You are asked to design a condenser that consists of a shell and tube heat exchanger having a single shell with multiple tube passes. The condenser is to be used in a Rankine cycle to condense high-quality steam into saturated water (at 46 °C). Cooling water enters the condenser at 15 °C and exits at 25 °C. The rate of heat that is removed by the condenser is 1 MW. The pressure drop per tube is limited to 5,000 N/m^2. Your design is to specify the tube's diameter, the number of tubes needed, and the length of the heat exchanger. Calculate what L and D are going to be when you use 40 tubes for n.
Hints:
The hot fluid is undergoing phase transformation. This means there are only 2 equations to consider in the design: Heat transfer equation and momentum equation associated with the cold water.
Neglect the tube's wall thickness and deal only with one diameter (i.e., inner diameter).
Assume a smooth surface for the tubes.
There is only 1 thermal resistor to consider in the overall thermal resistance equation (i.e., the thermal resistor associated with the cold water).
Use Darcy’s friction coefficient if you are using the following equations:
is the bulk mean water velocity in the tube.
Since we are dealing only with 2 equations and there are 3 unknowns (n, L, and D), the design has 1-DOF (i.e., infinite design possibilities).