A thick-walled cylindrical tube has inner and outer diameters of 2 cm and 5 cm, respectively. The tube is evacuated and contains a high-temperature radiation source along its axis giving a net radiant heat flux into the inner surface of the tube of 105 W/m2. The outer surface of the tube is convectively cooled by a coolant at 300 K with a convective heat transfer coefficient of 120 W/m2 K. If the conductivity of the tube material is 2.2 W/m K. Requried:
Determine the temperature distribution T (r) in the tube wall. Also determine the inner-surface temperature.

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)?