if you have a Matwhorks Matlab license, you may use the "nlinfit" function

http://it.mathworks.com/help/stats/nlinfit.html

you can use "Statistica"

Thank you Prof.Giuseppe Bianchi and Prof.HAYDER A. ABDULBARI

you can use the suitable package for best curve fitting. When you put the data betwwen the variables it automatically show the best fit curve and equation of correlation. you can also use the microsoft exel as a simple tool.

Dear Prof. Jai Kishan,

                                        I just have a word of caution which is whenever you run regressions use the PROBIT procedure for which there are a number of packages. That way you can improve upon the quality by improving the Probabilities of various specifications. SKM PhD QC FEPS(D)

Prof.Shailesh and Prof.soumitra. thank you. But when submit a research paper will the functionality of excel tool

Suseel!  the correlation or the model that is based on experimental data may be new or modified old one.  There are lot of software available that can do this job for u.  For example; as in ur concern Nu = f(Re, Pr, y/d), the dependent variable (Nu) is a function of independent variables (Re, Pr, y/d).  Use SPSS, datafit,  Table curve, and many more.  The model can be linear regression based or nonlinear regression based.  The weight as well as the coefficient for all RHS independents will be generated by software.  You have the options for many sensitivity, formations and suits to get the most optimum correlation.   This is all, as discussed, a parametric based.   However, you have the option to find model for experimental data  with NON-PARAMETRIC  based (like ACE) too.  Good Luck

Mr.Sussee,

First, you need to properly define the experiment,

1-Define dependent-independent variables.

2-Define boundary conditions (if exist).

3-Use critical thinking to create a simple equation, that might be correct.

4-Measurement should be done with high level of quality control.

5-Determine the type of regression (Multiple or Single) in your case multiple.

6-Identify what type of multiple regression (linear or non-linear).

7-Use the appropriate method.

8-Determine error percentage. 

These steps are normally done with a plotting software, but all the math work is personnel.

Regards,Hamam

There is an excellent text book which shows how to use matlab in this issue. The author of this book is Chapra, D. Also, in Excel program there is the trend line function which can provide prediction for limited cases but it is powerful tool. The most easier software in this regard in minitab program. Finley remember that you can get a polynomial correlation in most of these. If you need a a specific type of function Curve Expert program may help also.

Excellent and lucid reply for a researcher's query, Prof. Farag Shuaeib. Thank you so much.

And a basic researcher too and those who follows this query along with me will find the exact reply, Prof. Maqsood Iqbal. Am so much touched by the reply.

A step wise presentation of a reply can only be given by a researcher who stands in tehe foot of another researcher. I bow down in front of your expertise, Prof. Hamam Awad

There is no readymade answer to this question. You have to try different correlation models and settle on one that has the best index of correlation. It is normal to seek power law for correlation in heat transfer. This should lead multilinear regression in log-log form.

In heat transfer studies, usually, multiple linear regression model is used to predict the correlation from the experimental data sets. These correlations can be obtained using software tools also . One of the suggested software tools is Minitab.

There is a lecture series of NPTEL on "Linear Regression Analysis and Forecasting" by Prof.Shalabh , IIT Kanpur, available in youtube. This one addresses the basic concepts of simple and multiple linear regression model as well as the software implementation part. You may watch this lecture series to get an overall idea about predicting the correlation.

Thank you Prof.Muneeshwaran

You can provide the input in Xuru.org website and select the corresponding regression formats. You can get the equation.

There are different advanced logarithm software could be used in this issue. I recommend Eureqa or GeneXpro. Both software produce full statistical report regarding the generated models. There are awesome. They safe my time during my PhD research.

Dear Alzahrani,

Thanks for taking your time to reply. However, I have one more clarification needed to be answered. Are they User-friendly and free softwares?

Suseel Jai Krishnan. S

Dear Krishnan,

Yes, they are both user-friendly. There are not free; however, you can get a trial version for one month.

I. In the application of dimensional analysis to transport phenomena (engineering), dimensionless quantities are often correlated by means of empirical correlations that often follow (or closely follow) power laws. Power laws possess the attribute of scale invariance. From that follows a straight-line log–log plot, what often helps to identify a power law trend. Power laws often provide fairly good correlations with a minimal number of parameters.

II. For instance; for forced convection, we may quite generally express the Nusselt number as a function of both the Reynolds and the Prandtl numbers for great diversity of conditions, namely geometric, with simply 3 parameters: Nu = k·Rep·Prq. It may be even possible to further reduce the number of degrees of freedom by means of a predetermined constant (possibly the unit: p + q = cte. = 1), to impart a compensated 'weight' to each contribution. It may be convenient to take the parameters as time varied.

III. This very limited number of degrees of freedom may contribute to stabilize numerical procedures, namely those related with real-time parameter estimation, with real-time optimization, and with adaptive control; particularly if processes occurs concurrently, and if no prior 'learning phase' is reserved for just parameter estimation. Imposed (limited) disturbances may also play a stabilizing role. Both real-time optimization and with adaptive control may be suited to benefit from concurrent parameter estimation.

IV. The least-squares fitted parameters obtained after the logarithmic-linearized correlation are biased for the exponential correlation, but typically close to the unbiased estimates if obtained directly from the original power-law correlation.

V. The recursive least squares algorithm (RLS) allows for (real-time) dynamical application of least squares (LS) regression to a time series of time-stamped continuously acquired data points. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. RLS is the recursive application of the well-known LS regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. For RLS with forgetting factor (RLS-FF), acquired data is weighted according to its age, with increased weight given to the most recent data. No prior 'learning phase' is required.

VI. Application example ― While investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS-FF algorithm to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer, while giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The proposed (adaptive) control algorithm compared favourably with PID. The power dissipated by agitation was accessed by a torque meter (pilot plant). Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):

Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...