Discussion Forum

Something worth some consideration may be manipulation of the Arrenhius Equation algebraically so that the terms have the similar look of a linear equation.

We have had some success in using the following Arrenhius form:


k = A * e^(-Ea/R T)

ln(k) = -(Ea/R) ( 1/ T ) + ln(A)


Similar to:
Y = M * X + B


but care must be taken to use the absolute temperature scale (Kelvin or Rankine) so that solutions at 0degF or 0degC can be properly evaluated.

Hi Robert,

were you successful in finding the solution to your problem? I have a similar problem, where I cannot access a dependent variable from a subdomain and use it in a global equation.

Thank you,

Aleksandra

Here is what I have done...

Use the PDE, Coeffient Form (c)
Select the subdomains that will be active for the calculation... In Roberts case, the tissue...

Set f (source term) to A*exp(-deltaE/(R*T))
Set da (damping/Mass coefficient) to 1
All other variables to 0

I use Omega for c when I initiate the physics in the modeler...

Your equation will then be dOmega/dt = A*exp(-deltaE/(R*T)) or rearranged dOmega = integral (A*exp(-deltaE/(R*T)),dt) - see attached...

Thank you!

Make sure your Temperature variable is the one from the bioheat equation (Tb) or whatever physics you are capturing temperature from... T or T2 or Tb....

One problem that I have run into with this approach is that the numerical value for Omega can be so large as to cause problems. The most significant problem is that there is a huge Omega gradient that results. Yet typically, the mesh that is being employed has been optimized in terms of element size and spacing, for the thermal solution, and not for the solution of Omega. This causes inaccuracies in the solution for Omega.

One way to improve this is limit the magnitude of Omega. Since Omega greater than 5 is indicative of cellular destruction and destruction is not reversible, there is no need to keep accumulating damage much beyond 5 and create a huge Omega gradient that can lead to inaccuracies.

One way to implement this is to set f (source term) to a variable which is equal to a user-defined function rather than to A*exp(-deltaE/(R*T)). The function can be imported as a look-up table from Excel or matlab. I use excel to compute Omega from 273 K to the upper limit of my temperature range. Then I edit the table to clip the value of Omega to say 7 and import this modified table into COMSOL.

Couldn't you do the same thing by limiting f to calculating f up to 7.... (f<=7)(A*exp(-deltaE/(R*T))) that way it will only sum if the f term is less than or equal to 7.

Hi Jason,
I need help! I am trying to apply an Arrenhius damage integral DURING the solution of an thermal ablation problem using the heat Transfer and PDE coefficient form Modules (T and u are the dependent variables). In the end of the simulation, it appears the following message:
"Error:
Failed to find consistent initial values.
Out_of_memory_LU_factorization
Last time step is not converged."
Any help is WELCOME!
Best regards,
Cleber

Have you ran the simulation with the PDE, coefficient Form(c) disabled? Does the simulation run without the PDE?

It has been a while since I implemented this but I do not remember a u variable.... Only Temperature. What are you using for Ea and A?

-Jason

Hi Jason!
I have committed a mistake: I forgot to inform the description of fluid mechanics on my simulation. Actually, I am using the heat transfer, PDE coefficient Form(c) and incompressible Navier-Stokes modules. The u variable describes the fluid velocity in this last modality of Physics.
The values for Ea and A are:
Ea=6.65x10^5 J/mol;
A=1.98x10^106 1/s

The link below illustrates the window of the software COMSOL:
www.comsol.com/community/forums/general/download/file/12973/error%20Failed%20to%20find%20consistent%20initial%20values.JPG

Sincerely yours,

Cleber Pinheiro

A citation only:
The variables used in the simulation are:
T - HEAT TRANSFER MODULE;
u - VELOCITY OF THE FLUID;
u2 - VARIABLE FOR PDE COEFFICENT FORM (c).

The damage integral is defined as u2=integral(A*exp(-Ea/(R*T)dt). Moreover, one solves the equation d/dt(u2)=A*exp(-Ea/(R*T). I use u2 to designate Omega. The source term f is equal to A*exp(-Ea/(R*T))
The boundary conditions are set up as follow:
1) ZERO FLUX;
2) INITIAL VALUES: u2=0 and d/dt(u2)=0.
Best Regards,

Cleber Pinheiro

See attached reference, maybe you can reduce your problem to an algebraic equation.

Have you been able to run the thermal/fluid interaction without the Arrenhius damage integral? If the thermal/fluid interaction does not solve, that may be where your error is coming from.

Hi Jason!
yes, I run the thermal/fluid interaction without the Arrenhius damage integral (NO PROBLEMS in this simulation). So, the thermal/fluid interaction is independent of the damage integral.

Best regards,
Cleber Pinheiro

Hello all,
Here's something that pertains to discussion! The problem of convergence was resolved. Only I modified the mesh characteristics. I used the mesh type "fine". However, the arrhenius damage integral assumed negative values in COMSOL MULTIPHYSICS. What's this mean? What is the meaning of these values​​?
Sincerely yours,
--
Cleber Pinheiro

Couldn't you do the same thing by limiting f to calculating f up to 7.... (f<=7)(A*exp(-deltaE/(R*T))) that way it will only sum if the f term is less than or equal to 7.

Hello,

I know this post is kind of old, but can you elaborate on this approach?

Thanks,

EH