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Problem with Heat Source temperature dependence
Posted 2013年12月30日 GMT-5 08:44 Heat Transfer & Phase Change Version 4.3b 2 Replies
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Hello,
I am trying to simulate pulsed laser heating of silicon wafer. I am using heat transfer module. My problem is 2-dimensional - my wafer is a cylinder and laser is above the center of it placed perpendicular to the surface, so I use cylindrical coordinates. I use Heat Transfer in Solids physics. I have problem with Heat Source. I want it to be temperature dependent. Here is an expression i would like it to be, but I don't know how to obtain it:
Q(r,z,t)=exp(-integral(alpha,z',0,z))
alpha is an absorption coefficient - material property, which I defined by myself. It is temperature dependent but since in every point of my silicon wafer temperature varies, it makes alpha dependent of spatial coordinates r and z.
alpha = alpha(T(r,z))
In other words after every time step I need alpha to be integrated over z coordinate from 0 to z(respectively for each r and each z) and based on that i want to 'upgrade' my Heat Source Q(r,z,t).
I hope i was clear enough and you guys are able to help me
Andrzej Rudkowski
I am trying to simulate pulsed laser heating of silicon wafer. I am using heat transfer module. My problem is 2-dimensional - my wafer is a cylinder and laser is above the center of it placed perpendicular to the surface, so I use cylindrical coordinates. I use Heat Transfer in Solids physics. I have problem with Heat Source. I want it to be temperature dependent. Here is an expression i would like it to be, but I don't know how to obtain it:
Q(r,z,t)=exp(-integral(alpha,z',0,z))
alpha is an absorption coefficient - material property, which I defined by myself. It is temperature dependent but since in every point of my silicon wafer temperature varies, it makes alpha dependent of spatial coordinates r and z.
alpha = alpha(T(r,z))
In other words after every time step I need alpha to be integrated over z coordinate from 0 to z(respectively for each r and each z) and based on that i want to 'upgrade' my Heat Source Q(r,z,t).
I hope i was clear enough and you guys are able to help me
Andrzej Rudkowski
2 Replies Last Post 2014年1月14日 GMT-5 04:20
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Posted:
1 decade ago
I believe there is someone, who can easily solve my problem. I have to finish my bachelor thesis in a week and I am in a dead end because of that. Please, help me.
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Posted:
1 decade ago
Dear Mr. Rudkowski,
let's call your integral u. Then it is equal to the conditions uz=alpha and u(r,0)=0. So, I suggest to add a Coefficient Form PDE, to be found in the list of Mathematics interfaces. You set all coefficients to 0, except of beta2=1 and f=alpha. This equals the equation uz=alpha. Then you add a Dirichlet boundary condition for the lower boundary for the boundary condition u(r,0)=0. Now you can use u as a source term in your actual physics.
I hope this helps.
Regards
Bettina Schieche
let's call your integral u. Then it is equal to the conditions uz=alpha and u(r,0)=0. So, I suggest to add a Coefficient Form PDE, to be found in the list of Mathematics interfaces. You set all coefficients to 0, except of beta2=1 and f=alpha. This equals the equation uz=alpha. Then you add a Dirichlet boundary condition for the lower boundary for the boundary condition u(r,0)=0. Now you can use u as a source term in your actual physics.
I hope this helps.
Regards
Bettina Schieche