Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
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Chapter 14, Problem 14.23P
Insulation degrades (experiences an increase in thermal conductivity) if it is subjected to water vapor condensation. The problem may occur in home insulation during cold periods, when vapor in a humidified room diffuses through the drywall (plaster board) and condenses in the adjoining insulation. Estimate the mass diffusion rate for a 3 m× 5 m wall, under conditions for which the vapor pressure is 0.03 bar in the room air and 0.0 bar in the insulation. The drywall is 10 mm thick, and the solubility of water vapor in the wall material is approximately
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A tanker ship is transporting 0.798 kg/m3 of a rare gas in its tank. After the fill-up, the 1.94 m long pipe used to fill the tank was left open for 10.4 hours. In that time, 11.7 x10-4 kg of the gas diffuses out of the tank, almost nothing compared to the original quantity of gas in the tank. If the concentration of that gas in our atmosphere is typically zero, and the diffusion constant of that gas is 2.13 x10-5 m2/s, what is the cross-sectional area of the pipe?
1) A beaker with 10 cm in height is filled with liquid solvent n-hexane up to a level2 cm below the
top (mouth) of the beaker at 25°C and 1 bar. With a fan, dry air at 25°C and 1 bar is blown gently
across the mouth of the beaker, so that the hexane vapor transferred through the air and n-hexane
gas-vapor mixture by diffusion. Hexane concentration at the mouth of the beaker is negligible.
Assume that air does not dissolve in liquid hexane, and the liquid height in the beaker is constant
within observation period, hence the system is in steady-state. Molecular diffusivity of n-hexane
in air is DAB -2x10 m²/s at 25 °C and 1 bar, and vapor pressure of n-hexane is pa°-152 mmHg
at 25 °C.
a) Draw a schematic picture of the mass transfer in the beaker.
b) Discuss the type of mass transfer in the gas-vapor mixture.
c) Using the equation
dyA
N=-cD
4 + y , (N , + N,)
+ y, (N, +N,
d z
Derive the molar flux equation for the condition given, showing every step of integration.
d) Calculate the total…
Chapter 14 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 14 - Assuming air to be composed exclusively O2 and N2...Ch. 14 - Consider an ideal gas mixture of n species. (a)...Ch. 14 - A mixture of CO2 and N2 is in a container at 25C ,...Ch. 14 - A He-Xe mixture containing 0.75 mole fraction of...Ch. 14 - Estimate values of the mass diffusivity for binary...Ch. 14 - Consider air in a closed, cylindrical container...Ch. 14 - An old-fashioned glass apothecary jar contains a...Ch. 14 - Consider the evaporation of liquid A into a column...Ch. 14 - An open pan of diameter 0.2 m and height 80mm...Ch. 14 - A spherical droplet of liquid A and radius...
Ch. 14 - The presence of a small amount of air may cause a...Ch. 14 - A laboratory apparatus to measure the diffusion...Ch. 14 - A thin plastic membrane is used to separate helium...Ch. 14 - Prob. 14.16PCh. 14 - Consider the radial diffusion of a gaseous species...Ch. 14 - Prob. 14.18PCh. 14 - Prob. 14.19PCh. 14 - Prob. 14.20PCh. 14 - Hydrogen at a pressure of 2 atm flows within a...Ch. 14 - Prob. 14.22PCh. 14 - Insulation degrades (experiences an increase in...Ch. 14 - Prob. 14.24PCh. 14 - Helium gas at 25°C and 4 bars is stored in a...Ch. 14 - Prob. 14.26PCh. 14 - An experiment is designed to measure the partition...Ch. 14 - Ultra-pure hydrogen is required in applications...Ch. 14 - Nitric oxide (NO) emissions from automobile...Ch. 14 - Pulverized coal pellets, which may be approximated...Ch. 14 - To enhance the effective surface, and hence the...Ch. 14 - A platinum catalytic reactor in an automobile is...Ch. 14 - A novel process has been proposed to create a...Ch. 14 - Consider a spherical organism of radius r0 within...Ch. 14 - Prob. 14.35PCh. 14 - Consider combustion of hydrogen gas in a mixture...Ch. 14 - Prob. 14.37PCh. 14 - As an employee of the Los Angeles Air Quality...Ch. 14 - Prob. 14.39PCh. 14 - A large sheet of material 4() mm thick contains...Ch. 14 - Prob. 14.41PCh. 14 - Prob. 14.43PCh. 14 - Prob. 14.44PCh. 14 - Prob. 14.46PCh. 14 - If an amount of energy Q0(J/m2) is released...Ch. 14 - The presence of CO2 in solution is essential to...Ch. 14 - Consider a DVD similar to that of Problem 5.99. To...Ch. 14 - Prob. 14.50PCh. 14 - Prob. 14.51PCh. 14 - Prob. 14.52PCh. 14 - Prob. 14.55PCh. 14 - A person applies an insect repellent onto an...
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- 6. A sheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 6 10-11 m2/s, and the diffusion flux is found to be 1.2 10-7 kg/m2-s. Also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3. How far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3? Assume a linear concentration profile.arrow_forward4arrow_forwardAir at 90 0C and 1.00 atm (absolute) contains 10.0 mole% water. A continuous stream of this air enters a compressor–condenser, in which the temperature is lowered to 15.6 0C and the pressure is raised to 3.00 atm. The air leaving the condenser is then heated isobarically to 100 0C. Calculate the fraction of water that is condensed from the air, the relative humidity of the air at 100 0C, and the ratio m3 outlet air at 100 0C/m feed air at 90 0C.arrow_forward
- From an open water surface with air temperature 22°C, relative humidity is 40% and wind speed is 3 m/s, all measured at height 2 m above the water surface. Assume a roughness height of 0.03 cm. The net radiation is 200 W/m^2. Cp = 1005 J/kg-K A. Calculate the latent heat of vaporization (J/kg) B. Calculate the evaporation using Energy Balance Method (mm/day) C. Calculate the saturation deficit of the vapor pressure (Pa) D. Calculate the evaporation using Priestley-Taylor Method (mm/day)arrow_forwardDetermine the binary diffusion coefficient of H₂ in air at 600 K and 3 atm in m²/s. (A) 17.23x10-5 (B) 4.20x10-5 8.58x10-5 (D) 2.43x10-5arrow_forwardi need the answer quicklyarrow_forward
- True or False? Justify your answer. A. In a rectangular drug delivery device that consists of a drug reservoir and a diffusion barrier made of a polymer gel, the steady state diffusion (mass transfer) rate through a barrier of thickness 1 cm was found to be 20 mg/day. If the barrier thickness were to be doubled keeping the reservoir drug concentration the same, the mass transfer rate would be 10 mg/day. B. In a spherical drug delivery device consisting of a core reservoir surrounded by a polymer gel barrier, the steady state diffusion (mass transfer) rate through a barrier of thickness 1 cm was found to be 20 mg/day. If the barrier thickness were to be doubled keeping the reservoir drug concentration the same, the mass transfer rate would be 10 mg/day.arrow_forwardMethane is diffusing at steady state through a 0.5mm diameter and 4mm long tube containing nitrogen gas at 101.32 kPa and 298K. Methane entering the tube is at 2.31x10 Pa and leaving the tube at 1.013x10 Pa. The diffusivity of nitrogen in methane gas is 0.140 x10m/s. Calculate flux of methane. Mention the unit of the flux. Paragraph BIEEarrow_forwardAir at 90°C and 1.00 atm (absolute) contains 10.0 mole% water. A continuous stream of this air enters a compressor-condenser, in which the temperature is lowered to 15.6°C and the pressure is raised to 3.00 atm. The air leaving the condenser is then heated isobarically to 100°C. Calculate: (a) the fraction of water that is condensed from the air (b) the relative humidity of the air at 100°C (c) and the ratio of the volumetric flow of the outlet air to the volumetric flow of the feed air.arrow_forward
- Use the definition of the Sherwood number to calculate the mass transfer coefficient (in cm/s) for a scenario where the characteristic length is 0.034 m, the diffusivity is 0.00099 cm^2/s, and the Sherwood number is 3.5.arrow_forward2. Humid air at 35o C and a pressure of 1 atm and with 98% relative humidity enters a condenser in which the temperature is lowered isobarically (pressure is constant) to 15o C. Part of the water condenses and coexists with the remaining air. The remaining air leaves the condenser flowing through a 20-cm diameter duct at a velocity of 10 m/s. Calculate the rate (moles water/s) at which water condenses.arrow_forwardA dehumidifier brings in saturated wet air (100 percent relative humidity) at 30°C and 1 atm, through an inlet of 8-cm diameter and average velocity 3 m/s. After some of the water vapor condenses and is drained off at the bottom, the somewhat drier air leaves at approximately 30°C, 1 atm, and 50 percent relative humidity. For steady operation, estimate the amount of water drained off in kg/h. (This problem is idealized from a real dehumidifier.) (in kg/hr) Note: Use three decimal places and no need to input the unit.arrow_forward
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