Consider a Couette flow problem in which a fluid of viscosity u is flowing in between two plates. The top plate is moving with a speed of u, and has a temperature of Te whereas the bottom plate is fixed and has a temperature of Tw. In addition, a pressure gradient exists along the length of the plate, in the direction of the flow. Determine the enthalpy profile. Plot it with a suitable choice of numerical values a. for a non-zero pressure gradient and b. for zero pressure gradient and compare the two profiles, commenting on the physical impact of the pressure gradient.