A5cm od and 0.5cm thick copper pipe [k=386w/m.°c] has hot gas flowing inside at a temperature of 200°c with a heat transfer coefficient of 30w/m2.°c. the outer surface dissipates heat by convection into the ambient air at 20°c with a heat transfer coefficient of 15w/m2.°c. determine the heat loss from the pipe per meter length

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)?