TTM (two temperature model) for ultra-fast laser ablation

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Hello friends, I want to develop TTM (two temperature model) for ultra-fast laser ablation process. Frist laser gives the energy to the electron and the electron heated up. Now, this electron gives it energy to ion grid and relax quickly. The temperature rise in the electron and lattice can be represented by the Coupled differential equations. For solving the differential equation, the same temperature before the interaction with the laser pulses was assumed for both electron and lattice subsystem so the initial condition were given by Te(x,t=0)=Tl(x,t=0)=T0=300k but I don’t know how to give boundary condition.

I attached my model,PDE and boundary condition. if some one knows how to give this boundary condition in the coefficient form of PDE interface then let me know. For simplicity purpose I did not put thermodynamic parameter calculation part.



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