Chapter 14

What is Stefan flow? Write the expression for Stefan's law and indicate what each variable represents.

A researcher is using a 5 -cm-diameter Stefan tube to measure the mass diffusivity of chloroform in air at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). Initially, the liquid chloroform surface was \(7.00 \mathrm{~cm}\) from the top of the tube; and after 10 hours have elapsed, the liquid chloroform surface was \(7.44 \mathrm{~cm}\) from the top of the tube, which corresponds to \(222 \mathrm{~g}\) of chloroform being diffused. At \(25^{\circ} \mathrm{C}\), the chloroform vapor pressure is \(0.263 \mathrm{~atm}\), and the concentration of chloroform is zero at the top of the tube. If the molar mass of chloroform is \(119.39 \mathrm{~kg} / \mathrm{kmol}\), determine the mass diffusivity of chloroform in air.

A 1-in-diameter Stefan tube is used to measure the binary diffusion coefficient of water vapor in air at \(80^{\circ} \mathrm{F}\) and \(13.8\) psia. The tube is partially filled with water with a distance from the water surface to the open end of the tube of \(10 \mathrm{in}\). Dry air is blown over the open end of the tube so that water vapor rising to the top is removed immediately and the concentration of vapor at the top of the tube is zero. During 10 days of continuous operation at constant pressure and temperature, the amount of water that has evaporated is measured to be \(0.0025 \mathrm{lbm}\). Determine the diffusion coefficient of water vapor in air at \(80^{\circ} \mathrm{F}\) and \(13.8 \mathrm{psia}\).

The mass diffusivity of ethanol \(\left(\rho=789 \mathrm{~kg} / \mathrm{m}^{3}\right.\) and \(M=46 \mathrm{~kg} / \mathrm{kmol}\) ) through air was determined in a Stefan tube. The tube has a uniform cross-sectional area of \(0.8 \mathrm{~cm}^{2}\). Initially, the ethanol surface was \(10 \mathrm{~cm}\) from the top of the tube; and after 10 hours have elapsed, the ethanol surface was \(25 \mathrm{~cm}\) from the top of the tube, which corresponds to \(0.0445 \mathrm{~cm}^{3}\) of ethanol being evaporated. The ethanol vapor pressure is \(0.0684\) atm, and the concentration of ethanol is zero at the top of the tube. If the entire process was operated at \(24^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\), determine the mass diffusivity of ethanol in air.

Methanol ( \(\rho=791 \mathrm{~kg} / \mathrm{m}^{3}\) and \(\left.M=32 \mathrm{~kg} / \mathrm{kmol}\right)\) undergoes evaporation in a vertical tube with a uniform cross-sectional area of \(0.8 \mathrm{~cm}^{2}\). At the top of the tube, the methanol concentration is zero, and its surface is \(30 \mathrm{~cm}\) from the top of the tube (Fig. P14-104). The methanol vapor pressure is \(17 \mathrm{kPa}\), with a mass diffusivity of \(D_{A B}=0.162 \mathrm{~cm}^{2} / \mathrm{s}\) in air. The evaporation process is operated at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). (a) Determine the evaporation rate of the methanol in \(\mathrm{kg} / \mathrm{h}\) and \((b)\) plot the mole fraction of methanol vapor as a function of the tube height, from the methanol surface \((x=0)\) to the top of the tube \((x=L)\).

A tank with a 2-cm-thick shell contains hydrogen gas at the atmospheric conditions of \(25^{\circ} \mathrm{C}\) and \(90 \mathrm{kPa}\). The charging valve of the tank has an internal diameter of \(3 \mathrm{~cm}\) and extends \(8 \mathrm{~cm}\) above the tank. If the lid of the tank is left open so that hydrogen and air can undergo equimolar counterdiffusion through the 10 -cm- long passageway, determine the mass flow rate of hydrogen lost to the atmosphere through the valve at the initial stages of the process.

An 8-cm-internal-diameter, 30-cm-high pitcher halffilled with water is left in a dry room at \(15^{\circ} \mathrm{C}\) and \(87 \mathrm{kPa}\) with its top open. If the water is maintained at \(15^{\circ} \mathrm{C}\) at all times also, determine how long it will take for the water to evaporate completely.

The pressure in a pipeline that transports helium gas at a rate of \(5 \mathrm{lbm} / \mathrm{s}\) is maintained at \(14.5\) psia by venting helium to the atmosphere through a \(0.25\)-in-internal-diameter tube that extends \(30 \mathrm{ft}\) into the air. Assuming both the helium and the atmospheric air to be at \(80^{\circ} \mathrm{F}\), determine \((a)\) the mass flow rate of helium lost to the atmosphere through the tube, (b) the mass flow rate of air that infiltrates into the pipeline, and \((c)\) the flow velocity at the bottom of the tube where it is attached to the pipeline that will be measured by an anemometer in steady operation.

What is a concentration boundary layer? How is it defined for flow over a plate?

What is the physical significance of the Schmidt number? How is it defined? To what dimensionless number does it correspond in heat transfer? What does a Schmidt number of 1 indicate?