2. Consider a steady laminar flow between two parallel plates. The plates are separated by a distance L which is very small in comparison to the length and width of the plates. The lower plate is stationary and the upper plate moves at a constant speed V1. The lower plate is maintained at temperature T0, while the upper plate is maintained at temperature T1. a) Develop an expression for the temperature profile at a steady state between the plates. Assume the flow is fully developed (i.e., no dependence of velocity or temperature in the flow direction) and all physical properties are constant and there are no body forces acting on the fluid. Do not neglect viscous heating. b) The clearance space in a lubricated bearing can be considered to be bounded by two parallel plates. The surface velocity of the shaft V1=100ft/sec, and the oil viscosity =30lb/hrff. The thermal conductivity of the oil K=0.076Btu/fthrF and the gap is 0.002. If the temperature of the shaft is maintained at 150F and the bearing surface is at 100F, calculate the rate of heat transfer to the shaft and to the bearing