Defining thermal conductivity as a function of temperature

ASPECT
1

Hello,

I am trying to define thermal conductivity as a function of temperature within one compositional field in a model. My goal is to implement a linear increase in conductivity at high temperature.

I’m using the viscoplastic material model and do not see an option to use a function in the thermal conductivity input.

I thought of perhaps implementing the “compositing” option, which I haven’t tried before so I wanted to see if this is the best approach.

Any help would be appreciated.

Thank you!
Stephanie

2

Hi Stephanie,

As always, thank you for posting these questions to the forum!

Indeed, writing a new material model plugin that calculates a temperature-dependent thermal conductivity and composites this on top of the visco-plastic model is an option.

More specifically, the new plugin would overwrite the thermal conductivity calculated in the multicomponent_incompressible equation of state module.

Alternatively, one could just modify the multicomponent_incompressible EOS module to have a temperature-dependent thermal conductivity options (default would still be constant per material). I think the feature would be of broad general use, and as such am leaning towards this latter option.

The good news is implementing temperature-dependent thermal conductivity should be straightforward with either approach.

What is your required timeframe for implementing this? Would you be willing to discuss the idea at the next ASPECT user meeting? It would be good to get thoughts from the rest of the developers and users.

Cheers,
John

3

Hi John,

Thanks for your response. OK, I will try to work on what you have suggested and post updates/questions if I run into issues here.

As far as a timeline, I will start working today and will bring it up at the User Meeting next week as well.

Thanks again,
Stephanie

4

Following up after the User Meeting this AM:

While a change to the EOS module to allow general use of temperature-dependent thermal conductivity may be useful, we do not see it necessary to achieve the desired effect at this time.

Generally, mineral physics would suggest that thermal conductivity could vary with temperature by a factor of 2, so a future modification to permit the dependence may be of interest.

However, in my case I am using a linear increase in thermal conductivity at a specific range of temperatures in order to keep the adiabatic gradient and prevent the system from cooling, which may be better handled using an extended Boussinesq approximation.

Thanks all!
Stephanie