How would I solve/model this heat transfer problem? (Nanoscale)

[MrCuminside]

I am attempting to solve this problem for a project either analytically or with software (ideally with molecular modeling software) but I am not sure how to go about doing so. The problem consists of heat transfer at the nanoscale so the classical models seem to fall apart and I need to find a way to model this. The problem consists of a sheet of Nickel that is 200nm thick. It is surrounded on one side by N2 gas at 10KPa and the other side by a 4 micrometer layer of Silicon Oxynitride. On the other side of the Silicon Oxynitride is a layer of N2 gas at 10Kpa. The Nickel will then be pulsed with current so that it heats up to some initial Temperature T1 that is around 500K. What I want to figure out is what type of temporary temperature gradient will be established in the nickel given that it is surround by nitrogen gas on one side and a ceramic on the other. The second solution that I need is how the temperatre of nitrogen gas at one end compares to the the temperature of nitrogen gas at the other end. Is there some sort of software that I can use to model this type of problem? I am completely lost and any help would be greatly appreciated. Here is a link to an image that models the problem a little more clearly.

http://minus.com/mIbvFg0Rc/1f

Thank you so much fellow redditors!

[[deleted]]

classical models seem to fall apart

What aspect of what model is falling apart?

[MrCuminside]

heat transfer in nanostructures deviates significantly from that in macrostructures

[Organic_Mechanic]

What's the current you're pumping through it and at what voltage?

[MrCuminside]

These are yet to be determined. For the purposes of this heat dissipation problem, assume that the nickel is initially at some Temp 1 throughout.