Is there a way to calculate thermal conduction speed or time?

[goodphy]

Hello.

I'm working in the plasma physics and trying to calculate the thermal conduction time or speed.

Thanks to the people here replied my questions, I was able to calculate the thermal conductivity of the plasma with the given electron temperature in SI unit. (http://www.pma.caltech.edu/Courses/p...4/0419.1.K.pdf)

Plasma what I treated has cylindrical symmetry surrounded by the dielectric material.
Right now I need to calculate the time it takes that the energy or heat is transferred from the axis of the plasma to the wall with the given thermal conductivity.

I guess the time is function of not only conductivity but also temperature difference between two points thus let's assumed that the axis temperature is Te while dielectric is at room temperature.

Could you help me to find out how to calculate this?

I need to confirm that the thermal conduction is really important for our plasma or not.

 

[gtoguy97]

Thank you in advance!! The thermal conduction time or speed can be calculated using Fourier's Law of Heat Conduction, which states that the rate of heat transfer is proportional to the temperature gradient. This means that the thermal conduction speed can be calculated as follows:Speed = k * (Te - T0) / rWhere k is the thermal conductivity, Te is the temperature at the center of the plasma, T0 is the temperature of the dielectric material, and r is the radius of the plasma.So, to determine whether thermal conduction is important for your plasma, you will need to calculate the thermal conduction speed and compare it to other relevant timescales, such as the plasma period or the time required for other processes (such as diffusion). If the thermal conduction speed is significantly shorter than these other relevant timescales, then thermal conduction is likely to be an important factor in the dynamics of the plasma.