Heat and Mass Transfer: Fundamentals and Applications
6th Edition
ISBN: 9781260440058
Author: CENGEL, Yunus
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 3, Problem 224P
A 3-cm-long. 2-nuti x 2-mm rectangular cross-section aluminum fin
(a) 39
(b) 30
(c) 24
(d)18
(e) 7
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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 3 Solutions
Heat and Mass Transfer: Fundamentals and Applications
Ch. 3 - Consider heat conduction through a wall of...Ch. 3 - Consider heat conduction through a plane wall....Ch. 3 - What does the thermal resistance of a medium...Ch. 3 - Can we defme the convection resistance for a unit...Ch. 3 - Consider steady heat transfer through the wall of...Ch. 3 - How is the combined heat transfer coefficient...Ch. 3 - Why are the convection and the radiation...Ch. 3 - Consider steady one-dimensional heat transfer...Ch. 3 - Someone comments that a microwave oven can be...Ch. 3 - Consider two cold canned drinks, one wrapped in a...
Ch. 3 - The bottom of a pan is made of a 4-mm-thick...Ch. 3 - Consider a surface of area A at which the...Ch. 3 - How does the thermal resistance network associated...Ch. 3 - Consider steady one-dimensional heat transfer...Ch. 3 - Consider a window glass consisting of two...Ch. 3 - Prob. 16PCh. 3 - Consider a person standing in a room at 20C with...Ch. 3 - Consider an electrically heated brick house...Ch. 3 - A12-cm18-cm circuit board houses on its surface...Ch. 3 - Water is boiling in a 25-cm-diameter aluminum pan...Ch. 3 - A cylindrical resistor element on a circuit board...Ch. 3 - Prob. 22PCh. 3 - A1.0m1.5m double-pane window consists of two...Ch. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28EPCh. 3 - To defog the rear window of an automobile, a very...Ch. 3 - A transparent film is to be bonded onto the top...Ch. 3 - To defrost ice accumulated on the outer surface of...Ch. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Heat is to be conducted along a circuit board that...Ch. 3 - Prob. 37EPCh. 3 - Consider a house that has a 10m20-m base and a...Ch. 3 - Prob. 39EPCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - What is thermal contact resistance? How is it...Ch. 3 - Will the thermal contact resistance be greater for...Ch. 3 - Explain how the thermal contact resistance can be...Ch. 3 - A waII consists of two layers of insulation...Ch. 3 - Prob. 48CPCh. 3 - Consider two surfaces pressed against each other....Ch. 3 - Prob. 50PCh. 3 - Two 5-cm-diameter, 15-cm-long aluminum bars...Ch. 3 - Prob. 52PCh. 3 - Two identical aluminum plates with thickness of 30...Ch. 3 - A tvolayer wall is made of two metal plates, with...Ch. 3 - Prob. 55PCh. 3 - An aluminum plate and a stainless steel plate are...Ch. 3 - Prob. 57PCh. 3 - Prob. 58PCh. 3 - Prob. 59PCh. 3 - Prob. 60PCh. 3 - Prob. 61PCh. 3 - What are the two approaches used in the...Ch. 3 - The thermal resistance networks can also be used...Ch. 3 - When plotting the thermal resistance network...Ch. 3 - A 10-cm-thick vall is to be constructed with...Ch. 3 - Prob. 66EPCh. 3 - Prob. 67PCh. 3 - Prob. 68PCh. 3 - Prob. 69PCh. 3 - Prob. 70PCh. 3 - Prob. 71PCh. 3 - Prob. 72PCh. 3 - A 12-m-long and 5-m-high wall is constructed of...Ch. 3 - Prob. 74EPCh. 3 - Prob. 75PCh. 3 - Prob. 76PCh. 3 - Prob. 77PCh. 3 - What is an infinitely long cylinder? When is it...Ch. 3 - Can the thermal resistance concept be used for a...Ch. 3 - Consider a short cylinder whose top and bottom...Ch. 3 - Prob. 81PCh. 3 - Prob. 82PCh. 3 - Prob. 83PCh. 3 - Superheated steam at an average temperature 20C is...Ch. 3 - Prob. 85PCh. 3 - Prob. 86PCh. 3 - Prob. 87EPCh. 3 - Prob. 88EPCh. 3 - Prob. 89EPCh. 3 - Prob. 90PCh. 3 - Prob. 91PCh. 3 - Prob. 92PCh. 3 - Prob. 93EPCh. 3 - Prob. 94PCh. 3 - Prob. 95PCh. 3 - Prob. 96PCh. 3 - Liquid hydrogen is flowing through an insulated...Ch. 3 - Exposure to high concentrations of gaseous ammonia...Ch. 3 - A mixture of chemicals is flowing in a pipe...Ch. 3 - Ice slurry is being transported in a pipe...Ch. 3 - Prob. 101PCh. 3 - Prob. 102PCh. 3 - Prob. 103PCh. 3 - What is the critical radius of insulation? How is...Ch. 3 - Prob. 105CPCh. 3 - Prob. 106CPCh. 3 - Prob. 107CPCh. 3 - A pipe is insulated such that the outer radius of...Ch. 3 - A 0.083-in-diameter electrical wire at 90F is...Ch. 3 - Repeat Prob. 3-109E, assuming a thermal contact...Ch. 3 - Prob. 111PCh. 3 - Prob. 112PCh. 3 - Hot air is to be cooled as it is forced to flow...Ch. 3 - Prob. 114CPCh. 3 - Prob. 115CPCh. 3 - The fins attached to a surface are determined to...Ch. 3 - Explain how the fins enhance heat transfer from a...Ch. 3 - How does the overall effectiveness of a finned...Ch. 3 - Hot water is to be cooled as it flows through the...Ch. 3 - Consider two finned surfaces that are identical...Ch. 3 - The heat transfer surface area of a fin is equal...Ch. 3 - Does the (a) efficiency and (b) effectiveness of a...Ch. 3 - Two pin fins are identical, except that the...Ch. 3 - Two plate fins of constant rectangular cross...Ch. 3 - Two finned surfaces are identical, except that the...Ch. 3 - Obtain a relation for the fin efficiency for a fin...Ch. 3 - Prob. 127PCh. 3 - Consider a very long rectangular fin attached to a...Ch. 3 - Prob. 129PCh. 3 - Prob. 130PCh. 3 - Prob. 131PCh. 3 - Prob. 132PCh. 3 - Prob. 133EPCh. 3 - Prob. 134EPCh. 3 - Prob. 135PCh. 3 - Prob. 136PCh. 3 - Prob. 137PCh. 3 - Prob. 138PCh. 3 - Prob. 139PCh. 3 - Prob. 140PCh. 3 - Prob. 141PCh. 3 - Prob. 142PCh. 3 - Prob. 143PCh. 3 - Prob. 144PCh. 3 - Prob. 145PCh. 3 - Prob. 146PCh. 3 - The human body is adaptable to extreme climatic...Ch. 3 - Consider the conditions of Example 3-14 in the...Ch. 3 - Consider the conditions of Example 3-14 in the...Ch. 3 - Prob. 150PCh. 3 - What is a conduction shape factor? How is it...Ch. 3 - What is the value of conduction shape factors in...Ch. 3 - Prob. 153PCh. 3 - A thin-walled cylindrical container is placed...Ch. 3 - Prob. 155PCh. 3 - Prob. 156PCh. 3 - Prob. 157PCh. 3 - Prob. 158EPCh. 3 - Prob. 159PCh. 3 - Prob. 160PCh. 3 - Prob. 161PCh. 3 - Prob. 162PCh. 3 - Prob. 163PCh. 3 - Prob. 164PCh. 3 - Consider a house with a flat roof whose outer...Ch. 3 - Prob. 166PCh. 3 - Radioactive material, stored in a spherical vessel...Ch. 3 - What is the R-value of a wall? How does it differ...Ch. 3 - What is effective emissivity for a plane-parallel...Ch. 3 - Prob. 170CPCh. 3 - What is a radiant barrier? What kinds of materials...Ch. 3 - Consider a house whose attic space is ventilated...Ch. 3 - Prob. 173PCh. 3 - Prob. 174PCh. 3 - Prob. 175PCh. 3 - Prob. 176PCh. 3 - Prob. 177PCh. 3 - Prob. 178PCh. 3 - Determine the winter R-value and the U-factor of a...Ch. 3 - The overall heat transfer coefficient (the...Ch. 3 - Prob. 181EPCh. 3 - Determine the summer and winter R-values. in m2 ....Ch. 3 - The overall heat transfer coefficient of a wall is...Ch. 3 - Two homes are identical, except that the walls of...Ch. 3 - Prob. 185PCh. 3 - Consider two identical people each generating 60 V...Ch. 3 - Cold conditioned air at 12C is flowing inside a...Ch. 3 - Hot water is flowing at an average velocity of 1.5...Ch. 3 - Prob. 189PCh. 3 - Prob. 190PCh. 3 - Prob. 191PCh. 3 - Prob. 192PCh. 3 - Prob. 193PCh. 3 - Prob. 194PCh. 3 - Prob. 195PCh. 3 - Prob. 196PCh. 3 - Prob. 197PCh. 3 - A total of 10 rectangular aluminum fins...Ch. 3 - Prob. 199PCh. 3 - A plane wall surface at 200C is to be cooled with...Ch. 3 - Prob. 201PCh. 3 - Prob. 202PCh. 3 - Prob. 203PCh. 3 - Prob. 204PCh. 3 - A 0.6-rn-diameter, 1.9-rn-long cylindrical tank...Ch. 3 - Prob. 206PCh. 3 - Prob. 207PCh. 3 - A thin-walled spherical tank is buried in the...Ch. 3 - Heat is lost at a rate of 275 W per m2 area of a 1...Ch. 3 - Prob. 210PCh. 3 - Heat is generated steadily in a 3-cm-diameter...Ch. 3 - Prob. 212PCh. 3 - Prob. 213PCh. 3 - Prob. 214PCh. 3 - Prob. 215PCh. 3 - Prob. 216PCh. 3 - Consider two walls. A and B, with the same surface...Ch. 3 - Prob. 218PCh. 3 - A room at 20C air temperature is losing heat to...Ch. 3 - Prob. 220PCh. 3 - A 1-cm-diameter, 30cm-long fin made of aluminum...Ch. 3 - A hot surface at 80C in air at 20C is to be cooled...Ch. 3 - A cylindrical pin fin of diameter 0.6 cm and...Ch. 3 - A 3-cm-long. 2-nuti x 2-mm rectangular...Ch. 3 - Two finned surfaces with long fins are identical,...Ch. 3 - A 20-cm-diameter hot sphere at 120C is buried in...Ch. 3 - A 25-cm-diameter, 2.4-rn-long vertical cylinder...Ch. 3 - Prob. 228PCh. 3 - The walls of a food storage facility are made of a...Ch. 3 - The equivalent thermal resistance for the thermal...Ch. 3 - Prob. 231PCh. 3 - Prob. 232PCh. 3 - Prob. 233PCh. 3 - The fin efficiency is defined as the ratio of the...Ch. 3 - Prob. 235PCh. 3 - In the United States, building insulation is...Ch. 3 - Prob. 237PCh. 3 - A plane brick wall (k=0.7W/m.K) and is 10 cm...Ch. 3 - The temperature in deep space is close to absolute...Ch. 3 - In the design of electronic components, it is...Ch. 3 - Using cylindrical samples of the same material,...Ch. 3 - Find out about the wall construction of the cabins...Ch. 3 - Prob. 243PCh. 3 - A house with 200-m2 floor space is to be heated...
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