Sankar, it appears that the discussion is getting unnecessarily complex. For simple linear fits (y = mx+C) or power law such as the Nu = f(Re, Pr, A) correlation, Excel is best. It is easy to use and gives you the fitting equation as well as the superimposed curve. Only for more complicated cases like multiple non-linear regression, you need to go for Datafit etc. All the same, while you are on the job. I suggest you familiarize yourself with Datafit. It will be a useful tool in your bag.

correlation for the Nusselt number have been developed extensively during the last century. You only need a good text book.

But if published correlations do not fit your experimental conditions, you can directly use a FCD software. The convection heat tranfeer coefficien, h, is only a human artifact, it does not exist in Navier-Stokes equations. Conversely, nowadays you can find correlations by using CFD software.

Hi Federico, Thanks for your reply and suggestion. Could you pls suggest a open CFD software. I am having numerical data for which the correction has to develop. Pls suggest some ideas...

I understand the non-dimensional quantities Nu, Re and Pr. What do you mean by A?

To answer this question satisfactorily, it will be useful to know the geometry studied and the Re range of the flow. If you wish to extract a correlation from data that you have (which I presume are experimental data), you just need curve-fitting software, of which a mind-boggling variety is available on the internet as free download.

Your correlation will most probably be non-linear. You can linearize the equation by taking logarithm (for example: log Nu = Log C + m log Re + n log Pr), then use a linear regression analysis. You know sets of values Nu, Re and Pr. This regression will give you the constant C, and powers m and n.

Software like Datafit will give you these values directly without requiring you to first linearize.

I am surprised that there is no one in your college to help you with simple and trivial answers such as these!

Addendum to my earlier answer. If you have data only for one single fluid, your Pr is fixed (i.e., not a variable). In that case your correlation will appear as Nu = C1 x Re**m, the Pr**n having been absorbed into the constant C1. Since the power of Pr is typically 1/3 for a vast majority of situations, you can extract C from C1 thus: C = C1 /Pr**1/3.

In case your Pr has varied through a change of mean temperature in different experimental runs, you can use the data fitting approach I pointed out in my earlier post.

Sorry Sankar,

My institution provides me with a well known software, I cannot suggest any open CFDsince Inever tried them.

Hi Vijay, Thanks for the detailed answer and suggestions. I have my numerical data for which I need to fit correlation. In my query, A is aspect ratio.

Thanks Federico for your response....

In agreement with Vijay Raghavan, I suggest you to perform curve fitting. You can use previous related studies to find a good function and then adjust its coefficients using carve fitting methods or a software.

@Mohammad: How about the Datafit software to fit my numerical data to develop correlation relation? Your suggestions are highly appreciated.

Dear Sankar,

Frankly, i'm not familiar with Datafit software. I have usef Matlab functions, but if the initial function is very complex i use optimization methods such as particle swarm optimization (PSO) algorithm or genetic optimization method.

I have PSO as a function of matlab. If you have Matlab software, carve fitting will be easy. if you can expose the initial shape of your carve fitting function, maybe we could help you.

Best regards.

Sankar, it appears that the discussion is getting unnecessarily complex. For simple linear fits (y = mx+C) or power law such as the Nu = f(Re, Pr, A) correlation, Excel is best. It is easy to use and gives you the fitting equation as well as the superimposed curve. Only for more complicated cases like multiple non-linear regression, you need to go for Datafit etc. All the same, while you are on the job. I suggest you familiarize yourself with Datafit. It will be a useful tool in your bag.

Dear Sankar

I approximated some relationships for the heat transfer coefficient of a cuboid source mounted on orthotropic substrate that from numerical simulation results.

I used design of experiment (Tagushi approach) to determine the parameter mutual impacts (6 different ones ) and their interactions.

I added complementary simulations (centered variable technique) to take into account the non linearity of each parameter profile.

To fit the simulation results I don't recommend excel software, I will prefer tablecurve software which provides numerous functions and allows to better analyse fitting performances.

The final "long" expression is "really" accurate for random set of the parameters and can be easly implemented in excel.

Then from DOE equation you could establish a more conventional relationship.

Best Regards.

Dear Eric monier-vinard, Thanks for the wonderful response...Hope it would be very useful information for my goal....

Thanks and Regards, Sankar

Sankar Mani, Sorry if some answers cause you to pull out your hair in desperation. You asked a simple question and get answers that I am sure you cannot use.

Many answers seem to show the correspondent's erudition, rather than the primary purpose of helping the person who has the doubt. That in fact seems to be the trend in this Forum and I am sure the purpose of Research Gate is not that.

All I ask is "let your desire to help drive you, not the RG score!"

Vijay, I am not here in this forum to increase my RG score. I am matured enough to choose the best answer suits to my question and at the same time I know that all the answers can not be implemented to my problem. But it is always better to know the different ways of solving the problem and pros and cons of the existing methods...In that sense only I replied to Eric monier-vinard response....

Sankar, in choosing the proper length scale in you dimensionless groups is worth thinking about. The conventional ones are not always the best choices. For example, if you have a cavity in which you wish to hold the height fixed and want to see the influence of the gap width on your results, then choosing the height as the length scale in bout Ra and A, leads to a situation in which A is directly proportional to the gap width and Ra stays constant when A is varied. For an example see the paper on my list.

Heat Transfer Through a Double Pane Window

Seppo A. Korpela, Yee Lee, Jerry D. Drummond

Journal of Heat Transfer 08/1982; 104:539.

Dear Shiva,

Thanks a lot for sending the info. I tried through the excel and got good fit. Using the existing correlation, I generated the data and made a fit through the excel and got amazing accuracy. I hope your data file would definitely add more information for my query. Once again thanks for sharing such a useful info.

interested