Fitting Data to a Prescribed Equation

I have an equation of the following form

Nu=A*(0.75+0.013*ALFA)*(RE)^(m)*0.711^(1/3)

Where ALFA and RE are a set of prescribed values

ALFA=0 5 10 15 20 25 Re= 200000 300000 400000 500000

Nu is a set of values obtained from simulations

I know that my equation should look like the one previously shown, I would like to solve for the coefficients A and m so my prescribed values validate the equation

Any help please?

[dpb]

How do you expect to use the resulting correlation; as function which variables?

You use nonliner fitting; convert the measured data to values of the correlation at the points for which you have the values at those points for which you have the data.

You may have issues of correlation/estimation depending on the locations of those points; you've not given that much info; try it and find out what happens...

As for which tools to use for the fitting, depends on which toolboxes you have; there are routines in either the Curve Fitting or the Statistics TBs or you can use the fminsearch routine in base product having neither of the above....

[Abdallah Samad]

Hey thank you for your answer. I do understand the procedure you outlined but I have no idea how to write in MATLAB language.

THe figure shows the results of simulations I got. and on top of each table I put the associated correlations to which I would like to get my coefficient A and B.

[Kaushik Lakshminarasimhan]

Do the entries in the table correspond to values of Nu?

[Abdallah Samad]

Yes they do!

[dpb]

But you've still not told us which toolsets you have available to use...also, attach data as text so somebody could do something with it rather than just look at it.

[dpb]

Also, please clarify the equation -- is the power term at the end

RE^[m*Pr^1/3]

or

(RE^m)*Pr^1/3

or yet some other grouping? My initial fitting with the first isn't promising at all...

[Abdallah Samad]

Hi please attached the vales within the PDF As for the power term, its actually the second one you wrote Thank you very much !

Answer 1

[Nicolas Schmit]

If I am correct, what you are trying to do is to fit a nonlinear model to a data set. The MATLAB command to do that is fitnlm. Look here for an introduction to nonlinear regression.