Consider laminar flow between two parallel plates. The plates are electrically heated to give a uniform inward wall flux \(-q_{\mathrm{w}}\). Set a mesoscopic model to find the cup mixing average temperature in the system as a function of the flow direction. This will be needed for the temperature profile calculations in the asymptotic region.

Now propose that the temperature is the sum of a linear function of flow direction and some unknown function of the cross-flow direction. Use this in the governing differential equation and solve for the temperature profile in the asymptotic region.

Show that the Nusselt number is 140/17.