Design and optimization of a thermal system and heat exchangers

Water is to be delivered from source, S, to locations A1, A2, A3, and A4, as illustrated below. The corresponding demands for water (i.e., mass flow rates) at these locations are given in the table below. Also included in the table are the distances of these locations from the source, S.

You are to design an optimal (i.e., minimum cost) pipeline system for the water delivery as stated above. The water delivery operation is continuous for 10 years. The cost of the pipe is C1D1.5L where C1, D, and L are the proportionality constant, pipe diameter, and pipe length, respectively. The cost of a pump is C2Ρ where C2 and P are the proportionality constant and pumping power, respectively. Assume all the pumps have an efficiency of η = 85 percent. The electricity cost is 10 cents per kilo-watt-hour. Assume the interest rate is i = 5 percent (annual rate, compounded hourly). Note that you will need to determine the proper values of C1 and C2 on your own.

Water reaches the location A2 with a temperature of 40 C and it is to be cooled to 25 C with the stationary ambient air of T = 18 C. Design a heat exchanger to achieve this goal by determining the exposed surface area of the heat exchanger pipe to the ambient air. Assume that the heat transfer coefficients for the water inside the pipe and the air outside the pipe are hw = 800 W/m2K and ha = 10 W/m2K, respectively. However, the pipe outer surface exposed to air is equipped with fins with an effectiveness of 3.0.