The correlation of the Nusselt number proposed by Dittus and Boelter is appropriate for this profile. Please find the corresponding article attached.

Different empirical correlations are available for different regimes of flow in a duct. Generally a Dittus-Boelter equation is used to validate data for turbulent range. 

You can use the correlation of Nusselt numbe that was proposed by Dittus and Boelter for 2500

The answer to your question depends on several factors. First of all, if you are interested in rectangular ducts (like the one in your picture) you need to provide the aspect ratio of the duct, as it is an important parameter. Based on the aspect ratio you can identify the critical Reynolds number and check whether your flow is laminar, transitional or turbulent. After that you can search for a proper Nusselt correlation. For more information on these you can check:

1) Shah, R. K., & London, A. L. (1978). Lanimar Flow Forced Convection in Ducts: A Source Book for Compact Heat Exchanger Analytical Data. Chapter 7, Academic press.

2) Kakaç, S., Shah, R. K., & Aung, W. (Eds.). (1987). Handbook of single-phase convective heat transfer, Chapter 4. New York, Wiley.

The correlation of the Nusselt number proposed by Dittus and Boelter is appropriate for this profile. Please find the corresponding article attached.

The Dittus-Boelter correlation can be used for:

1) Turbulent forced convection in

2) Smooth circular pipe

In your case, if your geometry is rectangular (as it seems, judging by the attached picture) this correlation is not appropriate. If this is the case, you have to pay attention to the geometry details. Find the channel's aspect ratio (width/height) and then check for this specific aspect ratio the respective Nusselt number, because the Nusselt number for rectangular ducts is a also a function of their aspect ratio. Check the 2 references that I provided in my earlier answer.

If your geometry is circular (smooth) pipe you could use Dittus-Boelter correlation only if your flow is in the fully turbulent regime. But generally is not considered the most accurate, like Gnielinksi's or Churchill's correlation. You stated that you are interested in 2300

Dear Dr.Ali

Thank you for your answer and suggestion.

Based on your knowledge, Is there any more accurate equation than the Dittus-Boelter,s correlation for this problem?

Best Regards.

Dear Mr.Slimani  

Thanks a lot for your answer and suggestions.

As you mentioned, Dittus-Boelter,s correlation is used for  for 2500

 Dear Mr.Arvanitis

I do appreciate your attention to my question and your answers and suggestions.

I calculate the Reynolds Number based on the hydraulic diameter  for a channel  (attached fig.). 

Dear Ms.Kurucz

Thanks a lot for your answer.

you can read Introduction to Heat Transfer, written by Theodore L Bergmann & A.S Lavine

Well ansered @Konstantinos Arvanitis