Along rod of 60-mm diameter and thermophysical properties rho= 8000 kg/m3, c= 500 j/kg·k, and k= 50 w/m·k is initially at a uniform temperature and is heated in a forced convection furnace maintained at 750 k. the convection coefficient is estimated to be 1000 w/m2· k. what is the centerline temperature of the rod when the surface temperature is 550 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)?