Chapter 11, Problem 11.3P

A shell-and-tube heat exchanger is to heat an acidic liquidthat flows in untinned tubes of inside and outside diameters $D_i=10$ mm and $D_o=11$ mm, respectively. A hotgas flows on the shell side. To avoid corrosion of the tubematerial, the engineer may specify either a Ni-Cr-Mocorrosion-resistant metal alloy $\left({\rho }_m=8900{\text{ kg/m}}^3,k_m=8\text{ W/m}\cdot \text{K}\right)$ or a polyvinylidene fluoride (PVDF) plastic $\left({\rho }_p=1780{\text{ kg/m}}^3,k_p=0.17\text{ W/m}\cdot \text{K}\right)$ . The inner andouter heat transfer coefficients are $h_i=1500{\text{ W/m}}^2\cdot \text{K}$ and $h_o=200{\text{ W/m}}^2\cdot \text{K}$ , 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 muss associated with the two heat exchanger designs.
(c) The cost of the metal alloy per Unit muss is threetimes that of the plastic. Determine which tubematerial should be specified on the basis of cost.