Chapter 14

Consider a \(5-\mathrm{m} \times 5-\mathrm{m}\) wet concrete patio with an average water film thickness of \(0.3 \mathrm{~mm}\). Now wind at \(50 \mathrm{~km} / \mathrm{h}\) is blowing over the surface. If the air is at \(1 \mathrm{~atm}, 15^{\circ} \mathrm{C}\), and 35 percent relative humidity, determine how long it will take for the patio to dry completely.

Benzene \((M=78.11 \mathrm{~kg} / \mathrm{kmol})\) is a carcinogen, and exposure to benzene increases the risk of cancer and other illnesses in humans. A truck transporting liquid benzene was involved in an accident that spilled the liquid on a flat highway. The liquid benzene forms a pool of approximately \(10 \mathrm{~m}\) in diameter on the highway. In this particular windy day at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) with an average wind velocity of \(10 \mathrm{~m} / \mathrm{s}\), the liquid benzene surface is experiencing mass transfer to air by convection. Nearby at the downstream of the wind is a residential area that could be affected by the benzene vapor. Local health officials have assessed that if the benzene level in the air reaches \(500 \mathrm{~kg}\) within the hour of the spillage, residents should be evacuated from the area. If the benzene vapor pressure is \(10 \mathrm{kPa}\), estimate the mass transfer rate of benzene being convected to the air, and determine whether the residents should be evacuated or not.

Air at \(40^{\circ} \mathrm{C}\) and 1 atm flows over a \(5-\mathrm{m}\)-long wet plate with an average velocity of \(2.5 \mathrm{~m} / \mathrm{s}\) in order to dry the surface. Using the analogy between heat and mass transfer, determine the mass transfer coefficient on the plate.

A 2-in-diameter spherical naphthalene ball is suspended in a room at \(1 \mathrm{~atm}\) and \(80^{\circ} \mathrm{F}\). Determine the average mass transfer coefficient between the naphthalene and the air if air is forced to flow over naphthalene with a free stream velocity of \(15 \mathrm{ft} / \mathrm{s}\). The Schmidt number of naphthalene in air at room temperature is \(2.35\). Answer: \(0.0524 \mathrm{ft} / \mathrm{s}\)

Consider a 15-cm-internal-diameter, 10-m-long circular duct whose interior surface is wet. The duct is to be dried by forcing dry air at \(1 \mathrm{~atm}\) and \(15^{\circ} \mathrm{C}\) through it at an average velocity of \(3 \mathrm{~m} / \mathrm{s}\). The duct passes through a chilled room, and it remains at an average temperature of \(15^{\circ} \mathrm{C}\) at all times. Determine the mass transfer coefficient in the duct.

Does a mass transfer process have to involve heat transfer? Describe a process that involves both heat and mass transfer.

Consider a shallow body of water. Is it possible for this water to freeze during a cold and dry night even when the ambient air and surrounding surface temperatures never drop to \(0^{\circ} \mathrm{C}\) ? Explain.

During a hot summer day, a \(2-L\) bottle drink is to be cooled by wrapping it in a cloth kept wet continually and blowing air to it with a fan. If the environment conditions are \(1 \mathrm{~atm}, 80^{\circ} \mathrm{F}\), and 30 percent relative humidity, determine the temperature of the drink when steady conditions are reached.

Consider a thin layer of liquid water on a concrete surface. The surrounding air is dry with a convection heat transfer coefficient of \(50 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The liquid water has an emissivity of \(0.95\), and the air and surrounding temperature is \(30^{\circ} \mathrm{C}\). If the layer of liquid water has a uniform temperature of \(20^{\circ} \mathrm{C}\), determine the conduction heat flux through the concrete.

A 2-m-deep 20-m \(\times 20-\mathrm{m}\) heated swimming pool is maintained at a constant temperature of \(30^{\circ} \mathrm{C}\) at a location where the atmospheric pressure is \(1 \mathrm{~atm}\). If the ambient air is at \(20^{\circ} \mathrm{C}\) and 60 percent relative humidity and the effective sky temperature is \(0^{\circ} \mathrm{C}\), determine the rate of heat loss from the top surface of the pool by ( \(a\) ) radiation, \((b)\) natural convection, and (c) evaporation. ( \(d\) ) Assuming the heat losses to the ground to be negligible, determine the size of the heater.