Optimum temperatures in a shell and tube condenser with respect to exergy

This paper focuses on evaluation of the optimum cooling water temperature during condensation of saturated water vapor within a shell and tube condenser, through minimization of exergy destruction. First, the relevant exergy destruction is mathematically derived and expressed as a function of operating temperatures and mass flow rates of both vapor and coolant. The optimization problem is defined subject to condensation of the entire vapor mass flow and it is solved based on the sequential quadratic programming (SQP) method. The optimization results are obtained at two different condensation temperatures of 46 °C and 54 °C for an industrial condenser. As the upstream steam mass flow rates increase, the optimal inlet cooling water temperature and exergy efficiency decrease, whereas exergy destruction increases. However, the results are higher for optimum values at a condensation temperature of 54 °C, compared to those when the condensation temperature is 46 °C. For example, when the steam mass flow rate is 1 kg/s and the condensation temperature increases from 46 °C to 54 °C, the optimal upstream coolant temperature increases from 16.78 °C to 25.17 °C. Also, assuming an ambient temperature of 15 °C, the exergy destruction decreases from 172.5 kW to 164.6 kW. A linear dependence of exergy efficiency on dimensionless temperature is described in terms of the ratio of the temperature difference between the inlet cooling water and the environment, to the temperature difference between condensation and environment.