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 8, Problem 8.96P
Consider the air healer of Problem 8.38, but now with airflow through the annulus and steam flow through the inner tube. For the prescribed conditions and an outer tube diameter of
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2. Consider a polymeric membrane within a 6 cm diameter stirred ultrafiltration cell. The membrane is
30 μm thick. The membrane has pores equivalent in size to a spherical molecule with a molecular weight
of 100,000, a porosity of 80%, and a tortuosity of 2.5. On the feed side of the membrane, we have a
solution containing a protein at a concentration of 8 g L-1 with these properties: a = 3 nm and DAB = 6.0 ×
10-7 cm² s¹. The solution viscosity is 1 cP. The hydrodynamic pressure on the protein side of the
membrane is 20 pounds per square inch (psi) higher than on the filtrate side of the membrane. Assume
that the hydrodynamic pressure difference is much larger than the osmotic pressure difference
(advection >> diffusion). Determine the convective flow rate of the solution across the membrane.
1. Calculate the filtration flow rate (cm³ s¹) of a pure fluid across a 100 cm² membrane. Assume the
viscosity (µ) of the fluid is 1.8 cP. The porosity of the membrane is 40% and the thickness of the
membrane is 500 μm. The pores run straight through the membrane and these pores have a radius of
0.225 μm. The pressure drop applied across the membrane is 75 psi. (Note: 1 cP = 0.001 N s m²² = 0.001
Pa s.)
3. Tong and Anderson (1996) obtained for BSA the following data in a polyacrylamide gel for the
partition coefficient (K) as a function of the gel volume fraction (4). The BSA they used had a molecular
weight of 67,000, a molecular radius of 3.6 nm, and a diffusivity of 6 × 10-7 cm2 s-1. Compare the
Ogston equation
K=exp
+
to their data and obtain an estimate for the radius of the cylindrical fibers (af) that comprise the gel.
Hint: You will need to plot Ink as a function of gel volume fraction as part of your analysis. Please include
your MATLAB, or other, code with your solution.
Gel Volume Fraction (4)
KBSA
0.00
1.0
0.025
0.35
0.05
0.09
0.06
0.05
0.075
0.017
0.085
0.02
0.105
0.03
Chapter 8 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 8 - Fully developed conditions are known to exist for...Ch. 8 - What is the pressure drop associated with water at...Ch. 8 - Water at 27C flows with a mean velocity of 1 m/s...Ch. 8 - An engine oil cooler consists of a bundle of 25...Ch. 8 - For fully developed laminar flow through a...Ch. 8 - Consider pressurized water, engine oil (unused),...Ch. 8 - Velocity and temperature profiles for laminar flow...Ch. 8 - At a particular axial station, velocity and...Ch. 8 - In Chapter 1, it was stated that for...Ch. 8 - When viscous dissipation is included. Equation...
Ch. 8 - Consider a circular tube of diameter D and length...Ch. 8 - Consider flow in a circular tube. Within the test...Ch. 8 - Consider a cylindrical nuclear fuel rod of length...Ch. 8 - Consider the laminar thermal boundary layer...Ch. 8 - In a particular application involving fluid flow...Ch. 8 - A flat-plate solar collector is used w heat...Ch. 8 - Atmospheric air enters the heated section of a...Ch. 8 - Fluid enters a tube with a flow rate of 0.015kg/s...Ch. 8 - Water at 300 K and a flow rate of 5kg/s enters a...Ch. 8 - Slug flow is an idealized tube flow condition for...Ch. 8 - Superimposing a control volume that is...Ch. 8 - An experimental nuclear core simulation apparatus...Ch. 8 - Water at 20°C and a flow rate of 0.1kg/s enters a...Ch. 8 - Engine oil is heated by flowing through a circular...Ch. 8 - Engine oil flows through a 25mm -diameter tube at...Ch. 8 - In the final stages of production, a...Ch. 8 - An oil preheater consists of a single tube of 10mm...Ch. 8 - Engine oil flows at a rate of 1kg/s through a 5mm...Ch. 8 - Air at p=1atm enters a thin-walled ( D=5-mm...Ch. 8 - To cool a summer home without using a vapor...Ch. 8 - Batch processes are often used in chemical and...Ch. 8 - The evaporator section of a heat pump is installed...Ch. 8 - Water flowing at 2kg/s through a 40mm diameter...Ch. 8 - Consider the conditions associated with the hot...Ch. 8 - A thick-walled, stainless steel (AISI 316) pipe of...Ch. 8 - An air heater for an industrial application...Ch. 8 - Consider fully developed conditions in a circular...Ch. 8 - Consider the encased pipe of Problem 4.29, but now...Ch. 8 - Water flows through a thick-wailed tube with an...Ch. 8 - Atmospheric air enters a 10m -long. 150mm...Ch. 8 - NaK (45%/55). which is an alloy of sodium and...Ch. 8 - The products of combustion from a burner are...Ch. 8 - Liquid mercury at 0.5kg/s is lo be heated from 300...Ch. 8 - The surface of a 50-mm-diameter. thin-walled tube...Ch. 8 - Consider a horizontal, thin-walled circular tube...Ch. 8 - Consider pressurized liquid water flowing at...Ch. 8 - Cooling water flows through the 25.4-mm -diameter...Ch. 8 - The air passage for cooling a gas turbine vane can...Ch. 8 - The core of a high-temperature, gas-cooled nuclear...Ch. 8 - Air at 200kPa enters a 2-m -long, thin-walled tube...Ch. 8 - Heated air required for a food-drying process is...Ch. 8 - Consider laminar flow of a fluid with Pr=4 that...Ch. 8 - A common procedure for cooling a high-performance...Ch. 8 - One way to cool chips mounted on the circuit...Ch. 8 - Refrigerant- 134a is being transported a 0.1 kg/s...Ch. 8 - Oil at 150°C flows slowly through a long,...Ch. 8 - Exhaust gases from a wire processing oven are...Ch. 8 - A hot fluid passes through a thin-walled tube of...Ch. 8 - Consider a thin-walled tube of 10mm diameter and...Ch. 8 - Water at a flow rate of m =0.215kg/s is cooled...Ch. 8 - To maintain pump power requirements per unit flow...Ch. 8 - Consider a thin-walled, metallic tube of length...Ch. 8 - A circular tube of diameter D=0.2mm and length...Ch. 8 - Repeat Problem 8.66 for a circular tube of...Ch. 8 - Heat is to be removed from a reaction vessel...Ch. 8 - A healing contractor must heat 0.2kg/s of water...Ch. 8 - A thin-walled tube with a diameter of 6 mm and...Ch. 8 - A 50mm -diameter, thin—walled metal pipe covered...Ch. 8 - A thin-walled, uninsulated 0.3m -diameter duct is...Ch. 8 - Pressurized water at Tm,i=200C is pumped at...Ch. 8 - Water at 290K and 0.2kg/s flows through a Teflon...Ch. 8 - The temperature of flue gases flowing through the...Ch. 8 - In a biomedical supplies manufacturing process, a...Ch. 8 - Consider the ground source heat pump of Problem...Ch. 8 - For a sharp-edged inlet and a combined entry...Ch. 8 - Fluid enters a thin-walled rube of 5-mni diameter...Ch. 8 - Air at 3104kg/s and 27C enters a rectangular duct...Ch. 8 - Air at 25C flows at 30106kg/s within 100mm -long...Ch. 8 - A cold plate is an active cooling device that is...Ch. 8 - The cold plate design of Problem 8.82 has not been...Ch. 8 - A device that recovers heat from high-temperature...Ch. 8 - Air at 1 atm and 285K enters a 2-m -long...Ch. 8 - A double-wall heat exchanger is used to transfer...Ch. 8 - Consider laminar, fully developed flow in a...Ch. 8 - You have been asked to perform a feasibility study...Ch. 8 - A coolant flows through a rectangular channel...Ch. 8 - An electronic circuit board dissipating 50W is...Ch. 8 - To slow down large prime movers like locomotives,...Ch. 8 - A printed circuit board (PCB) is cooled by...Ch. 8 - Water at m=0.02kg/s and Tm,i=20C enters an annular...Ch. 8 - tFor the conditions of Problem 8.93, how tong must...Ch. 8 - Referring 10 Figure 8.11, consider conditions in...Ch. 8 - Consider the air healer of Problem 8.38, but now...Ch. 8 - Consider a concentric tube annulus for which the...Ch. 8 - It is common practice (o recover waste heat from...Ch. 8 - A concentric lube arrangement, for which the inner...Ch. 8 - Consider sterilization of the pharmaceutical...Ch. 8 - An engineer proposes to insert a solid rod of...Ch. 8 - An electrical power transformer of diameter 230mm...Ch. 8 - A bayonet cooler is used to reduce the temperature...Ch. 8 - The mold used in an injection molding process...Ch. 8 - Prob. 8.107PCh. 8 - Prob. 8.108PCh. 8 - Consider the microchannel cooling arrangement...Ch. 8 - The onset of turbulence in a gas flowing within a...Ch. 8 - Due to its comparatively large thermal...Ch. 8 - A novel scheme for dissipating heat from the chips...Ch. 8 - An experiment is designed to study microscale...Ch. 8 - Determine the tube diameter that corresponds to a...Ch. 8 - An experiment is devised to measure liquid flow...Ch. 8 - In the processing of very long plastic tubes of...Ch. 8 - Air at 300K and a flow rate of 3kg/h passes upward...Ch. 8 - What is the convection mass transfer coefficient...Ch. 8 - Air flowing through a tube of 75mm diameter passes...Ch. 8 - Consider gas flow of mass density and rate m...Ch. 8 - Atmospheric air at 25C and 3104kg/s flows through...Ch. 8 - Air at 25C and 1atm is in fully developed flow at...Ch. 8 - A humidifier consists of a bundle of vertical...Ch. 8 - The final step of a manufacturing process in which...Ch. 8 - Dry air is inhaled at a rate of lo liter/win...Ch. 8 - A mass transfer Operation is preceded by laminar...
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