Question

Correlation between sphere diameter and nusselt number

Answer 1

Nusselt number are given as

where h is the convective heat transfer coefficient of the flow, L is the characteristic length, k is the thermal conductivity of the fluid.

The general formula for the characteristic length is the volume of a system divided by its surface.

A typical use-case is calculating flow through circular tube in order to examine flow conditions (i.e. the Reynolds number). In those cases, the characteristic length is the diameter of the pipe. so in your case L will be equal to diameter of pipe.