Write out in detail all the terms for \(\tilde{\tau}: abla v\) in rectangular Cartesian coordinates.

Now assume a Newtonian fluid; use the generalized version of Newton's law of viscosity for the stress tensor \(\tilde{\tau}\) and expand \(\tilde{\tau}: abla \boldsymbol{v}\). Thus derive the expression for the viscous dissipation rate in Cartesian coordinates.

How does it simplify for a simple-shear-driven flow between two rectangular channels?

How does it simplify for a pressure-driven flow between two parallel channels?