Thermal Conductivity

<...Does the Inside Temperature of a medium affect Thermal Conductivity?...>

It depends how close to a phase transition the system is.

It is inside Electric Arc Furnace

Does that make a difference, then?

Yes, It does makes a difference.

What difference does it make?

It makes a difference in the computation of heat losses and the temperature gradients in the wall.

If one considers the conductivity at 20°C and the one at 2000°C their ratio is 4:1.

The temperature field has, via its gradients, an effect on thermal strains and stresses and this makes a difference makes a difference. Of course the Young module has to be as well considered as variable in the last computations.

Okay, I'm with you on that.

What difference does the fact that the heat source is electric arc make in this discussion?

None, from the conductivity point of view. The incoming heat will be not only convection or conduction but as well radiated. Since radiation depends on the difference of the 4th absolute temperature power it can become the major input.

"None, from the conductivity point of view." I agree completely.

However, I am curious why our original poster would tell us in post #5, "Yes, It does makes a difference."

I am not in his head and he does not share his thoughts with us. As you noticed most of OP do not communicate only ask.

Agreed.

BTW where did the OP go?

Except note that OP referenced alumina "brick", not the (presumably crystalline) aluminum oxide material that your Google results applied to. OP is asking about high temperature insulation, which would be porous. The information would have to be found in manufacturer's specs, or (long shot) someone here who has used this type of insulation and happens to know its approximate specs.

What is your goal?

Reduced energy costs? Increased production? Cooler working environment? Better temperature control?

Alumina Brick has poor thermal conductivity. The temperature profile across the cross section (inside to outside) will be in the unsteady state for a long time. Heat loss will also be in the unstaedy state for this period. One can consider thin slices of the insulation parallel to the inner surface and get conductivity for each slice at the slice temperature and integrate over the section to get a weighted average value for the insulation as a whole.

Transient behavior is NOT only function of conductivity ! It is depending on the thermal difusibility which is the ratio between conductibility AND accumulating capability = cp*ρ.

For ceramic Al 2 O 3 as the graph shows the higher the temperature the lower the difusibility since k devreases AND cp increases.

It is possible to approximate the k- variation with a mathematical function (in same paper it is already done) and integrate the heat transfer equation for the steady state heat transfer, it is much more difficult to do it for the transient period.

If the residence time is short the losses can be less than after steady state is reached.

Your statement is valid for ALL conduction related heat transfer situations not only for this one, it is nothing special if you ever used to analyse heat insulation problems.

The melting point of Alumina Brick (AL₂o3) = 2000⁰ C

How can it be exposed to inside temperature of 2000^oC? Preposterous!

Therefore the question of "Thermal Conductivity of Alumina Brick (AL₂o3) exposed to inside temperature of 2000^oC?" does not arise.

Formula: Al2O3Density: 3.95 g/cm³Melting point: 2,072° CMolar mass: 101.961 g/molBoiling point: 2,977° C