A concentric tube heat exchanger of length L = 2m is used to thermally process a pharmaceutical product flowing at a mean velocity of u_m,c = 0.1 m/s with an inlet temperature of T_c,i = 20°C. The inner tube of diameter D_i  =10 mm is thin walled, and the exterior of the outer tube (D_o = 20 mm) is well insulated. Water flows in the annular region between the tubes at a mean velocity of u_m,h = 0.2 m/s with an inlet temperature of T_h,i = 60°C. Properties of the pharmaceutical product are v = 10 X 10^-6 m²/s, k = 0.25 W/m · K, p = 1100 kg/m³, and c_p = 2460 J/kg · K. Evaluate water properties at T_h = 50°C.

(a) Determine the value of the overall heat transfer coefficient U.
(b) Determine the mean outlet temperature of the pharmaceutical product when the exchanger operates in the counter flow mode.
(c) Determine the mean outlet temperature of the pharmaceutical product when the exchanger operates in the parallel-flow mode.