Consider a concentric tube heat exchanger with hot and cold water inlet temperatures of 200 and 35°C, respectively. The flow rates of the hot and cold fluids are 42 and 84 kg/h, respectively. Assume the overall heat transfer coefficient is 180 W/m² ∙ K.

(a) What is the maximum heat transfer rate that could be achieved for the prescribed inlet conditions?

(b) If the exchanger is operated in counter flow with a heat transfer area of 0.33 m², determine the outlet fluid temperatures.

(c) With all other conditions remaining the same, plot the effectiveness and fluid outlet temperatures as a function of the product VA for the range from 50 to 1000 W/K. As VA becomes very large, what is the asymptotic value for T_h,o?

(d) What is the largest possible heat transfer rate that could be achieved for the prescribed inlet conditions, if the exchanger is operated in parallel flow and is very long? What is the effectiveness of the exchanger in this configuration?

(e) For operation in parallel flow, plot the effectiveness and fluid outlet temperatures as a function of the product VA for the range from 50 to 1000 W/K. As UA becomes very large, what are the asymptotic values for T_h,o and T_c,o?