# Point me toward an equation! Thermal conductivity

| Posted in Energy Efficiency and Durability on

Hey all,
I’m back with a bit of a mad scientist question for a DIY project to preheat water in a cold but very sunny environment (High Desert 4500 feet).

I’m currently looking at Ohm’s law and using solar panels to heat an element in a sand battery (I know it’s a fad right now…or is that just me?).  I know in Norway they’re using the batteries for DHW after the sun’s gone down…which is basically what I’m after.

The point of the battery is to heat up well beyond the boiling point of water.  So is there an equation where you could figure out how to diminish the amount of external insulation on one side of the battery so the 400 degree +/- could be slowed to where the outer wall could hover at around 140 degrees?  If I’m figuring for a Delta of 250 degrees through the insulation, how do I calculate the U-factor or R value of that insulation to keep the water on the far side from boiling?

Or should I run a sealed circuit of oil through the hot sand and then cycle it through the water tank?

I’m curious what one does (also with solar collectors, which are usually filled with glycerin.  There are so many variables in this question I don’t really expect an answer, but if anyone has been down this road and can steer me toward books, websites or experts, I’d appreciate it.

Mark

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1. | | #1

sabotcat,

You might find the following link useful both for prior art and contacts that might provide practical insights. The myriad details that go into making heat storage of the type you are pursuing are daunting to say the least. Building for the lowest energy demand should be a primary goal if starting from scratch. The equations you will need are quite extensive.

https://forum.buildhub.org.uk/topic/30897-calculating-for-the-use-of-sand-for-a-thermal-store/

Be aware that at least two chemical based paths to storing energy are being developed. One uses a morphological chemical change to "lock in" energy that can be tapped at much later times. I don't recall how long the hold can be maintained. I have misplaced info on the second method. Storage of either is purported to be safe though I suspect bulky. The engineering details and system management may well prove to be the achilles heel of both. However, they do enjoy the advantage of no standby losses or extreme insulation requirements.

Similar advances are being made in window coatings that will radically alter energy management in large buildings, hopefully with knock on benefits to residental building. Of course, we will need to not blow ourselves up ecologically (or literally) for long enough to see these new technologies enter real life. The pending collapse of assorted ice shelves and the North Atlantic circulator current might finally get peoples attention

1. | | #3

thanks! Thoughtful answer! I've got the site open and appreciate it. Just trying to prewarm water on it's way to a heat pump water heater to increase the COP. Going to jump into the calcs you supplied this evening! I'll report back!

1. Expert Member
| | #9

Note that pre-heating the water reduces the COP of a heat pump water heater. You still save energy, just not as much as you would with other types of water heaters.

2. Expert Member
| | #2

I hate it when people borrow terms from other sciences, like "battery" or "flywheel," to talk about heat. Because it implies that heat works in ways that it doesn't.

Storing heat tends to be difficult and not cost-effective. I've never seen a scheme for storing heat on a residential scale that really pencils out, beyond say using a hot water tank to supply hot water faster than the heating element can produce it.

1. | | #4

DC Contrarian
You never disappoint. Yes, reading my post you'd see I was using this collection of sand (a battery like a collection of cells or a collection of artillery) precisely to impart some of its stored heat to water I was trying to preheat prior to heading into my Heat Pump Water heater.

But the other stuff you say, of course is true. Though I'll have to look up "Flywheel" I've never seen it used for anything but a heavy wheel that once set into motion tends to remain in motion. Like in Hydro electric power. Always helpful to be reminded of the world of things that don't work, even if it doesn't answer the question!

Onward!

1. Expert Member
| | #5

Let's be real. The reason people talk of "heat batteries" is not because they're collections, but because they want you to think they're somehow analogous to electrical batteries. You put electricity into a battery and you get electricity back, you should be able to put heat into a heat battery and get heat back, right?

What makes an electrical battery useful is that the electricity you get out of it comes out at pretty much a constant voltage. If there is an analogy between electricity and heat, then temperature would be analogous to voltage. And a device where you put heat in and get it out again at a constant temperature would be quite useful. But any device that depends simply on the heat capacity of the contents -- like a sand "battery" -- isn't going to work like that, every unit of heat you add raises the temperature, and every unit of heat you remove is going to lower the temperature. That's just how it works.

The reason a constant-temperature storage device is useful is that when you're storing heat, the hotter the place you're storing it the slower it flows. And when you're withdrawing it, the colder the store the slower it flows. What you want is something that can give you constant flows both when storing and withdrawing.

Phase change materials have that property. But even the cheapest ones are too expensive for any sort of residential use. Molten salts however do seem promising for storing solar on industrial scale.

3. | | #6

I'll try to be real here.

I appreciate the analysis, and you're right about the differences between the two batteries. My question was simply is there a way to insulate a sand "not battery" in such a way that you could predict the amount of heat that would reach to cool side of the insulation. So much of our building science is devoted to maximum efficiency from the insulation. I was asking if there was a way to calculate insulation so I could have a predictable level of heat (although always diminishing as the heat transferred...I do understand that!). Think of it as me trying to constrict the amperage so that my "not battery" doesn't discharge too quickly. If you want to respond to the question, I'm anxious to hear what you think. If not...just tell me how my definition of a flywheel is off base.

onward!

1. Expert Member
| | #7

Heat flow is always governed by the equation:
Heat flow =(temperature difference)*area/insulation

In US customary units, heat flow will be in BTU/hr, temperature difference will be in F, area will be in square feet and insulation will be in R-value.

So in order to maintain a temperature difference, you have to have a heat flow -- you have to be continually removing heat from the cold side. If you don't it will heat up to the same temperature as the hot side and only then will the heat flow stop.

So if you want the cool side to get no hotter than 140F, when the hot side is at 400F, you have to have some way of shutting the heat flow off once you get where you want to be. So typically what you'll do is run water through a heat exchanger, and once you don't need any more hot water you stop sending water through the heat exchanger. You also need to drain any water that's in the heat exchanger out so that it doesn't boil and turn into steam and turn your heat exchanger into a bomb.

What gets tricky is doing that while keeping your water at household pressure.

Another approach would be to have two heat exchangers, and use a fluid that won't boil at 400F. So you run the fluid through one heat exchanger in the sand and another one in the water. When the water gets hot enough you just stop the pump.

4. Expert Member
| | #8

High temp silicone heat transfer fluid is not as expensive as I expected but still not cheap. Add in the cost of the high temperature pumps and heat exchanger and ROI for this pre-heat is never. Never mind the cost of the actual sand storage/element/insulation.

You really can't beat water for heat storage. A large insulated tank with a copper coil in it is about as cheap heat storage as you'll find. Plumb so the DHW goes through the coil so only a small amount of potable water is kept is kept at this intermediate temperature. You will still need to occasionally bring the whole setup up to pasteurization temperature to keep bacteria at bay.

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