Exhaust gases flowing through a double-pipe heat exchanger at a rate of 0.3 kg/s to be cooled from 400°c to 120°c by water in the annulus initially at 10°c. the inner pipe has a diameter of 33 cm and negligible thickness. the specific heat capacities of the gases and water may be taken as 1130 and 4190 j/kgk respectively, and the gas and water heat transfer coefficients are 150 and 665 w/m2k. find the heat exchanger length required when the cooling water flow is 0.4 kg/s, (a) for parallel flow and (b) for counter flow.

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)?