry, you are quite right. I should have realised this.


Inlet temp is up to 40C with a flow rate of 6 lpm

At 6 lpm, with a 3.5 kW heating element the max temp rise is 8C so the max outlet temp is 48C

You have turbulent flow - there aren't any calculations to solve your problem. You can calculate how much heat is required to raise the average temperature at some given flow rate, but the detailed interaction needed for what seems to be quest for the exact and only possible maximum perfect answer to get to some exact, but not lime depositing condition in the exactly smallest volume is not quantifiable.

The factors you have are not sufficient. Even in non-turbulent flow, the shape affects flow.

Put thermocouples into the heating element and use a feedback control to ensure the heater temp is never too high regardless of input water temperature.

A 3.5 kW shower would be a dribble if fed with cold water.

Where is 40C water coming from, which is all you need for a shower. This isn't making sense.

An 3.5 kW instant water heater is for washing hands.

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3DDave is going the same route I was thinking. The overall kw rating or heat flux of the element in this configuration is going to be difficult to calculate. Consider, you want the most surface area possible since your surface temperature is limited to 60-65C. You may need a much higher max wattage element and as suggested use a thermocouple-controlled loop to keep the surface temperature within tolerance. This may be a trial-and-error sort of testing to get things worked out.

The system has a heat exchanger in that recovers heat from use shower water. The preheated Coldwater can reach 35C.

There is a preheat mode in the system where we recirculate water Using a pump past the heating element to heat the inner workings of the system. In this scenario the inlet temperature can reach for 40c

Seems like a very complex system for a 5 minute shower....

But limescale is really a chemical issue.

Or try one of those electronic things which claim to reduce limescale.

Warm water coming in may increase deposition.

Remember - More details = better answers
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So is a heat pump

There are many used cases where the system is particularly suitable

Quote:

our current heating element which is 27W/cm2 (3600W/135cm2=27W/cm2

The picture looks like two heating elements. Are they in series or parallel? Are the numbers you provide for one or both?

Quote:

this design we get to 8w/cm2 ( 3.14*10*1360mm = 427.04cm². 3.5 kW / 427 = 8.19)

Same question, are there going to be two of these or are you trying to do the work of the two in the first picture using just one element?

As for 3DDave's comment, that's why you give yourself some overhead. In your favor water has very high thermal conductivity. If you can regulate your heater current so that the outlet temperature is max 48C you still have nearly 30°C of fudge room before scale formation starts. Consider sizing your heater so that it has 30% excess capacity (standard assumptions for HX design) and use a temperature controller to turn it down the rest of the way.

Google tells me safety requirements are for a max hot water temp of 50degC to prevent scalding for domestic instant water heaters. With a max permissible heating surface temp of 75degC to avoid or minimise surface scale,

Q = UA dt, Q/A = U. dt, where Q/A = w/m2 of heat transfer per m2 of heating element surface area

Table 11-2 in Perry Chem Engg Handbook states a U value of 70btu/hr/ft2/degF = 400w/m2/degK for agitated heat transfer to coils immersed in water for condensing steam in the coils. Using this

Q/A = 400x(75-50) = 10 000 w/m2 = 6.45w/in2 heating density = 1w/cm2 at the hot end, and it is slightly more at the cold end with water feed at 40degC.

Use longitudinal fintube elements to get more surface area. Am not having any luck finding a supplier for these at the moment on the net - most of them are transverse fintube, which may probably be impossible to clean in case they do scale up.

OP,
I'm glad georgeverghese brought Q = UA dtlog into this thread, because at the end of the day, this is going to be the controlling statement/equation. The wildcard here in my mind is a solid value for U. I am not sure of your background in thermo but you seem to know some. "U" - overall heat transfer coefficient is 1/U=1/h1=+L/lamda+1/h2
where: h = convective heat transfer coefficient, W/(m2°C) [Btu/(hr-ft2°F)], L = thickness of the wall, m [ft], λ = thermal conductivity, W/(m°C) [Btu/(hr-ft°F)]. The "U" variable describes the heat movement from the heating element, though its sheath and into the water.

Quote:

400w/m2/degK for agitated heat transfer to coils immersed in water for condensing steam in the coils.

My initial gut reaction was this was not accurate because the driver of latent heat transfer does not exist in this scenario but the more I thought about it, an argument could be made for a higher and lower U value in my mind. I will do some more digging or maybe someone more versed in this application will pop on and clear things up. At any rate, I think the "U" value may fall somewhere between 300 and 500, so 400 may be appropriate for a back of a napkin calculation.
My back of napkin calc took a different approach of the required cooling rate to keep the element below 65 C based on a flow rate of 6 lpm and delta T of 25 deg. I came up with 20w/cm^2 as the max surface flux allowed to not exceed 65C. This is assuming a huge number of things and should NOT be used for design purposes. I am only bringing it up to say that your design of 8W/cm^2 seems reasonable. I could see some fairly easy ways of testing this, but I would need to know more information about your original design (see previous questions).

sorry - i thought i replied but i must have hit preview instead of post

Quote (Heaviside1925)

The picture looks like two heating elements. Are they in series or parallel? Are the numbers you provide for one or both?

they are in parallel. Total surface area across both elements where heat is emitted is 135 cm2 with total power output of 3600W

Quote (Heaviside1925)

Same question, are there going to be two of these or are you trying to do the work of the two in the first picture using just one element?

This will most likely be a single coil with a surface area of 427 cm2 and a power output of 3500W

can you share your back of the napkin calculations? i would very much appreciate it

The current design example photo looks like the result of a positive feedback loop. The energy output along the length of the heater is a constant, but to accomplish that as the water entering at one end heats, the temperature increases to emit energy that energy along the heater. The hotter the water gets the hotter the heating element gets.

In the current design example photo does the water enter along the centerline?

As the temp increases in the flow direction the power into the heater needs to decrease at each incremental location in order to limit the temperature gain.

Quote (3DDave)

In the original example photo does the water enter along the centerline?

the 1" threaded hole on the side is where the heating element attaches

the inlet is to the left and the outlet is to the right

This is a teardown of a shower unit - https://youtu.be/ZwuhFLsowRc?t=908

Note that the two heating elements are separately operated and provide different amounts of power, with the lower power element closer to the outlet. Also note that the water inlet is not axial and there is a counter-flow aspect to the outlet tube to help average the heat transfer.

Ok - then depending on how the element is installed the current design elements could have their flow restricted against the walls of the housing causing that taper to the lime buildup.

Quote (3DDave)

Ok - then depending on how the element is installed the current design elements could have their flow restricted against the walls of the housing causing that taper to the lime buildup.

can you explain in simpler terms?

Quote:

can you share your back of the napkin calculations? i would very much appreciate it

I do not typically do that unless it's a very simple case. I will point where I am looking.
Consider the enthalpy of water, i.e. heat content per mass. You can look them up here: https://www.spiraxsarco.com/resources-and-design-t...
With a flow rate you are moving heat out of the system, and you are putting heat into with your heating element. Consider the different enthalpies of water at 40, 50 and 65 C. From that you can determine the amount of heat in each state. Convert volumetric flow to mass flow and you now have a relationship between rate of heat entering the system vs heat leaving the system. You also have a relationship Q = UA dtlog of the rate at which the heat moves from the element into the water. Consider with water, at low pressures and temps, it's very easy just to move a decimal place to go from cm to m and m^3 to kg. This is how I arrived at the number I provided. BUT there are considerations around flow velocity and how the fluid stream interacts with the surface of the element that I do not know and could have a sizable effect on the final number.
A test you could run, monitor your existing element surface temp at the max flow rate of 6 lpm with 40 deg inlet water. If exceeds 65 deg C increase flow until you have a flow rate that keeps the surface temp below 65C. Now you have relationship between W/cm^2 and flow rate, where you can calculate the max W/cm^2 at 6 lpm. You may even find that 6 lmp exceeds the flow required, which would mean there are transient states, such as low flow and such, where the elements' surface temp is exceeding 65C, in which case, there would need to be additional controls to keep the surface temp from exceeding 65C.

Because the water remained colder to the inside it delayed limescale formation; where it was impeded on the outside the limescale formed closer to the inlet.

Picture if the heating element was tight against the wall; very little flow would happen and the water would be much hotter than if it was in free-flowing conditions. Of course the hotter the water, the less heat transfer from the element, which means the element gets hotter yet, spiralling up to a higher temperature. The temperature gradient results in a lime scale deposition gradient.

Talk to tech reps at companies like Wattco or Chromalox also to give you values of U with your limitations.

Quote (georgeverghese)

Talk to tech reps at companies like Wattco or Chromalox also to give you values of U with your limitations.

i do not think its that simple, because the design of the heating chamber will affect the flow rate m/s of water over the heating element which will massively effect the heat transfer and therefore the peak temp on the heating element

i did not consider that the water is actually moving very slowly in the heating chamber because it goes from a circular pipe with a cross sectional area of 78,54 mm2 to a Cuboid with a cross sectional area 2916 mm2 (less the cross section of the heating element).

the speed of water in the heating chamber will be very low.

i will need to both increase the surface area of the heating element and decrease the area of the heating chamber - but i need to be careful that i do not add new problems by doing so

You're still doing about 20 to 25mm/sec flow velocity in the heater which if its say 3300mm long is still only about 12 seconds residence time.

sounds about right to me.

you're still getting a lot of flow over the elements.

But the missing point here is that for that level of scaling, you're really going to need to look at altering chemical properties of the water by installing a water softener and filter to remove or displace the ions which are causing you the issue.

There are loads of those little electric ones which no one can be sure they will work or the ones using different salts which you need to replace on a regular basis. Trying to solve this by reducing the surface temp and heat flux of your heater element is, IMHO, the wrong approach.

Think of the other elements you can't change in your washing machine or dishwasher??

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

It is almost certain you'll need a recirculation pump / recycle loop to keep velocities high enough to get good U values, else elements will scale up. Take a bleed stream off the recycle loop as the exit hot water stream. If you are serious about preventing scale, you'll have to get off the well beaten track cut throat manufacturers travel on.

Quote:

I have already developed the design route to solution and informed the OP.

Who is the OP?

Quote (Jack Benson)

Who is the OP?

You are. (I think it stands for Original Poster - certainly what it means)

Quote:

I have already developed the design route to solution and informed the OP.

Brand new account and first post. Unless you know this person already, like any public forum, spam, trolls and posers... Some folks use a web link to a page with their contact information on it, but it doesn't appear that Jack Benson provided that, so I have no idea how adThp thinks they informed anyone.

Also, zeusfaber

Quote:

Heaviside, I suspect the design pictured is the third of the two types you describe. A variant of your one-pass design

Thank you for the clarification, I found the owner's manual online after I first posted, and it appears to function as you described. I forgot to give you credit for that earlier.

Quote (Heaviside1925)

Brand new account and first post. Unless you know this person already, like any public forum, spam, trolls and posers... Some folks use a web link to a page with their contact information on it, but it doesn't appear that Jack Benson provided that, so I have no idea how adThp thinks they informed anyone.

I didn’t get a message from them

This forum doesn't have direct messages and discourages posting email addresses as that attracts harvester bots, so no surprise about not getting any messages.

adThp I meant no disrespect. It was the way your post, that was deleted, read, that thew me off. You indeed have been a member here much longer than I have. From a quick read of your 11 points you posted, you seem very knowledgeable in this subject matter.

Quote:

Forums are a lovely place to 'shoot the breeze', but, sadly, not a place to attempt to engineer a new product - especially given the lime constraints. For this, for goodness sake, go to an expert, pay your money, and reap the rewards for a long time. The value of $0 advice is precisely that - $0.

I fully agree with this for the most part. I do feel that this forum can serve a purpose in terms of making up the gap between knowledge vs. application. Sometimes that gap may be filled with a couple paragraph explanation from someone who applies this knowledge professionally or pointing to a standard. Other times in involves educating the OP that even though they may have the knowledge, that there is years practical understanding that is required in order to apply that knowledge and that this forum would not be the appropriate place to provide that.
As for this poster, they appear to have a working prototype, just are having an issue with lime scaling. As a solution they are attempting to design a new heating element and are asking for advice as to how to empirically validate their design. I understand this is likely not the route that a subject matter expert would recommend for proper product design, but consideration may still be provided concerning heat transfer and fluid dynamics concerning the design. In this sense, results may trump theory and the poster's design may function as they intended, even though it's efficiency may be poor. I would agree that the best route is likely to engage someone like yourself in a professional manner.
As an aside. I know some professionals on this forum provide a link to their own page in their signature since there is no method for direct contact sharing. I would be interested in learning about your designs if such a link was provided on your signature.

I have suffered showers from those instant units from Canada to Chile and points in between.
Many electric, some propane heated.
Never saw a thermostat or mixing valve.
A flow switch turned the element on, full.
Temperature was controlled with the valve setting;
More flow, lower temperature.
Some were somewhat under powered.
If you wanted warmer water you turned the valve to slow the flow.
Turn the valve a little, still to cool.
Turn the valve a little further, a little warmer but still not warm enough.
Turn the valve a little further and OOPS TOO MUCH.
The flow switch just cut off and YOU JUST GOT HIT WITH A BLAST OF COLD WATER.
I hate them.
A design common in the third world is an open nichrome coil with the water flowing directly over the energized element.
Thee water then passes through a grounded screen.
In the third world the screen is not always grounded properly.
These instant shower heaters are common at diving resorts.
A much travelled recreational diver shared a secret with my;
"Always grab an empty styrofoam cut from the dining room and take it to your room.
Use the styrofoam cup to adjust the water valve and you won't get a shock in the shower.
I hate them.

--------------------
Ohm's law
Not just a good idea;
It's the LAW!

respectfully, you do not know the design of our system.

I am well aware of the cheap dangerous water heaters you are talking about, and our system is not like this.

We can give a constant in shower water temp of 42C with a 3.6 kW heating element at a flow rate of 6 lpm when the cold water is 7C.

in shower there is a standard or thermostatic mixer tap - nothing electric. We meet CE standards and localised standards regarding connecting systems to mains water supplies.


i was asking a very specific questions about energy density on a heating element and how to manage limescale.

this now makes sense.

i have spoken to adThp on fiverr.com and he did some heat loss calculations for me.

i dont know why you (adThp ) did not mention this is who you are in this post or on the messages you sent me to be on fiverr recently.

the entire system is correctly earthed. the PCB has a fuse and the system must be installed on an RCD protected circuit.

we take our responsibilities for electrical safety seriously.

I am struggling to understand how this thread has got so twisted.

this thread is about energy density and limescale formation - not about electrical safety based on what you think you know about our system.

Quote (Jack Benson)

I am struggling to understand how this thread has got so twisted.

Well that's what happens sometimes during the course of a thread when people don't have all the information supplied or it arrives in bits and pieces...

People generally mean well by questioning things not specifically asked for to provide their experience on the issues which arise during the discussion.

So you can take these or leave them, i's up to you.

We don't know you, your experience, your product or who else you've been talking to and we get plenty on these boards who attempt to do things way out of their knowledge envelope with potentially high risk consequences.

Looking back at your picture of the limescaled elements, they do seem to be quite close together and with a relatively low velocity in the heater with scaling starting at the "hot" end that you're getting hot spots on the elements. Maybe give the elements more space? or cause the flow in the heater to swirl more and create less of a uniform flow down the heater. Maybe?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

Quote (adThp)

It is surface temperature that affects limescale deposition. Energy density is not your challenge. You simply are not sufficiently qualified to draw this conclusion. Heater companies have been selling units into lime-challenged regions for years.

yes of course - and when i approached you to quote for helping me i was asking you to prepare an Excel file that took into account the inlet water temperature and the flow m/s of water over the heating element as well as many other factors. i know that energy density is not the deciding factor, but given many other variables are relatively fixed in my device its one parameter i can play with.

Quote (LittleInch)

People generally mean well by questioning things not specifically asked for to provide their experience on the issues which arise during the discussion. So you can take these or leave them, i's up to you.

i appreciate everyone's help and input. I know you are doing this in your own free time and expect nothing for it. I value this forum and it has been very helpful. so thank-you to everyone who has helped on this thread and others.