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12-Amethyst

What could I have been overlooking

I am trying to solve the main equation of the attached article. I can easily reproduce table 3 of the article but am not able to reproduce table 4 and 5. Would someone be so kind what to look what could cause this behavior? Thanks in advance!

ACCEPTED SOLUTION

Accepted Solutions
21-Topaz I
(To:FDS)

Hi,

Forgot to enclose.

7 REPLIES 7
23-Emerald I
(To:FDS)

First, you're carrying units, Mathcad 15 won't deal with units in ode solvers.

Second, you have an undefined variable "D" in the definition of the function D(t,R); that's likely to be a problem too.

Third, D(t,R) needs to be a vector function defining derivatives for rkfixed to work.  I'm pretty sure that yours is a program, not a vector.

12-Amethyst
(To:FDS)

Dear Fred, My excuses I attached the wrong worksheet. But even without units I cannot reproduce table 4 and 5 while I can reproduce table 3

21-Topaz I
(To:FDS)

Hi

The problem is using the units.  Odesolvers only operate on numbers they are not unit aware.

You need to reduce the variables with units to a value only by multiplying by the correct units to do this.

I have used the gm/cm/s unit system so you can see what has been done.

Formula (1) is not unit consistent raising e to a power, the power LambdaDt must be dimensionless quantity in Mathcad

Formula (2) for Lambda has units. D has units and t has units.

function erf with parameters Lambda,D, and t called "error function" is undefined as it is an errer fuinction set it to zero.

I have chosen the gm,cm,s unit system but it depends how the author did it and there is a mix of units

Shown is how to get the solver to work. It is not getting the 2.3 minutes answer and expect this is a unit thing.

Have enclosed Mathcad 14/15 file, and a pdf.

Regards

21-Topaz I
(To:FDS)

Hi,

Needs one more change in equation for f_RT with pressure supplied in torr but needs to be in gm*g/cm^2.

Article answer 4.6 minutes or 276 seconds, this worksheet 282 seconds.

12-Amethyst
(To:terryhendicott)

Dear Terry, thanks for your comments. I made a mistake in my original mail by sending the wrong version. In attachment you will find a version without units. I agree that table 3 where the N2 concentration is changed gives the same results but I cannot obtain the same results for table 4 and 5 where flow and solubility are changed. So I assume I made somewhere a mistake.

21-Topaz I
(To:FDS)

Hi,

Table 4 Line 18  Temp = 27, Q = 0.40, adjusting all values for 27 deg,  I get the right answer.

Have enclosed the erf errorfunction but i am right it is an insignificant quantity.

21-Topaz I
(To:FDS)

Hi,

Forgot to enclose.

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