Not my specialist field but I tried putting literally ' Nusselt number for a developing turbulent flow in the entrance region for a duct ' into Google and obtained some useful and relevant information .
The Nusselt number is the ratio of convective to conductive heat transfer in a flow. It's fundamentally defined as:
The Nusselt number depends on the convection flow's parameters, sometimes summarized in the convective coefficient "h". Your options are to calculate the convective coefficient for your application, or sometimes correlations are developed which use the flow parameters (such as Rayleigh number, forced vs. free convection, geometry aspects, etc.)