1D heat conduction or two temperature model (ultrashort pulse laser processing)

Hi guys, I am facing a problem of the temperature calculation after a 12 picosecond pulse laser irradiation. I am a new learner of MATLAB so I think that there may be some mistakes in my program though I can run it. cuz the results is not good at all. the function I used is :

dT/dt=D*d^2T/dx^2+alpha*I0*(1-r)/(cp*p)*exp(-alpha*x),

D is the thermal diffusivity with the unit of m^2/s, alpha absorption coefficient /m ,I0 lalser intensity W/m^2 and r reflectivity , cp and p are the heat capacity and mass density of the material . and the IC and BC are: T(x,t=0)=300k; dT/dx(x=0)=dT/dx(x=L)=0, L is the depth of material. and my code is as below:

clear all;
%%%time and space
Xstart=0;
Xend=3e-4;
dx=9.829e-7; % space step
x=Xstart:dx:Xend;
x=x(:);
Nx=length(x);
tstart=0;
tend=50e-12; %end of time
dt=0.5e-12; %time step
t=tstart:dt:tend; Nt=length(t);
%%%physical parameters
D=1.81e-4; % thermal diffusivity
k=400; % thermal conductivity
alpha=21000; % absorption coefficient
I0=1.69e14; %laser intensity
r=0.27; %reflectivity
cp=690; %heat capacity
p=3200; % mass density
f=D*dt/dx^2;
e=dt*alpha*I0*(1-r)/(cp*p);
%
T0=300; %IC
T=T0*ones(Nx,1);
for j=1:Nt-1
if t(j)>12e-12 %after 12ps, laser pulse is over
e=0;
end
B=diag((1+2*f)*ones(Nx,1))-diag(f*ones(Nx-1,1),1)-diag(f*ones(Nx-1,1),-1);
C=T(:,j)+e.*exp(-alpha*x);
%%boundary condition
%left B(1,1)=1;
B(1,2)=-1;
C(1)=0;
%right B(end,end)=1;
B(end,end-1)=-1;
C(end)=0;
T(:,j+1)=B\C; end
plot(t*1e12,T(1,:),'r-');% surface temperature
xlabel('t/Ps')
ylabel('T/K')

thanks for your help and sorry for my poor english :)

Answer 1

[deng]

anyone?

[arnold]

Hi deng, have you ever implemented a two temperature model in matlab? I'd be very interested in it.

[Rajan Jain]

@deng did you manage to correct your program? I understand I am about a decade late to comment on your post, but do you happen to know about the corrections used for nanosecond regime?

I am working on a project which does not consist of ultra-short, but nano-second laser irradiation of composite material.