The heat transfer coefficient for hydrogen flowing over a sphere is to be determined by observing the temperature–time history of a sphere fabricated from pure copper. The sphere, which is 20.0 mm in diameter, is at 80°C before it is inserted into the gas stream having a temperature of 27°C. A thermocouple on the outer surface of the sphere indicates 40°C 97 s after the sphere is inserted into the hydrogen.
1. Assume and then justify that the sphere behaves as a spacewise isothermal object and calculate the heat transfer coefficient.

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)?