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engineering
heat and mass transfer fundamentals and applications
Questions and Answers of
Heat And Mass Transfer Fundamentals And Applications
A spherical particle of radius \(r_{1}=5 \mathrm{~mm}\) is suspended by a thin wire within a cylindrical tube of inner radius \(r_{2}=15 \mathrm{~mm}\) and length \(L=0.5 \mathrm{~m}\). Determine the
Consider the following grooves, each of width \(W\), that have been machined from a solid block of material.(a) For each case obtain an expression for the view factor of the groove with respect to
Determine the shape factor, \(F_{12}\), for the rectangles shown. 3 m -6 m- 1 m 6 m 2 6 m 1 0.5 m 1 2 1 m 1 m- (a) Perpendicular rectangles without a common edge. (b) Parallel rectangles of unequal
A drying oven consists of a long semicircular duct of diameter \(D=1.5 \mathrm{~m}\).Materials to be dried cover the base of the oven while the wall is maintained at \(1200 \mathrm{~K}\). What is the
Consider coaxial, parallel, black disks separated a distance of \(0.20 \mathrm{~m}\). The lower disk of diameter \(0.40 \mathrm{~m}\) is maintained at \(500 \mathrm{~K}\) and the surroundings are at
A cylindrical cavity of diameter \(D\) and depth \(L\) is machined in a metal block, and conditions are such that the base and side surfaces of the cavity are maintained at \(T_{1}=950 \mathrm{~K}\)
Two plane coaxial disks are separated by a distance \(L=0.80 \mathrm{~m}\). The lower disk \(\left(A_{1}\right)\) is solid with a diameter \(D_{o}=0.80 \mathrm{~m}\) and a temperature \(T_{1}=300
The arrangement shown is to be used to calibrate a heat flux gage. The gage has a black surface that is \(8 \mathrm{~mm}\) in diameter and is maintained at \(10^{\circ} \mathrm{C}\) by means of a
Equation 1.7 is subject to several restrictions, such as the surroundings being isothermal and large relative to the smaller surface. Consider the small and large surfaces to be isothermal concentric
A flat-bottomed hole \(8 \mathrm{~mm}\) in diameter is bored to a depth of \(24 \mathrm{~mm}\) in a diffuse, gray material having an emissivity of 0.8 and a uniform temperature of \(1000
Consider a double-pane window. The glass surface may be treated with a low-emissivity coating to reduce its emissivity from \(\varepsilon=0.95\) to \(\varepsilon=0.05\). Determine the radiation heat
Two large parallel plates are maintained at \(T_{1}=500\) and \(T_{2}=300 \mathrm{~K}\), respectively. The hot plate has an emissivity of 0.9 while that of the cold plate is 0.7 .(a) Determine the
Consider the attic of a home located in a hot climate. The floor of the attic is characterized by a width of \(L_{1}=8 \mathrm{~m}\) while the roof makes an angle of \(\theta=30^{\circ}\) from the
Liquid oxygen is stored in a thin-walled, spherical container \(0.75 \mathrm{~m}\) in diameter, which is enclosed within a second thin-walled, spherical container \(1.1 \mathrm{~m}\) in diameter. The
A cryogenic fluid flows through a tube \(20 \mathrm{~mm}\) in diameter, the outer surface of which is diffuse and gray with an emissivity of 0.05 and temperature of \(77 \mathrm{~K}\). This tube is
A long conduit is constructed with diffuse, gray walls \(0.5 \mathrm{~m}\) wide. The top and bottom of the conduit are insulated. The emissivities of the walls are \(\varepsilon_{1}=0.45,
Two parallel, aligned disks, \(0.35 \mathrm{~m}\) in diameter and separated by \(0.1 \mathrm{~m}\), are located in a large room whose walls are maintained at \(300 \mathrm{~K}\). One of the disks is
A molten aluminum alloy at \(950 \mathrm{~K}\) is poured into a cylindrical container that is well insulated from large surroundings at \(300 \mathrm{~K}\). The inner diameter of the container is
A cubical furnace \(2.5 \mathrm{~m}\) on a side is used for heat treating steel plate. The top surface of the furnace consists of electrical radiant heaters that have an emissivity of 0.85 and a
Consider a circular furnace that is \(0.5 \mathrm{~m}\) long and \(0.5 \mathrm{~m}\) in diameter. The two ends have diffuse, gray surfaces that are maintained at 400 and \(500 \mathrm{~K}\) with
Three long, \(20-\mathrm{mm}\)-diameter cylindrical bars are to be heat-treated in an oven. The bars are initially at a temperature of \(300 \mathrm{~K}\), while the oven walls are charcoated and at
Two convex objects are inside a large vacuum enclosure whose walls are maintained at \(T_{3}=300 \mathrm{~K}\). The objects have the same area, \(0.2 \mathrm{~m}^{2}\), and the same emissivity, 0.2.
A laboratory oven has a cubical interior chamber \(1 \mathrm{~m}\) on a side with interior surfaces that are of emissivity \(\varepsilon=0.85\).Determine the initial rate of radiation heat transfer
Consider Problem 6.14. The stationary plate, ambient air, and surroundings are at \(T_{\infty}=T_{\text {sur }}=20^{\circ} \mathrm{C}\). If the rotating disk temperature is \(T_{s}=80^{\circ}
The spectral absorptivity of a large diffuse surface is \(\alpha_{\lambda}=0.9\) for \(\lambda(a) In case (a) the surface is exposed to the sun, which provides an irradiation of \(G_{S}=1200
Hot coffee is contained in a cylindrical thermos botthe that is of length \(L=0.3 \mathrm{~m}\) and is lying on its side (horizontally).The coffee container consists of a glass flask of diameter
Pure, solid silicon is produced from a melt, as, for example, in Problem 1.37. Solid silicon is semitransparent, and the spectral absorption coefficient distribution for pure silicon may be
A furnace having a spherical cavity of \(0.4-\mathrm{m}\) diameter contains a gas mixture at \(1 \mathrm{~atm}\) and \(1400 \mathrm{~K}\). The mixture consists of \(\mathrm{CO}_{2}\) with a partial
Wet pharmaceutical tablets are processed in an infrared dryer consisting of a cylindrical drum \(\left(D_{d}=0.5 \mathrm{~m}\right)\) that rotates slowly about a stationary cylindrical infrared
A mixture of \(\mathrm{CO}_{2}\) and \(\mathrm{N}_{2}\) is in a container at \(45^{\circ} \mathrm{C}\), with each species having a partial pressure of 0.75 bar. Calculate the molar concentration, the
A container holds a mixture of \(\mathrm{O}_{2}\) and \(\mathrm{H}_{2}\) at a total pressure of 1 bar. The mass fraction of \(\mathrm{O}_{2}\) is 0.75 . If the temperature of the mixture is
Estimate values of the mass diffusivity \(D_{\mathrm{AB}}\) for binary mixtures of the following gases at \(350 \mathrm{~K}\) and \(1 \mathrm{~atm}\) : ammonia-air and hydrogen-air.
An old-fashioned glass apothecary jar contains a patent medicine. The neck is closed with a rubber stopper that is \(20 \mathrm{~mm}\) tall, with a diameter of \(15 \mathrm{~mm}\) at the bottom end,
An open vertical tube of diameter \(5 \mathrm{~mm}\) and height \(100 \mathrm{~mm}\) (above water at \(27^{\circ} \mathrm{C}\) ) is exposed to ambient air at \(27^{\circ} \mathrm{C}\) and \(25 \%\)
A laboratory apparatus to measure the diffusion coefficient of vapor-gas mixtures consists of a vertical, small-diameter column containing the liquid phase that evaporates into the gas flowing over
A thin plastic membrane is used to separate helium from a gas stream. Under steady-state conditions the concentration of helium in the membrane is known to be 0.02 and \(0.008 \mathrm{kmol} /
A spherical rubber container of diameter \(200 \mathrm{~mm}\) and wall thickness \(1 \mathrm{~mm}\) contains a gas at a pressure of \(5 \mathrm{bar}\). The container is placed in air of pressure \(1
Hydrogen at a pressure of \(5 \mathrm{~atm}\) flows within a tube of diameter \(40 \mathrm{~mm}\) and wall thickness \(1.0 \mathrm{~mm}\). The outer surface is exposed to a gas stream for which the
Oxygen gas is maintained at pressures of \(1.5 \mathrm{bar}\) and 0.5 bar on opposite sides of a rubber membrane that is \(0.75 \mathrm{~mm}\) thick, and the entire system is at \(25^{\circ}
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
Consider Example 14.4. Find the time required for the pressure in the container to drop by \(1 \%\) and by \(10 \%\), taking into account that as the interior pressure drops so does the leakage rate.
Helium gas at \(25^{\circ} \mathrm{C}\) and 6 bar is contained in a glass cylinder of \(100-\mathrm{mm}\) inside diameter and \(5-\mathrm{mm}\) thickness. What is the rate of mass loss per unit
An experiment is designed to measure the partition coefficient, \(K\), associated with the transfer of a pharmaceutical product through a polymer material. The partition coefficient is defined as the
Nitric oxide (NO) emissions from automobile exhaust can be reduced by using a catalytic converter, and the following reaction occurs at the catalytic surface:\[\mathrm{NO}+\mathrm{CO} \rightarrow
A platinum catalytic reactor in an automobile is used to convert carbon monoxide to carbon dioxide in an oxidation reaction of the form \(2 \mathrm{CO}+\mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2}\).
A large sheet of material \(50 \mathrm{~mm}\) thick contains dissolved hydrogen \(\left(\mathrm{H}_{2}\right)\) having a uniform concentration of \(3 \mathrm{kmol} / \mathrm{m}^{3}\). The sheet is
A common procedure for increasing the moisture content of air is to bubble it through a column of water. Assume the air bubbles to be spheres of radius \(r_{o}=\) \(1 \mathrm{~mm}\) and to be in
Steel is carburized in a high-temperature process that depends on the transfer of carbon by diffusion. The value of the diffusion coefficient is strongly temperature dependent and may be approximated
A thick plate of pure iron at \(1000^{\circ} \mathrm{C}\) is subjected to a carburization process in which the surface of the plate is suddenly exposed to a gas that induces a carbon concentration
Hydrogen gas is used in a process to manufacture a sheet material of 6-mm thickness. At the end of the process, \(\mathrm{H}_{2}\) remains in solution in the material with a uniform concentration of
A person applies an insect repellent onto an exposed area of \(A=0.1 \mathrm{~m}^{2}\) of their body. The mass of spray used is \(m=2\) grams, and the spray contains \(15 \%\) (by mass) active
Show that, for water at 1-atm pressure with \(T_{s}-T_{\text {sat }}=\) \(8^{\circ} \mathrm{C}\), the Jakob number is much less than unity. What is the physical significance of this result? Verify
A long, 2-mm-diameter wire passes an electrical current dissipating \(4700 \mathrm{~W} / \mathrm{m}\) and reaches a surface temperature of \(118^{\circ} \mathrm{C}\) when submerged in water at \(1
The hysteresis behavior of the boiling curve becomes less pronounced as the difference between the minimum and maximum (critical) heat fluxes becomes small. Calculate the ratio of the maximum to
Water at atmospheric pressure boils on the surface of a large horizontal copper tube. The heat flux is \(90 \%\) of the critical value. The tube surface is initially scored; however, over time the
The bottom of a copper pan, \(200 \mathrm{~mm}\) in diameter, is maintained at \(113^{\circ} \mathrm{C}\) by the heating element of an electric range. Estimate the power required to boil the water in
A 0.3 -m-diameter, 5 -mm-thick horizontal copper disk is heated from below at a rate of \(70 \mathrm{~kW}\). The top of the disk is polished, and exposed to a water bath at atmospheric pressure.
Saturated ethylene glycol at \(1 \mathrm{~atm}\) is heated by a horizontal chromium-plated surface which has a diameter of \(200 \mathrm{~mm}\) and is maintained at \(480 \mathrm{~K}\). Estimate the
Estimate the power \(\left(\mathrm{W} / \mathrm{m}^{2}\right)\) required to maintain a brass plate at \(\Delta T_{e}=10^{\circ} \mathrm{C}\) while boiling saturated water at \(1 \mathrm{~atm}\). What
Determine the minimum and maximum possible surface temperatures of a polished, horizontal copper tube of diameter \(D=35 \mathrm{~mm}\), in water at atmospheric pressure, associated with a heat flux
A disk-shaped turbine rotor is heat-treated by quenching in water at \(p=1 \mathrm{~atm}\). Initially, the rotor is at a uniform temperature of \(T_{i}=1100^{\circ} \mathrm{C}\) and the water is at
A steel bar, \(25 \mathrm{~mm}\) in diameter and \(300 \mathrm{~mm}\) long, with an emissivity of 0.85 , is removed from a furnace at \(455^{\circ} \mathrm{C}\) and suddenly submerged horizontally in
Saturated water at \(1 \mathrm{~atm}\) and velocity \(3 \mathrm{~m} / \mathrm{s}\) flows over a cylindrical heating element of diameter \(10 \mathrm{~mm}\). What is the maximum heating rate
Saturated steam at 0.2 bar condenses with a convection coefficient of \(6000 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) on the outside of a brass tube having inner and outer diameters of 16 and
Consider a container exposed to a saturated vapor, \(T_{\text {sat }}\), having a cold bottom surface, \(T_{s}Assuming a linear temperature distribution for the liquid, perform a surface energy
Determine the total condensation rate of water onto the front surface of a vertical plate that is \(10 \mathrm{~mm}\) high and \(1 \mathrm{~m}\) in the horizontal direction. The plate is exposed to
A \(3 \mathrm{~m} \times 3 \mathrm{~m}\) vertical plate is exposed on one side to saturated steam at atmospheric pressure and on the other side to cooling water that maintains a plate temperature of
Condensation rates can be restricted by the speed of sound of the vapor phase. Hence, condensation can approach a sonic limit. Consider an \(S=2 \mathrm{~mm}\) wide, \(L=200 \mathrm{~mm}\) long
The condenser of a steam power plant consists of a square (in-line) array of 900 tubes, each of \(25-\mathrm{mm}\) diameter. Consider conditions for which saturated steam at 0.135 bars condenses on
Determine the total condensation rate and heat transfer rate for the process of Problem 10.35 when the pipe is oriented at angles of \(\theta=0,30,45\), and \(60^{\circ}\) from the horizontal.Data
Consider Problem 10.33. In an effort to increase the condensation rate, an engineer proposes to apply an \(L=100-\mu \mathrm{m}\)-thick Teflon coating to the exterior surface of the brass tube to
Consider the thermosyphon of Problem 10.54. In many applications, a more realistic scenario is one where the condensation section is cooled by an external, flowing fluid. Determine the thermosyphon
An industrial boiler consists of tubes inside of which flow hot combustion gases. Water boils on the exterior of the tubes. When installed, the clean boiler has an overall heat transfer coefficient
A finned-tube, cross-flow heat exchanger is to use the exhaust of a gas turbine to heat pressurized water. Laboratory measurements are performed on a prototype version of the exchanger, which has a
Consider Example 7.7. Determine the heat rate using the \(\varepsilon\)-NTU method. Assume the air flows in a duct of height \(N_{T} S_{T}\) where \(N_{T}=8\) tubes per row and \(S_{T}\) is the
The hot and cold inlet temperatures to a concentric tube heat exchanger are \(T_{h, i}=200^{\circ} \mathrm{C}, T_{c, i}=100^{\circ} \mathrm{C}\), respectively. The outlet temperatures are \(T_{h,
Consider a concentric tube heat exchanger with an area of \(60 \mathrm{~m}^{2}\) operating under the following conditions:(a) Determine the outlet temperature of the cold fluid.(b) Is the heat
A concentric tube heat exchanger for cooling lubricating oil consists of a thin-walled inner tube of \(25-\mathrm{mm}\) diameter carrying water and an outer tube of \(45-\mathrm{mm}\) diameter
The compartment heater of an automobile exchanges heat between warm radiator fluid and cooler outside air. The flow rate of water is large compared to the air, and the effectiveness, \(\varepsilon\),
A shell-and-tube heat exchanger with one shell and two tube passes is designed to heat liquid water flowing at \(3.0 \mathrm{~kg} / \mathrm{s}\) from 25 to \(65^{\circ} \mathrm{C}\) using hot air.
A shell-and-tube heat exchanger (1 shell pass, 2 tube passes) is to be used to condense \(3.0 \mathrm{~kg} / \mathrm{s}\) of saturated steam at \(330 \mathrm{~K}\). Condensation occurs on the outer
A heat exchanger has inlet and outlet temperatures of 90 and \(45^{\circ} \mathrm{C}\) for the hot fluid and 15 and \(42^{\circ} \mathrm{C}\) for the cold fluid. Can you tell whether this exchanger
An energy storage system is proposed to absorb thermal energy collected during the day with a solar collector and release thermal energy at night to heat a building. The key component of the system
Using the results shown in Table 11.3, determine an expression for the ratio of the effectiveness of a counterflow heat exchanger to that of a parallel flow heat exchanger. Considering the same heat
The oil in an engine is cooled by air in a cross-flow heat exchanger where both fluids are unmixed. Atmospheric air enters at \(10^{\circ} \mathrm{C}\) and \(0.5 \mathrm{~kg} / \mathrm{s}\). Oil at
It is proposed that the exhaust gas from a natural gaspowered electric generation plant be used to generate steam in a shell-and-tube heat exchanger with one shell and one tube pass. The steel tubes
A concentric tube heat exchanger uses water, which is available at \(25^{\circ} \mathrm{C}\), to cool ethylene glycol from 110 to \(70^{\circ} \mathrm{C}\). The water and glycol flow rates are each
Water is used for both fluids (unmixed) flowing through a single-pass, cross-flow heat exchanger. The hot water enters at \(80^{\circ} \mathrm{C}\) and \(15,000 \mathrm{~kg} / \mathrm{h}\), while the
Derive Equation 11.35a. = 1 exp(-NTU) (11.35a)
A liquefied natural gas (LNG) regasification facility utilizes a vertical heat exchanger or vaporizer that consists of a shell with a single-pass tube bundle used to convert the fuel to its vapor
Work Problem 11.53 for the situation where the seawater is introduced to the top of the vaporizer, resulting in counterflowing natural gas and seawater.Data From Problem 11.53:-A liquefied natural
Hot exhaust gases are used in a shell-and-tube exchanger to heat \(3.0 \mathrm{~kg} / \mathrm{s}\) of water from 30 to \(90^{\circ} \mathrm{C}\). The gases, assumed to have the properties of air,
In a manufacturing operation, a 1-mm-thick tubular steel collar is to be shrink-fitted onto a 3-mm-diameter pin of circular cross section. Prior to initiating the shrink-fit operation, the collar is
A horizontal, opaque surface at a steady-state temperature of \(80^{\circ} \mathrm{C}\) is exposed to an airflow having a free stream temperature of \(25^{\circ} \mathrm{C}\) with a convection heat
The top surface of an \(L=5\)-mm-thick anodized aluminum plate is irradiated with \(G=1000 \mathrm{~W} / \mathrm{m}^{2}\) while being simultaneously exposed to convection conditions characterized by
A horizontal semitransparent plate is uniformly irradiated from above and below, while air at \(T_{\infty}=310 \mathrm{~K}\) flows over the top and bottom surfaces, providing a uniform convection
A radiation detector has an aperture of area \(A_{d}=10^{-6} \mathrm{~m}^{2}\) and is positioned at a distance of \(r=2 \mathrm{~m}\) from a surface of area \(A_{s}=10^{-4} \mathrm{~m}^{2}\). The
The emitted intensity from a non-conducting material may be approximated as follows:\[\begin{array}{ll}I_{e}=I_{n} & 0 \leq \theta \leq \pi / 3 \\I_{e}=I_{n}\left(3-\frac{6 \theta}{\pi}\right) & \pi
The energy flux associated with solar radiation incident on the outer surface of the earth's atmosphere has been accurately measured and is known to be \(1368 \mathrm{~W} / \mathrm{m}^{2}\). The
A spherical aluminum shell of inside diameter \(D=2 \mathrm{~m}\) is evacuated and is used as a radiation test chamber. If the inner surface is coated with carbon black and maintained at \(800
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