A shell-and-tube heat exchanger (1 shell pass, 2 tube passes) is to be used to condense 2.73 kg/s of saturated steam at 340 K. Condensation occurs on the outer tube surfaces, and the corresponding convection coefficient is 10,000 W/m² ∙ K. The temperature of the cooling water entering the tubes is 15°C, and the exit temperature is not to exceed 30°C. Thin-walled tubes of 19-mm diameter are specified, and the mean velocity of water flow through the tubes is to be maintained at 0.5 m/s.

(a) What is the minimum number of tubes that should be used, and what is the corresponding tube length per pass?

(b) To reduce the size of the heat exchanger, it is proposed to increase the water-side convection coefficient by inserting a wire mesh in the tubes. If the mesh increases the convection coefficient by a factor of two, what is the required tube length per pass?