Consider a layer of insulation installed around a steam pipe. The radius of the pipe is R1 and the thickness of the insulation is R3-R1.The stream is maintained at a temperature TW and the air surrounding the insulation is at a temperature To and flows cross wise over the pipe. The air is flowed over the steam pipe at high enough velocity so a thermal boundary layer develops over the surface described by a heat transfer coefficient h. Required:
Beginning with the heat equation, calculate the total quantity of heat being conducted per unit time (heat flow) through the insulation, Q (units: energy/time).

Aplate clutch has a single pair of mating friction surfaces 250-mm od by 175-mm id. the mean value of the coefficient of friction is 0.30, and the actuating force is 4 kn. a) find the maximum pressure and the torque capacity using the uniform-wear model. b) find the maximum pressure and the torque capacity using the uniform-pressure model.

Burgers vector is generally parallel to the dislocation line. a)-true b)-false

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)?