How do i set the reference temperature for developing region on natural convection
 

i have researching the natural convection inside vertical pipe
flows through the vertical pipe is driven by natural convection force

i am looking for inside surface heat transfer coefficient varying with diameter, length(GrL=3*10^8 - 4*10^10) and Prantdl number(0.7, 20, 2,014).
(wall condition is constant temp)

it is difficult to define reference temperature in pipe.

i made up the central line and apply the line average temperature for ref. temp.

is it make sence for develpoing region. or tell me another ways

thanks for all.

more question
 

also i have gained very high heat transfer coefficient that i establish the high reference temp.

i think it is not make sence for thin, long pipe. it looks something was wrong.