2.7c. Mass transfer in an annular space.
a) In studying rates of diffusion of naphthalene into air, an investigator replaced a 30.5-cm section of the inner pipe of an annulus with a naphthalene rod. The annulus was composed of a 51-mm-OD brass inner pipe surrounded by a 76-mm-ID brass pipe. While operating at a mass velocity within the annulus of 12.2 kg of air/m2-s at 273 K and 1 atm, the investigator determined that the partial pressure of naphthalene in the exiting gas stream was 0.041 Pa. Under the conditions of the investigation, the Schmidt number of the gas was 2.57, the viscosity was 175 mP, and the vapor pressure of naphthalene was 1.03 Pa. Estimate the mass-transfer coefficient from the inner wall for this set of conditions. Assume that equation (2-52) applies.
Solution
b) Monrad and Pelton (Trans. AIChE, 38, 593, 1942) presented the following correlation for heat-transfer coefficient in an annular space:
where do and di are the outside and inside diameters of the annulus, de is the equivalent diameter defined as
Write down the analogous expression for mass transfer and use it to estimate the mass-transfer coefficient for the conditions of part a). Compare both results.
Solution
2.8c. The Chilton-Colburn analogy: flow across tube banks.
Winding and Cheney (Ind. Eng. Chem., 40, 1087, 1948) passed air at 310 K and 1 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-mm-OD tubes (d = 38 mm) spaced on 57-mm centers, with the rows 76 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' is the maximum mass velocity through the tube bank, in kg/m2-s, and kG is in kmol/m2-s-Pa.
a) Rewrite equation (2-68) in terms of the Colburn jD -factor. The diffusivity of naphthalene in air at 310 K and 1 atm is 0.074 cm2/s.
Solution
Properties of dilute mixtures of naphthalene in air at 310 K and 1 atm:
Dimensional constant in the given correlation:
b) Estimate the mass-transfer coefficient to be expected for evaporation of n-propyl alcohol into carbon dioxide for the same geometrical arrangement when the carbon dioxide flows at a maximum velocity of 10 m/s at 300 K and 1 atm. The vapor pressure of n-propyl alcohol at 300 K is 2.7 kPa.
Solution
Properties of dilute mixtures of propyl alcohol in carbon dioxide at 300 K and 1 atm:
c) Zakauskas (Adv. Heat Transfer, 8, 93, 1972) proposed the following correlation for the heat-transfer coefficient in a staggered tube bank arrangement similar to that studied by Winding and Cheney:
Use the mass-transfer expression analogous to equation (2-69) to estimate the mass-transfer coefficient of part b). Compare the results.
Solution