Add energy transfer equation to the model

[pcosme]

[pcosme]

Se não me enganei em lado nenhum nas contas a evolução da energia será dada por:

Ora o terceiro termo não me parece compatível com uma equação de conservação típica (du/dt+df(u)/dx=0)

[pcosme]

ERRATA na equação anterior v_0 deve ser substituído por v_F. portanto
dt n = dx n^{3/2}v + S^2/v_F^2 dxn = 0

[pcosme]

I've created a new branch to tackle this issue
cf. commit 4b7b0b8

[pcosme]

I'm closing this issue as it is no longer a priority

[pcosme]

Now that we have @ifgrd26 on the team to tackle the heat exchange I'll reopen this issue.

Furthermore, look what i just found out at https://arxiv.org/abs/2010.04984 just submitted on 10 Oct 2020

Theoretical analysis of injection driven thermal light emitters based on graphene encapsulated by hexagonal boron nitride
V Ryzhii, T Otsuji, M Ryzhii, V Leiman, P P Maltsev, V E Karasik, V Mitin, M S Shur
We develop the device model for the proposed injection (electrically) driven thermal light emitters (IDLEs) based on the vertical Hexagonal Boron Nitride Layer/Graphene Layer/ Hexagonal Boron Nitride Layer (hBNL/GL/hBNL) heterostructures and analyze their dynamic response. The operation of the IDLEs is associated with the light emission of the hot two-dimensional electron-hole plasma (2DEHP) generated in the GL by both the lateral injection from the side contacts and the vertical injection through the hBNL (combined injection) heating the 2DEHP. The temporal variation of the injection current results in the variation of the carrier effective temperature and their density in the GL leading to the modulation of the output light. We determine the mechanisms limiting the IDLE efficiency and the maximum light modulation frequency. A large difference between the carrier and lattice temperatures the IDLEs with an effective heat removal enables a fairly large modulation depth at the modulation frequencies about dozen of GHz in contrast to the standard incandescent lamps. We compare the IDLEs with the combined injection under consideration and IDLEs using the carrier Joule heating by lateral current.
The obtained results can be used for the IDLE optimization.

So it seems that we are on the right track 😃

[pcosme]

At commit 75d869b Joule heating was implemented and tested, one clearly see the temperature rising on the left side

MOVIE_velocity_stream_S.30.00vF.5.00vis.0.030odd.0.000l.0.000wc.0.00therm.0.30.mp4