Thermodynamics of Resistive Heating at Low Power

[bob012345]

Summary:: This is a question about resistive heating at low power in a thermally sealed chamber.

Suppose one has a resistive wire inside a small very well insulated chamber that can stand very high temperatures such as 1500C. For applications such as a kiln, the heating element is powered at high power ~kW's to get very hot and the heat builds in the kiln to high temperatures. But if the heating element is powered at low power say~100W but for a long time will the temperature in the chamber ever reach high temperatures assuming insignificant heat loss or is there some thermodynamic limiting factor? In terms of total energy input one hour at 1kW is the same as 10 hours at 100W. My hunch is that the temperature will build and as it does it heats the element also which still significantly conducts so it gets even hotter and continues the cycle so it will ultimately get to high temperature.

 

[russ_watters]

...will the temperature in the chamber ever reach high temperatures assuming insignificant heat loss or is there some thermodynamic limiting factor?

Heat loss is the limiting factor.

 

[DaveE]

Summary:: This is a question about resistive heating at low power in a thermally sealed chamber.

Suppose one has a resistive wire inside a small very well insulated chamber that can stand very high temperatures such as 1500C. For applications such as a kiln, the heating element is powered at high power ~kW's to get very hot and the heat builds in the kiln to high temperatures. But if the heating element is powered at low power say~100W but for a long time will the temperature in the chamber ever reach high temperatures assuming insignificant heat loss or is there some thermodynamic limiting factor? In terms of total energy input one hour at 1kW is the same as 10 hours at 100W. My hunch is that the temperature will build and as it does it heats the element also which still significantly conducts so it gets even hotter and continues the cycle so it will ultimately get to high temperature.

The steady state temperature will be achieved when the heat lost from the chamber equals the heat input from the heater. The chamber temperature at steady state is a metric for the quality of the chamber insulation from the external environment. In simple models this is called the thermal resistance (or thermal impedance).

How long it takes to reach thermal equilibrium (steady state) is determined by the mass, or thermal capacity, of the stuff in the chamber that must be heated up to the steady state temperature.

This looks like a nice simple treatment of the steady state thermal problem:
https://www.sfu.ca/~mbahrami/ENSC 388/Notes/Staedy Conduction Heat Transfer.pdf

 

[Baluncore]

In terms of total energy input one hour at 1kW is the same as 10 hours at 100W. My hunch is that the temperature will build and as it does it heats the element also which still significantly conducts so it gets even hotter and continues the cycle so it will ultimately get to high temperature.

Remember that the chamber can never become hotter than the element. If the elements are to operate at the same temperature, but at different powers, the 1 kW element will need to have 10 times the surface area of the 100 watt element, since the 1 kW element will need to radiate 10 times more energy from the same surface temperature.

 

[bob012345]

Remember that the chamber can never become hotter than the element. If the elements are to operate at the same temperature, but at different powers, the 1 kW element will need to have 10 times the surface area of the 100 watt element, since the 1 kW element will need to radiate 10 times more energy from the same surface temperature.

I think the element will always be hotter than the chamber because given a resistive element at temperature T in equilibrium with the chamber, if current flows through that element it will get hotter by some ΔT raising the chamber temperature and so on. I just want to use a lower power flow which will of course have a significantly cooler element temperature at the start but eventually get red hot.

 

[russ_watters]

Remember that the chamber can never become hotter than the element. If the elements are to operate at the same temperature, but at different powers, the 1 kW element will need to have 10 times the surface area of the 100 watt element, since the 1 kW element will need to radiate 10 times more energy from the same surface temperature.

Unstoppable force vs immovable object. Here, a heating element cannot operate at constant temperature. It's temperature will rise as the temperature of the air surrounding it rises. Typically though the resistance increases with temperature and thus heat output decreases with temperature.

 

[bob012345]

Unstoppable force vs immovable object. Here, a heating element cannot operate at constant temperature. It's temperature will rise as the temperature of the air surrounding it rises. Typically though the resistance increases with temperature and thus heat output decreases with temperature.

For a Nichrome element the resistivity increases about 20% between 100C and 1000C. Not too bad.

 

[Baluncore]

Pure "elemental metal" heating elements closely follow resistance proportional to absolute temperature. Alloys such as nichrome are selected for heating elements because they have a much lower temperature coefficient of resistance.

Typically though the resistance increases with temperature and thus heat output decreases with temperature.

If required there is the option to accurately regulate power to the element, so it can be quite independent of changing element resistance.

Yes, the element will increase it's temperature in advance of the kiln contents.
To radiate 10 times the heat, will require 10 times the area, or 10 times the temperature difference, or a blend of those two. The product of element area by temperature difference will be proportional to the power.

If element area is not changed, then there will be a greater temperature advance for the higher powered element, which will distort the hypothetical proportional time ratio, unless the element power is regulated, or the element mass is very small compared with the internal thermal mass of the kiln and contents.

 

[russ_watters]

So, I guess the question is: is this scenario theoretical or real world? We shouldn't have to be guessing about features and constraints.

 

[bob012345]

So, I guess the question is: is this scenario theoretical or real world? We shouldn't have to be guessing about features and constraints.

Well, I asked because I am playing around with the concept of what I call a 'thermal battery' which would be a smallish device to store one to a few kW-hrs worth of heat which could be later released somewhat like space heater on a cold winter night.

 

[russ_watters]

Well, I asked because I am playing around with the concept of what I call a 'thermal battery' which would be a smallish device to store one to a few kW-hrs worth of heat which could be later released somewhat like space heater on a cold winter night.

Well that's definitely a thing. I'd suggest using more low-grade heat, like heating water up to 90C/190F.

1 kWh is 3.6 MJ. With a 70C delta-T you'd need 51 kg (L) of water.

What is the electricity source?

 

[bob012345]

Well that's definitely a thing. I'd suggest using more low-grade heat, like heating water up to 90C/190F.

1 kWh is 3.6 MJ. With a 70C delta-T you'd need 51 kg (L) of water.

What is the electricity source?

I originally thought of water but the limited temperature means a lot of water making it heavy and cumbersome and also it might leak. In less than a couple liters of volume one can I principle store ~1kWhr of heat using sand or even iron or steel ball bearings or fire bricks. For example for firebrick or sand ~2 liter volume stores ~1kWhr at 1000C. This does not include the insulation required.

The source of electricity could be wall power AC or solar panels DC depending on the design. It could be designed for both. Obviously it would be better to store solar heat directly from the sun since the panel conversion losses 80% but it is hard to cheaply get high temperatures directly thus solar panels to do resistive heating. Focusing sunlight is expensive compared to cheap solar panels.

 

[hmmm27]

You might consider this type of thing : waxes or other compounds which have their liquid<>solid phase change in the human comfort zone.

 

[bob012345]

You might consider this type of thing : waxes or other compounds which have their liquid<>solid phase change in the human comfort zone.

That is an excellent idea. It would be more expensive and heavier though. Probably safer if the melting temperature of the wax were as you suggest in the human comfort range. But it certainly would make sense using lower power resistive heating elements. This might be a good match for direct capture of solar energy on a smaller scale. Let me work a few numbers. I have to see if it has advantages over water @90C. Thanks!

 

[DaveE]

I have to see if it has advantages over water @90C.

There should be a big advantage because the latent heat of fusion is usually large.
For example it takes roughly the same amount of energy to melt ice from 0^oC solid to 0^oC liquid as it takes to raise its temperature from 0^oC liquid to 80^oC liquid.
Also, the temperature is stable during melting.

 

[bob012345]

There should be a big advantage because the latent heat of fusion is usually large.
For example it takes roughly the same amount of energy to melt ice from 0^oC solid to 0^oC liquid as it takes to raise its temperature from 0^oC liquid to 80^oC liquid.
Also, the temperature is stable during melting.

The latent heat of fusion for wax ranges from 200-300kJ/kg at some temperature while water going from 25C to 95C stores ~300kJ/kg using ~12 L of water. Using a wax of latent heat ~220kJ/kg stores the same energy in ~16kg of wax which is ~18L. The wax would certainly be easier to insulate at a lower temperature. The cost for the wax is about $2/kg. It is easy to see how to get the energy out of the water, just pipe some air through it and you get warm air. I am not sure how to get the energy out of the molten wax by controlling the solidification process easily. Just expose it to the room air and blow a fan over it? That is similar to what I would do with hot sand but in a more controlled way by designing the container to leak heat at a specific rate without its outer insulating jacket.

 

[gmax137]

1 kWh is 3.6 MJ. With a 70C delta-T you'd need 51 kg (L) of water.

Check that, I get closer to 12 kg water.

Actually I work in Btu, and get 27 pounds mass. A factor of 4.2 "better."

 

[Baluncore]

Water has the storage advantage that it can be pumped through a radiator. Adding solid iron to the water reservoir is bad, it increases the weight but reduces the thermal capacity by volume. The addition of glycol to the water increases the storage temperature range available.

Air has advantages in that it can be blown through a radiator, a gravel bed or a heat storage brick, then released directly into the living space. Air makes a good thermal transfer fluid.

For a non-pumped system, animal fat such as lard, can be blended to give a phase transition regulated wall temperature. The problem comes with containment. It requires storage in a parallel grid of tubes that have internal heating wires. That makes change of the blended phase change material possible.

 

[hmmm27]

For a non-pumped system, animal fat such as lard, can be blended to give a phase transition regulated wall temperature.

I will happily fund a system that runs on bacon, just on general principles.

The problem comes with containment. It requires storage in a parallel grid of tubes that have internal heating wires. That makes change of the blended phase change material possible.

Why internal heating wires ? I think the OP's project concerns using PV panel waste-heat - not electricity - to charge up a thermal battery.

[edit: I sidetracked myself, here... the original post specifically inquires about heating, electrically)

 

[Baluncore]

Why internal heating wires ? I think the OP's project concerns using PV panel waste-heat - not electricity - to charge up a thermal battery.

Phase change materials cannot be pumped when solid. To drain the system you must melt the contents. Rancid fat might be a problem that, with time, requires a change of the fat, lard, or dripping.

Sunlight on the outside of the wall, (behind glass), will add to the passive energy store without raising the regulated temperature.
To add heat to the wall from say PV, you can use the internal wire elements. But you will need to keep one wire spare to recover from a fused heating element.

Live pigs also generate heat and methane fuel.

 

[bob012345]

I think my original question was answered. I can use resistive heating at a lower power. Thanks for all the comments! For the moment I still think hot sand or rocks offers the simplest and most compact design for my small devices. There is a company in Finland called Polar Night Energy developing hot sand storage on a large scale for winter district heating. They store excess renewable energy as heat in the summer for use in the winter.

 

[russ_watters]

Check that, I get closer to 12 kg water.

Actually I work in Btu, and get 27 pounds mass. A factor of 4.2 "better."

Yep, I forgot to divide by the specific heat of water (4.2 J/g-K). See, that's the advantage of IP units; you don't need all these esoteric conversions!

 

[russ_watters]

I think my original question was answered. I can use resistive heating at a lower power. Thanks for all the comments! For the moment I still think hot sand or rocks offers the simplest and most compact design for my small devices.

I still worry about the usability and safety of higher grade heat, but it could work. Keep us posted on how this project goes!

[edit] P.S. I think PF needs a slogan. Something like: "PF: Because you wanted a sledgehammer, right?"

 

[bob012345]

I still worry about the usability and safety of higher grade heat, but it could work. Keep us posted on how this project goes!

[edit] P.S. I think PF needs a slogan. Something like: "PF: Because you wanted a sledgehammer, right?"

BTW, any recommendations on simulation programs for thermal analysis. Free web based would be nice. I am going to try Simscale first and see if that can do it.

 

[russ_watters]

BTW, any recommendations on simulation programs for thermal analysis. Free web based would be nice. I am going to try Simscale first and see if that can do it.

What, exactly, are you trying to simulate? I do most of my simulations low-end, with a spreadsheet. I'll look into Simscale -- you wouldn't believe what my company pays to outsource CFD analysis.

 

[bob012345]

What, exactly, are you trying to simulate? I do most of my simulations low-end, with a spreadsheet. I'll look into Simscale -- you wouldn't believe what my company pays to outsource CFD analysis.

The temperature rise and stored heat content over time as well as the heat loss based on material properties and device geometry. Basically a 100W source encapsulated inside a material such as a heat brick or sand surrounded by insulation layers and ultimately a steel jacket. I think it's going to be about 20 cm in diameter and about 30 cm tall but it could be bigger. I hope very soon also to do some simple experiments.

 

[russ_watters]

The temperature rise and stored heat content over time as well as the heat loss based on material properties. Basically a 100W source encapsulated inside a material such as a heat brick or sand surrounded by insulation layers and ultimately a steel jacket. I hope very soon also to do some simple experiments.

I would use a spreadsheet for that. There's nothing complex about it. You can even include the performance change of the heating element with increasing temperature without too much trouble.

 

[bob012345]

I'd have to think about how to set it up. Seems like it involves differential equations in 3D.

 

[Baluncore]

Seems like it involves differential equations in 3D.

3D is not required for a simple bulk storage average.

The construction of a dry sand pit for thermal storage could be improved by the inclusion of some empty vertical tubes that would work as thermal siphons. The aim is to prevent hot areas within the body of sand by circulating hot air up through the sand and down through the tubes during electrical heating. The heating elements should be placed in the sand at the bottom of the pit, away from the vertical tubes.

Where should the hot air be extracted from the pit, and where should the cool air be returned ?
Could chemical odours or microbes take up residence in the sand, to spread into your environment later ?

 

[bob012345]

3D is not required for a simple bulk storage average.

The construction of a dry sand pit for thermal storage could be improved by the inclusion of some empty vertical tubes that would work as thermal siphons. The aim is to prevent hot areas within the body of sand by circulating hot air up through the sand and down through the tubes during electrical heating. The heating elements should be placed in the sand at the bottom of the pit, away from the vertical tubes.

Where should the hot air be extracted from the pit, and where should the cool air be returned ?
Could chemical odours or microbes take up residence in the sand, to spread into your environment later ?

I do not plan to circulate hot air through the sand since this is a small device. There may be some air pockets designed inside the inner core to distribute the heat evenly. I conceive of an outer jacket I can simply lift off and expose an inner jacket designed to radiate heat at ~1kW when fully charged. There could be a small fan to blow air over the device. If the temperature gets as hot as I hope ~1000C or greater, I won't have a microbe problem. I think of this device as more of a small kiln redesigned and repurposed as a space heater.

 

[hmmm27]

Bucket o' Magma. I wonder how much a paint-can sized Dewar would cost.

A ~9cm dia opening should radiate 1kw @ 1,000C

 

[bob012345]

Bucket o' Magma. I wonder how much a paint-can sized Dewar would cost.

A ~9cm dia opening should radiate 1kw @ 1,000C

Of course there would have to be some sort of safety screen covering the opening just like in a resistive element space heater. Good idea about the Dewar.

 

[fluidistic]

To radiate 10 times the heat, will require 10 times the area, or 10 times the temperature difference, or a blend of those two. The product of element area by temperature difference will be proportional to the power.

The power radiated goes like T to the fourth power, T being.the absolute temperature. To me, this implies that you need to multiply the delta T (between the wire and its environment) by only the quartic root of 10 if you want to x10 the power emitted, i.e. 1.78, roughly. What am I missing?

 

[Baluncore]

What am I missing?

I don't know.
I think you are assuming black body radiation from the element. But some energy radiated from the element to the sand would be reflected back to the element.
I was assuming the thermal resistance of the layer of sand that surrounds the heating element would limit heat transfer to the sand.