you are absolutely correct there is a minus sign (i solved it with a minus sign)... and if i put dirac delta function doesn't that mean that the solution is in terms of a green's function?
Yes, you are 100% right. I used Fourier series, and it worked out.
The boundary conditions I used are: T(0,t)=T(L,t)=0 and T(x,0)=0.
And after performing Fourier series, i got a homogeneous differential equation where i used separation of variables.. At the end i got an integral dependent on 2...
ha, i meant partial diff equation (tried to fix the title didn't know how to)
So separation of variables and Fourier transform? Or just separation of variables?
coming to think about it, using taylor series is pointless because the integral of a gaussian in known...
I still need some guidance on how to approach it though
Yes, this is exactly what the equation looks like.
I've never used mathematica... Context of problem: we have a pulsed laser that is heating up a pexiglas sheet, we want to determine by how much does the temperature rise per pulse. The exponentials refer to the heat source (laser) in gaussian...
ρCp (∂T/∂t) + k (∂2T/∂x2) = exp(-σt2)exp(-λx2)φo
i have this equation... i was thinking of taylor series expansion to solve it and make it easier...
any ideas on how to solve?
Thanks for the help ! But that's not what our purpose is... if anything we are trying to achieve a heating load without deforming the plexiglas sheet.
After having a long discussion with my prof., he bashed the formulas we used above... and now I'm currently working on deriving the formula for...
Brilliant! I will definitely try both ways out. I do believe that for my case I don't need to do boundary conditions, but it is still fun to see how that works out!
Thank you for the help, i really appreciate it!
alright Andy, I got it. But my prof. seems to be certain it will heat up!
I will definitely let you know what happens on monday.
Thank you for the help
It definitely would, but for all i know it would cost more than the prof is willing to put.
Also, i think finding an attenuator with the required characteristics is a bit hard. I'll re-look into it for sure.
Well it really isn't up to me.
Is there any way you can explain your point about the calculations not being applicable for what I have as characteristics for the laser?
Again I appreciate your replies and helpful insights!
Thank you
I was thinking that the heat flux would be equal to the intensity of the laser multiplied by the exp(-ax). Where a is the absorption coefficient of plexi and x is the thickness.
Thoughts?
A pulse time (not rate) of 20 ns and pulse energy of 500 mJ gives a peak power of 25 MW (check your units). But that's not comparable to a 25 MW continuous output- to do that, you need the pulse repetition rate- say it's 10 Hz. Your time-averaged power output is then 5 W.
Does this help?
Yes...