Incompressible flow doesn't certainly implies that density is constant..!

Hi Guys , this time I have something very interesting to share with you all ..........Do you know incompressibility of fluid it doesn't  mean that  its density  is constant , are u guys shocked ?
When we talk about incompressibility its about the flow we are referring to and when we say that the flow is incompressible it means that , if we will going to follow a packet of fluid inside the domain of the flow its density will not change.

Let me explain you with an example , consider the fully developed laminar flow in a pipe shown above; now the shear rate is more at the wall and its zero at the center, as a result energy will dissipate in the form of heat which will increase the wall temperature  while the  temperature at the center will be less . So , density will be higher at the center and low at the walls but the flow will be incompressible if we are following a certain packet of fluid and its density doesn't change through out the path it travels.