free convection
 

Do anybody know the correlations to find the HTC for free convection inside the pipe. I have a pipe with stationary gas inside the pipe and need to plug the heat transfer coefficient in terms of temperature to calculate the surface temperature (inside surface). any online link for the empirical relations ?

I don't think you will be able to find any empirical correlations for this since is not free convection, the gas on the inside of the pipe would have no cooling and continue to raise in temperature unchecked.