Question

(30 points in total) A shell-and-tube heat exchanger consists of a shell of inside diameter, D, and length I the shell outside the tubes. within the exchanger is $2,000, and the cost of the shell is given by f tubes. One fluid flows through the tubes and the other in ned I is a number o The initial cost of the heat exchanger tubing that will be contai G-si ,800+D2.5L Because of the fouling, the exchanger is required t an annual cost, but the manufacturer will clean the exchanger for an initial one-time fee given as be cleaned annually. The cost of cleaning is Cr-$350 DL Thus, the initial cost of the exchanger is given as С-С,+Cr+ 2,000 e it is known that a total tube length of 150 m must be used for the 200 tubes per unit area (m2) shell for the minimum initial cost conditions. of the shell cross-section. Determine the diameter, D, and length, L, of the heat exchanger a) Show the objective and constraint of this optimization problem (10 pts) b) Find the values of D and L of this heat exchanger shell (20 pts).

Answer 1

cost of the heat exchange COS should be minimum constseint eguahon 1リ ost of heqL exchanged オD2. 0.5 1718, 73 D +2の0+33y·225 느 de o d2 0.5

1 718.873 33 225 D 2 2 at 5327 d D2 dD2 .. . cost u,l, be minimum gt. D: 0, 5329 m 3 T 0532