Thermodynamics of Resistive Heating at Low Power

[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.