Dear Minh,

if you are working with a fully developed laminar regime, it's possible to analytically attack the problem. 

A step by step solution can be found in the Heat Transfer Textbook from Holman (Chapter 5.10 - 4th edition) or in "A Heat Transfer Textbook" from Lienhard & Lienhard (4th edition - Chapter 7.2 p352).

Under the aforementioned assumption, the resulting Nusselt number is 48/11 ~= 4.364

Ps: The Lienhard textbook is free to download. (http://web.mit.edu/lienhard/www/ahtt.html)

Best regards.

Hi Nicolas, thanks for the answer. The flow is assumed to be thermally developing. 

Hi Minh,

when you state that the flow is thermally developing, you're considering a constant heat flux along the tube? Or it is variable?

Greetings.

Hi Nicolas, It is variable as well, so does the temperature. I am trying to calculate local convective at every control volumes along a pipe.

I would suggest you look at the Cengel textbook:

Cengel, Y.A.,2006 .Heat and Mass Transfer:A Practical Approach. McGraw-Hill

Education (Asia), Singapore.

Depending on the Re of your laminar flow you could establish a forced convection, natural convection, or mixed convection (natural+forced) regime.

Then it is necessary to establish the isothermal or uniform heat flux assumption.

If the geometrý of your tube is not uniform, then using the Grashoff number will do the trick (from the below-presented correlations)

For the isothermal case, you can use the Depew & Agust (1971) correlation (See referenced paper below)

For the uniform heat flux, the Morcos and Bergles (1975) correlation.

Both correlations can also be found in page 4-53 from the Heat and Mass Transfer Handbook from the Mechanical Engineering Handbook Series (CRC Press - 1999) (attached to this answer)

Depew, C.A. and August, S.E. 1971. Heat transfer due to combined free and forced convection in a

horizontal and isothermal tube, Trans. ASME 93C, 380

Morcos, S.M., and Bergles, A.E. 1975. Experimental investigation of combined forced and free laminar

convection in a horizontal tube, Trans. ASME 97C, 212.