A shell-and-tube heat exchanger is to heat an acidic liquid that flows in un-finned tubes of inside and outside diameters D_i = 10 mm and D_o = 11 mm, respectively. A hot gas flows on the shell side. To avoid corrosion of the tube material, the engineer may specify either a Ni-Cr-Mo corrosion-resistant metal alloy (P_m = 8900 kg/m³, k_m = 8 W/m ∙ K) or a polyvinylidene fluoride (PVDF) plastic (p_p = 1780 kg/m³, k_p = 0.17 W/m ∙ K). The inner and outer heat transfer coefficients are h_i = 1500 W/m² ∙ K and ho = 200 W/m² ∙ K, respectively.

(a) Determine the ratio of plastic to metal tube surface areas needed to transfer the same amount of heat.

(b) Determine the ratio of plastic to metal mass associated with the two heat exchanger designs.

(c) The cost of the metal alloy per unit mass is three times that of the plastic. Determine which tube material should be specified on the basis of cost.