Hi,

Natural heat transfer coefficient inside any tube will depend on many parameters like length, radius and more importantly angle inclination of tube (which will be not there in forced convection). As I see in the literature (AL-ARABI et al. (1991)) for uniformly heated case it will depend on inlet and average temperature of tube. The correlation in their (AL-ARABI et al. (1991)) formulation is given in the attached picture. For more detail you may go through their paper (link is given below).

Article Heat transfer by natural convection from the inside surface ...

An experimental investigation on natural convection of air in a vertical channel International Journal of Heat and Mass Transfer

Volume 36, Issue 3, February 1993, Pages 611-616

Nu = 0.9282 Ra0.2035(s/H)0.8972; Re = 0.5014 Ra0.3148(s/H)0.418

Dear Sina Keshavarz

This is very standard problem and you can find in any text book of heat transfer.

Few books are suggested below:

Heat Transfer: A Practical Approach by Yunus A. Cengel

Fundamental of Heat and Mass Transfer by Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine