Hi,

I guess that x and y are some additional dimensionless numbers... What is your problem exactly ? Do you seek a method to fit that expression, or did you already try do it unsuccessfully ?

Anyway, you can take the log of the expression, and write it for each experimental point you have (say x_n, y_n, Re_n, Nu_n). You get an overconstrained system of many equations (one per point) with 3 unknowns a b c.

There remains to look for the best triplet (a,b,c) matching this system approximately. The operator "\" in MATLAB for example can do that in a single line for you.

Note that Nu does not necessary expresses as a power law of the other dimensionless numbers. If the above method fails, it could be an indication that

this is the case for you.

Hope this helps.

You have to adopt regression technique either linear or nonlinear to obtain the equation in the desired form with powers.Then you have to check SD whether is within limits are not before accepting it.

Observe that the equation for Nusselt developed by the earlier authors for free convection with pure fluids is mostly of the structure Nu = C Ra**a* Pr**b. If you wish to develop an equation for a new geometry or with a new fluid for which the existing equations are not applicable, u have to identify from the experimental data, the parameters influencing the value of Nusselt. Include those parameters that you think are important and undertake regression analysis (see any numerical methods text book) with the inclusion of Ra and Pr. Since most of the experimental data involving heat transfer coefficient are non linear, u can use softwares that are readily available in the net.

Thank you professor sharma.

If you have more than two parameters for correlation (Nu=C Re^a Pr^b. Usually do the following, for given value of X, try to relate Nu=f(Re, Pr) as explained by Sharma and others. Repeat the procedure for more values of X. Then try to correlated C with X.

You should convert it to logarithmic form, for example:

Nu= C . Re^a . Pr^b .

So it can be Ln (Nu) = Ln (C) + a Ln (Re) + b Ln (Pr)

So you should convert all values of Nu, Re, and Pr to Ln (Nu) and Ln (Re) and Ln (Pr). These converted values will be the input to any regression software as data fit program

So the obtained correlated formula will be in the linear form Y = a X+ b Z + g

these constant will be used but C= exp (g)