Design a plate and frame heat exchanger for the following problem:
Hot water at 0.0063 m^3/s, 82.2°C, enters a plate and frame heat exchanger and is cooled to 57.2°C. Cold water enters this same exchanger at 0.00756 m^3/s, 37.8°C. The plates are made of stainless steel (316SS) with a heat transfer area of 0.316 m^2 per plate. The plate spacing is 5.08 mm, the plate width is 381 mm, and the plate thickness is 1.016 mm.
Hint: You should use iteration method to solve this problem. Assume a value for number of plates and solve the problem to find q_c, q_h and q_by LMTD. If q_c = q_h = q_by LMTD, your assumption is good. Otherwise repeat the procedure with a new guess for number of plates.