Calculating Thermal Conductivity for Furnace & Lead Bath

[cie00011]

I have a problem. I am designing a probe to first be put through a furnace for 5 minutes (Temp: 1030C) and then straight into a lead bath (Temp: 530C for 3 minutes). I need to be able to calculate the required thickness of insulation.

For the formula k=(Q/t)*((L)/(A*ΔT))

I know ΔT as I need an internal temperature not greater then 45C, I know A, k and t. my problem is L and Q. is there an easier way to calculate this? Am I missing something?

The furnace can be split up into zones, but for the concepts, the above is correct. what process should i do?

Cheers,

 

[Aaron Barnard]

To calculate the required thickness of insulation, you need to determine the rate of heat transfer (Q) from the outside of the probe to the inside. This can be calculated using the formula: Q = kA(ΔT)/L, where k is the thermal conductivity of the material, A is the area of the probe that is exposed to the furnace, ΔT is the temperature difference between the inside and outside of the probe, and L is the thickness of the insulation. Once you have determined the rate of heat transfer, you can then use the formula t = Q/(k(ΔT)/L) to calculate the required insulation thickness.

 

[astrokreng]

I would first recommend using a thermal conductivity calculator or software to help with your calculations. These tools can take into account the specific properties of the materials involved and make the process much easier and more accurate.

If you do not have access to such tools, then you can use the formula provided, but you will need to determine the values for Q and L. Q represents the heat flow rate, which can be calculated by multiplying the temperature difference (ΔT) by the thermal conductivity (k) and the surface area (A) of the probe. L represents the distance or thickness of the insulation.

To determine Q, you will need to know the specific heat capacity of the materials involved and the time (t) that the probe will be exposed to each temperature. This can be calculated using the formula Q=m*c*ΔT, where m is the mass of the probe and c is the specific heat capacity.

To determine L, you will need to consider the thermal conductivity of the insulation material and the desired temperature change (ΔT) that you are trying to achieve. You can use the formula ΔT=(Q*t)/(k*A*L) to solve for L.

If the furnace is divided into zones, you will need to calculate the heat flow rate for each zone separately and then add them together to determine the total Q. Similarly, if the insulation material has different thermal conductivities in different areas, you will need to calculate L for each section and then add them together to determine the total thickness of insulation needed.

In conclusion, while the formula provided is correct, it may be easier and more accurate to use a thermal conductivity calculator or software to assist with your calculations. If that is not possible, you will need to determine the values for Q and L using the methods described above. I hope this helps and good luck with your probe design!