Questions and Answers of Fundamentals Momentum Heat

Consider the €œdrug patch€ shown in Problem 26.4. The patch consists of a pure solid drug source mounted on top of a water-swollen polymer, which acts as a controlled diffusion
Consider the micro scale apparatus shown in the figure on the next page. This apparatus is designed to deliver a small, steady stream of methanol (MeOH) vapor to a separate device that reforms the
Chicken eggs possess a hard, porous shell of calcite mineral. Cylindrical pores of 10 micron (µm) diameter running through the 0.5 mm thickness of the shell permit the exchange of gases to the
Consider the €œdrug patch€ shown in the figure on the next page. The drug patch consists of a pure drug source mounted on top of a gel diffusion barrier. The gel diffusion
Consider a single, porous, spherical, inert mineral particle. The pores inside the particle are filled with liquid water (species B). We are interested in analyzing the molecular diffusion of the
A common process for increasing the moisture content of air is to bubble it through a column of water. The air bubbles are assumed to be spheres having a radius of 1.0 mm, and are in thermal
“Sour” natural gas is contaminated with hydrogen sulfide. The H2S vapors are commonly treated removed by passing the gas through a packed bed of adsorbent particles. In the present process,
Two disks are oriented on parallel planes separated by a distance of 10 in., as shown in the accompanying figure. The disk to the right is 4 in. in diameter and is at a temperature of 500°F. The
One hundred thousand pounds per hour of water are to pass through a heat exchanger, which is to raise the water temperature from 140 to 200°F. Combustion products having a specific heat of 0.24
A single-pass, shell-and-tube heat exchanger will be used to generate saturated steam by cooling a hot CO2 gas stream. In the present process, boiler feed water at 100°C (373 K) and 1 atm
Consider the novel €œnanostructured€ catalyst surface shown in the figure below. The catalyst support consists of an ordered array of cylindrical nanowells€ of 50 nm
The spherical gel capsule shown in the figure at the top of the next column is used for long-term, sustained drug release. A saturated liquid solution containing the dissolved drug (solute A) is
The chemical vapor deposition of silane vapor (SiH4) forms a thin film of solid silicon as described in example 1, Chapter 25. Consider that the simplified CVD unit shown in Figure 25.5 is operating
Consider the diffusion of solute A into the single cylindrical pore shown in the figure below. The end of the pore at z = L is sealed. The pore space is initially filled with inert fluid
The design of €œartificial organs€ for growing transplant able human tissues require that the cell type of interest, for example pancreatic cells, be grown and sustained within a
Consider the drug treatment system shown in the figure below. A hemispherical cluster of unhealthy cells is surrounded by a larger hemisphere of stagnant dead tissue (species B), which is turn
Consider the catalytic reaction process shown in the figure below. The control volume has two catalytic zones: a porous catalyst (catalyst I) that fills the control volume, and a nonporous catalyst
Consider the process shown in the figure below, where carbon monoxide (CO) gas is being oxidized to carbon dioxide (CO2). This process is similar to how the catalytic converter in your car works to
Consider one of the cylindrical channels of inner diameter d that run through an isomerization catalyst, as shown in the figure below. A catalyst coats the inner walls of each channel. This catalyst
A device has been proposed that will serve as a €œblood oxygenator€ for a heart€“lung bypass machine, as shown in the figure below. In this process, blood containing no
A liquid flows over a thin, flat sheet of a slightly soluble solid. Over the region in which diffusion is occurring, the liquid velocity may be assumed to be parallel to the plate and to be given by
The moisture in hot, humid, stagnant air surrounding a cold-water pipeline continually diffuses to the cold surface where it condenses. The condensed water forms a liquid film around the pipe, and
A hemispherical droplet of liquid water, lying on a flat surface, evaporates by molecular diffusion through still air surrounding the droplet. The droplet initially has a radius R. As the liquid
Show that the (25-11) may be written in the form ӘрА + (V-Pav) — DABVРА 3D ГА дr
Derive equation (25-11) for component A in terms of molar units, starting with the control-volume expression for the conservation of mass. ƏCA - RA = 0 д V · NA +: (25-11)
The case-hardening of mild steel involves the diffusion of carbon into iron. Estimate the diffusion coefficient for carbon diffusing into fcc iron and bcc iron at 1000 K. Learn about the structures
Electronic properties are imparted to crystalline silicon by diffusing an elemental impurity called a €œdopant€ into this material at high temperature. At 1316 K, the
In a chromatographic separation process, a biomolecule of 20 nm diameter is diffusing into a random porous particle with void fraction (e) of 0.70 filled with elution solvent. However, the
A size-exclusion based molecular separation process is being developed to purify a mixture of proteins dissolved in aqueous solution at 20°C. The solution is dilute and approximates the properties
It is desired to concentrate species A from a dilute mixture of solutes A and B dissolved in liquid water using a porous membrane. The membrane contains cylindrical pores in uniform parallel array.
The diffusion rate of the enzyme ribonuclease into a porous chromatography support material was measured at 298 K. An effective diffusion coefficient of 5.0 × 10–7 cm2/s was obtained from an
Protein mixtures in aqueous solution are commonly separated by molecular sieve chromatography. An important aspect of this separation process is the diffusion of the protein into the porous matrix of
As part of a bioseparations process, glucose (solute A) in aqueous solution (solvent B) is diffusing across a microporous membrane. The thickness of the membrane is 2.0 mm, and the pores running
Benzene, a contaminant in groundwater, is diffusing into an inert porous mineral particle at 25°C. The particle has a void fraction of 0.40 with a mean pore diameter of 0.30 mm, and the pores are
The rate of an electrochemical process for plating of solid copper onto a surface from a cupric chloride solution is affected by mass-transfer processes. Estimate the molecular diffusion coefficient
Benzene (species A) is often added to ethanol (species B) to denature the ethanol. Estimate the liquid-phase diffusion of benzene in ethanol (DAB), and ethanol in benzene (DBA) at 288 K by two
Estimate the liquid diffusion coefficients of the following solutes that are transferred through dilute solutions:a. Methanol in water at 288 Kb. Water in methanol at 288 Kc. n-butanol in water at
The diffusion of oxygen (O2) through living tissue is often first approximated as the diffusion of dissolved O2 in liquid water. Estimate the diffusion coefficient of O2 in water by the Wilke–Chang
The Stokes–Einstein equation is often used to estimate the molecular diameter of large spherical molecules from the molecular diffusion coefficient. The measured molecular diffusion coefficient of
A microchannel reactor is being developed for the reforming of methane gas (CH4) to CO2and H2gas using steam (H2O vapor) at high temperature. Prior to entering the reforming reactor, CH4(species A)
Compare the effective diffusion coefficient for a dilute mixture of oxygen gas (O2, species A) in nitrogen gas (N2, species B) at 20°C and 1.0 atm within the following materials:a. Straight 10 nm
A process is being developed to deposit a thin film of silicon electronic grade silicon (Si) onto the inner surface of a hollow glass optical fiber by thermal decomposition of silane (SiH4) to solid
Steam reforming of hydrocarbons is one way to make hydrogen gas (H2) for fuel cell applications. However, the H2-rich product gas produced by steam reforming is contaminated with 1.0 mole% of carbon
A gas separation process has been proposed to remove selectively two pollutants, hydrogen sulfide (H2S) and sulfur dioxide (SO2), from an exhaust gas stream containing 3.0 mole% H2S, 5.0 mole% SO2,
Tetrachlorosilane (SiCl4) gas is reacted with hydrogen gas (H2) to produce electronic-grade polycrystalline silicon at 800°C and 1.5 × 105 Pa according to the reaction equation:SiCl4(g)
Estimate the gas phase diffusion coefficient of ammonia (NH3) in air at 1.0 atm and 373 K by making use of Brokaw equation in the calculations. The dipole moment (μp) for NH3 is 1.46 debye, and the
Estimate the value of the gas-phase diffusion coefficient for the following gas pairs using the Hirschfelder equation:a. Carbon dioxide and air at 310 K and 1:5 × 105 Pab. Ethanol and air
Estimate the molar concentration of 0.50 wt% (0.0050 mass fraction) benzene (C6H6) dissolved in liquid ethanol (C2H5OH) at 20°C. The density of liquid ethanol is 789 kg/m3 at 20°C. This solution of
Consider the following properties of the atmosphere of the planet Mars at a particular measurement point on the surface, as measured by the Mars Rover:Average surface pressure: 6.1 mbarAverage
In a gas-phase diffusion mass-transfer process, the steady-state flux of species A in a binary mixture of A and B is 5.0 × 10–5 kgmole A/m2s, and the flux of B is 0 (zero). At
The general form of the Stefan€“Maxwell equation for mass transfer of species i in an n-component ideal gas mixture along the z-direction for flux is given byShow that for a gas-phase
Starting with Fick’s rate equation for the diffusion of A through a binary mixture of components A and B, provea. NA + NB = cVb. nA + nB = ρ vc. jA + jB = 0
Starting with the Fick€™s rate equation for the diffusion of A through a binary mixture of components A and B, given byShow thatand state all assumptions needed to arrive at this result. NA
A gas consisting of 20% CO2and 80% oxygen and nitrogen leaves a lime kiln at 2000°F and enters a square duct measuring 6 in. by 6 in. in cross section. The specific heat of the gas is 0.28
A gas of mixture at 1000 K and a pressure of 5 atm is introduced into an evacuated spherical cavity with a diameter of 3 m. The cavity walls are black and initially at a temperature of 600 K. What
A duct with square cross section measuring 20 cm by 20 cm has water vapor at 1 atmosphere and 600 K flowing through it. One wall of the duct is held at 420 K and has an emissivity of 0.8. The other
A small (1/4-in.-diameter Ã— 1 in. long) metal test specimen is suspended by very fine wires in a large evacuated tube. The metal is maintained at a temperature of 2500°F, at which
A gray, diffuse circular heater with a diameter of 15 cm is placed parallel to a second gray, diffuse receiver with a spacing of 7.5 between them. The backs of both surfaces are insulated and
A heavily oxidized aluminum surface at 755 K is the source of energy in an enclosure, which radiantly heats the side walls of a circular cylinder surface as shown, to 395 K. The side wall is made of
Evaluate the heat transfer leaving disk 1 for the geometry shown in Problem 23.33. In this case the two disks comprise the bases of a cylinder with side wall at constant temperature of 350°F.
Evaluate the net heat transfer between the disks described in Problem 23.33 if they are bases of a cylinder with the side wall considered a nonconducting, re-radiating surface. How much energy will
If a third rectangular plate, with both surfaces having an emissivity of 0.8 is placed between the two plates describedin Problem 23.31, how will the answer to part (a) of the problem be affected?
Two parallel rectangles have emissivities of 0.6 and 0.9, respectively. These rectangles are 1.2 m wide and 2.4 m high and are 0.6 m apart. The plate having ε = 0.6 is maintained at 1000 K and the
Two parallel black rectangular surfaces, whose back sides are insulated, are oriented parallel to each other with a spacing of 5 m. They measure 5 m by 10 m. The surroundings are black at 0 K. The
A circular heater, measuring 20 cm in diameter, has its surface temperature maintained at 1000°C. The bottom of a tank, having the same diameter, is oriented parallel to the heater with a separation
A cylindrical cavity is closed at the bottom and has an opening centered in the top surface. A cross section of this configuration is shown in the sketch. For the conditions stated below, determine
A dewar flask, used to contain liquid nitrogen, is made of two concentric spheres separated by an evacuated space. The inner sphere has an outside diameter of 1 m and the outer sphere has an inside
A room measuring 12 ft by 20 ft by 8 ft high has its floor and ceiling temperatures maintained at 85°F and 65°F, respectively. Assuming the walls to be re-radiating and all surfaces to have an
The hemispherical cavity shown in the figure has an inside surface temperature of 700 K. A plate of refractory material is placed over the cavity with a circular hole of 5 cm diameter in the center.
The circular base of the cylindrical enclosure shown may be considered a re-radiating surface. The cylindrical walls have an effective emissivity of 0.80 and are maintained at 540°F. The top of
A 12-ft-long, 3-in.-OD iron pipe ε = 0.7, passes horizontally through a 12 × 14 × 9 ft room whose walls are maintained at 70°F and have an emissivity of 0.8. The pipe surface is at a temperature
A heating element in the shape of a cylinder is maintained at 2000°F and placed at the center of a half-cylindrical reflector as shown. The rod diameter is 2 in. and that of the reflector is 18
A circular duct 2 ft long with a diameter of 3 in. has a thermocouple in its center with a surface area of 0.3 in.2. The duct walls are at 200°F, and the thermocouple indicates 310°F. Assuming the
A cryogenic fluid flows in a 20-mm-diameter tube with an outer surface temperature of 75 K and an emissivity of 0.2. A larger tube, having a diameter of 50 mm, is concentric with the smaller one.
If the 7.5-cm-diameter hole in Problem 23.18 were drilled to a depth of 5 cm, what heat loss would result?Data From Problem 23.18A 7.5-cm-diameter hole is drilled in a 10-cm-thick iron plate. If the
A 7.5-cm-diameter hole is drilled in a 10-cm-thick iron plate. If the plate temperature is 700 K and the surroundings are at 310 K, determine the energy loss through the hole. The hole sides may be
Two very large black plane surfaces are maintained at 900 and 580 K, respectively. A third large plane surface, having ε = 0.8, is placed between these two. Determine the fractional change in
A large cavity with a small opening, 0.0025 m2 in area, emits 8 W. Determine the wall temperature of the cavity.
A sheet-metal box in the shape of a 0.70-m cube has a surface emissivity of 0.7. The box encloses electronic equipment that dissipates 1200 W of energy. If the surroundings are taken to be black at
A furnace that has black interior walls maintained at 1500 K contains a peephole with a diameter of 10 cm. The glass in the peephole has a transmissivity of 0.78 between 0 and 3.2 µm and 0.08
A small circular hole is to be drilled in the surface of a large, hollow, spherical enclosure maintained at 2000 K. If 100 W of radiant energy exits through the hole, determine (a) the hole diameter,
The sun’s temperature is approximately 5800 K and the visible light range is taken to be between 0.4 and 0.7 mm. What fraction of solar emission is visible? What fraction of solar emission lies in
Determine the fraction of total energy emitted by a black body, which lies in the wavelength band between 0.8 and 5.0 mm for surface temperatures of 500, 2000, 3000, and 4500 K.
The distribution of solar energy incident on Earth can be approximated as being from a black body at 5800 K. Two kinds of glass, plain and tinted, are being considered for use in windows. The
A greenhouse is constructed of silica glass that is known to transmit 92% of incident radiant energy between wavelengths of 0.35 and 2.7 mm. The glass may be considered opaque for wavelengths above
The filament of an ordinary 100 W light bulb is at 2910 K and it is presumed to be a black body. Determine (a) the wavelength of maximum emission and (b) the fraction of emission in the visible
Determine the wavelength of maximum emission for (a) the sun with an assumed temperature of 5790 K, (b) a light bulk filament at 2910 K, (c) a surface at 1550 K, and (d) human skin at 308
A tungsten filament, radiating as a gray body, is heated to a temperature of 4000°R. At what wavelength is the emissive power maximum? What portion of the total emission lies within the
A radiation detector, oriented as shown in the sketch, is used to estimate heat loss through an opening in a furnace wall. The opening in this case is circular with a diameter of 2.5 cm. The detector
A black solar collector, with a surface area of 60 m2, is placed on the roof of a house. Incident solar energy reaches the collector with a flux of 800 W/m2. The surroundings are considered black
An opaque gray surface with ε = 0.3 is irradiated with 1000 W/cm. For an effective convective heat-transfer coefficient of 12W/m2 · K applying, and air at 20°C adjacent to the plate, what will be
A satellite may be considered spherical, with its surface properties roughly those of aluminum. Its orbit may be considered circular at a height of 500 miles above Earth. Taking the satellite
The sun is approximately 93 million miles distant from Earth, and its diameter is 860,000 miles. On a clear day solar irradiation at Earth’s surface has been measured at 360 Btu/h ft2 and an
For the heat exchanger described in Problem 22.27, it is observed, after a long period of operation, that the cold stream leaves at 184°F instead of at the design value of 220°F. This is for the
A shell-and-tube heat exchanger with two shell passes and four tube passes is used to exchange energy between two pressurized water streams. One stream flowing at 5000 lbm/h is heated from 75 to
Water flowing at a rate of 10 kg/s through 50 tubes in a double-pass shell-and-tube heat exchanger heats air that flows on the shell side. The tubes are made of brass with outside diameters of 2.6 cm
Determine the required heat-transfer surface area for a heat exchanger constructed from 10-cm OD tubes. A 95% ethanol solution (cp = 3.8l0kJ/kg · K), flowing at 6.93 kg/s is cooled from 340 to 312 K
If the overall heat-transfer coefficient, initial fluid temperature, and total heat-transfer area determined in Problem 22.2 remain the same, find the exit oil temperature if the configuration is
A finned-tube cross flow heat exchanger with both fluids unmixed is used to heat water (Cpw = 4.2 kJ/kg · K) from 20°C to 75°C. The mass flow rate of the water is 2.7 kg/s. The hot stream
A water-to-oil heat exchanger has entering and exiting temperatures of 255 and 340 K, respectively, for the water and 305 and 350 K, respectively, for the oil. What is the effectiveness of this heat

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