Heat flux known as the heat flow rate intensity is a flow of energy per unit of area per unit of time. One method of measuring heat flux is by using a heat flux sensor, or heat flux transducer, to directly measure the amount of heat being transferred to/from the surface that the heat flux sensor is mounted to. You may have noticed that this is proportional to heat transfer rate. However, Mussels number is proportional to heat transfer rate. This implies that both dependent and independent factors in your question are almost the same.
By performing the experiment, i got an enhancement in the Nusselt number ratio with heat flux. This time i am not sured about the physics who support it but i am working on it.