Consider flow in between two parallel plates located a distance H from each other. Fluid flow is driven by the bottom plate moving to the right with a velocity of U (note, NO pressure gradient). The top plate has a fixed temperature of TT and the bottom plate has a temperature of Tb. Starting with the governing equations for incompressible flow, find the velocity profile and the temperature profile for the flow in between the plates. In addition, what is an expression for the heat flux at the bottom plate (assuming a thermal conductivity of k)

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?