What Exactly is the Nusselt Number in Convective Heat Transfer Problems and are There Alternatives?

The often used Nusselt number is critically questioned with respect to its physical meaning. Based on a rigorous dimensional analysis, alternative assessment numbers are found that in a systematic way separately account for the quantitative and qualitative aspect of a heat transfer process. The qualitative aspect is related to the entropy generated in the temperature field of a real, irreversible heat transfer. The irreversibility can be quantified by referring it to the so-called entropic potential of the energy involved in the transfer process.