Winding and Cheney (1948) passed air at \(310 \mathrm{~K}\) and \(1 \mathrm{~atm}\) through a bank of rods of naphthalene. The rods were in a staggered arrangement, with the air flowing at right angles to the axes of the rods. The bank consisted of 10 rows containing alternately five and four \(38-\mathrm{mm}-\mathrm{OD}\) tubes \((d=38 \mathrm{~mm})\) spaced on \(57-\mathrm{mm}\) centers, with the rows \(76 \mathrm{~mm}\) apart. The mass-transfer coefficient was determined by measuring the rate of sublimation of the naphthalene. The data could be correlated by

where \(G_{y}\) is the maximum mass velocity through the tube bank, in \(\mathrm{kg} / \mathrm{m}^{2} \cdot \mathrm{s}\), and \(k_{G}\) is in \(\mathrm{kmol} / \mathrm{m}^{2} \cdot \mathrm{s} \cdot \mathrm{Pa}\).
(a) Rewrite equation (2-104) in terms of the Colburn \(j_{D}\) factor. The diffusivity of naphthalene in air at \(310 \mathrm{~K}\) and \(1 \mathrm{~atm}\) is \(0.074 \mathrm{~cm}^{2} / \mathrm{s}\).

(b) Estimate the mass-transfer coefficient for evaporation of \(n\)-propyl alcohol into carbon dioxide over the outer surface of the tubes, for the same geometrical arrangement, when the carbon dioxide flows at a maximum velocity of \(10 \mathrm{~m} / \mathrm{s}\) at \(300 \mathrm{~K}\) and \(1 \mathrm{~atm}\). The vapor pressure of \(n\)-propyl alcohol at \(300 \mathrm{~K}\) is \(2.7 \mathrm{kPa}\). The diffusivity of \(n\)-propyl alcohol in \(\mathrm{CO}_{2}\) at \(300 \mathrm{~K}\) and \(1 \mathrm{~atm}\) is \(0.076 \mathrm{~cm}^{2} / \mathrm{s}\).

(c) Zhukauskas (1972) proposed the following correlation for the heat-transfer coefficient in a staggered tube bank arrangement like that studied by Winding and Cheney:

Use the mass-transfer expression analogous to equation (2-105) to estimate the mass-transfer coefficient of part (b). Compare the results.

Transcribed Image Text:

kg = 3.86109G0.56 y y 5