A private company called AFH580S PTY (Ltd) generates electricity and supplies it to the main grid using superheated steam. The company employs cogeneration to meet various heating requirements. The water-steam mixture at the exit from the turbine is condensed and transformed into condensate at a temperature of 210°C. This condensate, with a specific heat capacity of 4.2 kJ/kg oC, is then pumped at a rate of 3.3 kg/s to heating units that provide warmth to the company's offices. Your Chief Engineer has tasked you with calculating the total length of the heat exchanger required by using the effectiveness-NTU method to achieve the following heating of the working fluid:
The pumped condensate enters the annular space of a double-pipe-counter flow heat exchanger, raising the temperature of the working fluid flowing inside the smaller pipe from 25°C to 95°C.
The working fluid flows at a rate of 2.5 kg/s with a specific heat capacity of 4.13 kJ/kg oC. The overall heat transfer coefficient is 0.89 kW/m2 oC. The inner tube of the double-pipe-counter flow heat exchanger has high thermal conductivity. This inner tube is also thin-walled with an internal diameter of 23 mm.