Asteam pipe 8m long has an external diameter of 100mm and it is covered by lagging 50mm thick. the pipe contains steam at 198°c and the temperature of the atmosphere surrounding the pipe is 18 c. the thermal conductivity of the lagging is 0.15w/mk. the surface heat transfer coefficient is 10w/m2k. assuming the pipe has the same uniform temperature as the steam, calculate the heat loss and the surface temperature of the lagging.

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)?