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arnair811-Visitor
1-Visitor
March 6, 2019
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Help needed in obtaining steady state volume fraction profile

  • March 6, 2019
  • 1 reply
  • 4846 views

Hi,

     I need to solve this equation to get an expression for volume fraction, phi (x). For the given constants, phi (x) vs x should look similar to that in figure. Kindly check attachment. I tried to solve it symbolically but it keeps showing an error.

 

Regards

Best answer by Werner_E

.) Don't use and define a range for the independent variable x in front of the calculation- Just use it for plotting.

.) You can't solve for a function, so use just Phi and not Phi(x)

.) There is no closed analytic solution to your equation. That means that the symbolic solver is useless here. Just use the numeric solver and turn the solve block into a function of x as shown below:

B.png

1 reply

W
Werner_E25-Diamond IAnswer
25-Diamond I
March 6, 2019

.) Don't use and define a range for the independent variable x in front of the calculation- Just use it for plotting.

.) You can't solve for a function, so use just Phi and not Phi(x)

.) There is no closed analytic solution to your equation. That means that the symbolic solver is useless here. Just use the numeric solver and turn the solve block into a function of x as shown below:

B.png

    A
    arnair811-VisitorAuthor
    1-Visitor
    March 6, 2019

    Hi,

    Thanks a lot Werner. I have one more question. This solution is at steady state (t= infinity). To understand phi (x,t) vs x for different time t, one needs to integrate the expression (please check pg 2 of mathcad file). Could you please tell me how to go about doing it?

     

    Regards

    W
    Werner_E25-Diamond I
    25-Diamond I
    March 6, 2019

    Obviously a partial DE. But you are using Phi as variable as well as as function of x and t. You should clear this situation before you go on.

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