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engineering
heat and mass transfer fundamentals and applications

Questions and Answers of Heat And Mass Transfer Fundamentals And Applications

Consider a plane composite wall that is composed of two materials of thermal conductivities \(k_{\mathrm{A}}=0.09 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and \(k_{\mathrm{B}}=0.03 \mathrm{~W} /
The performance of gas turbine engines may be improved by increasing the tolerance of the turbine blades to hot gases emerging from the combustor. One approach to achieving high operating
Consider a power transistor encapsulated in an aluminum case that is attached at its base to a square aluminum plate of thermal conductivity \(k=240 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\),
A lightweight aggregate concrete slab of density \(ho=\) \(1500 \mathrm{~kg} / \mathrm{m}^{3}\) consists of a solid, stone mix concrete matrix within which are small spherical pockets of air.
A truncated solid cone is of circular cross section, and its diameter is related to the axial coordinate by an expression of the form \(D=a x^{3 / 2}\), where \(a=2.0 \mathrm{~m}^{-1 / 2}\).The sides
To maximize production and minimize pumping costs, crude oil is heated to reduce its viscosity during transportation from a production field.(a) Consider a pipe-in-pipe configuration consisting of
A thin electrical heater is wrapped around the outer surface of a long cylindrical tube whose inner surface is maintained at a temperature of \(6^{\circ} \mathrm{C}\). The tube wall has inner and
A 3-mm-diameter electrical wire is insulated by a 2-mm-thick rubberized sheath \((k=0.13 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\), and the wire/sheath interface is characterized by a thermal
A spherical Pyrex glass shell has inside and outside diameters of \(D_{1}=0.15 \mathrm{~m}\) and \(D_{2}=0.30 \mathrm{~m}\), respectively. The inner surface is at \(T_{s, 1}=150^{\circ} \mathrm{C}\)
A hollow aluminum sphere, with an electrical heater in the center, is used in tests to determine the thermal conductivity of insulating materials. The inner and outer radii of the sphere are 0.18 and
A spherical tank for storing liquid oxygen is to be made from stainless steel of \(0.75-\mathrm{m}\) outer diameter and \(6-\mathrm{mm}\) wall thickness. The boiling point and latent heat of
A spherical tank of 4-m diameter contains a liquifiedpetroleum gas at \(-60^{\circ} \mathrm{C}\). Insulation with a thermal conductivity of \(0.06 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and
Liquid nitrogen \((T=77 \mathrm{~K})\) is stored in a thin-walled, spherical container that is covered with a uniformly thick insulation layer of thermal conductivity \(k=0.15\) \(\mathrm{W} /
An uncoated, solid cable of length \(L=1 \mathrm{~m}\) and diameter \(D=40 \mathrm{~mm}\) is exposed to convection conditions characterized by \(h=55 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)
A plane wall of thickness \(0.2 \mathrm{~m}\) and thermal conductivity \(30 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) having uniform volumetric heat generation of \(0.4 \mathrm{MW} /
Large, cylindrical bales of hay used to feed livestock in the winter months are \(D=2 \mathrm{~m}\) in diameter and are stored end-to-end in long rows. Microbial energy generation occurs in the hay
An air heater may be fabricated by coiling Nichrome wire and passing air in cross flow over the wire. Consider a heater fabricated from wire of diameter \(D=\) \(2 \mathrm{~mm}\), electrical
Derive Equations C.2, C.5, and C. 8 of Appendix C.Data From Equation C.2, C.5, C.8:- T(r) = T.2 + 4k 4k (1)-(1)+ (T..2-T1) In(r/r) In(ra/ra) (C.2)
Derive Equations C.3, C.6, and C. 9 of Appendix C.Data From Equation C.3, C.6, C.9:- T(r) = T,,2 + -(T,.2 - Ts,1) 6k 6k (1/r)-(1/r) (1/r) - (1/r) (C.3)
Steady-state conditions exist within the one-dimensional composite cylinder shown. The three materials have thermal conductivities of \(k_{\mathrm{A}}, k_{\mathrm{B}}=2 k_{\mathrm{A}}\), and
For the conditions described in Problem 1.39, determine the temperature distribution, \(T(r)\), in the container, expressing your result in terms of \(\dot{q}_{o}, r_{o}, T_{\infty}, h\), and the
A high-temperature, gas-cooled nuclear reactor consists of a composite cylindrical wall for which a thorium fuel element \((k \approx 57 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) is encased in
A long cylindrical rod of diameter \(240 \mathrm{~mm}\) with thermal conductivity of \(0.6 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) experiences uniform volumetric heat generation of \(24,000
Radioactive wastes are packed in a thin-walled spherical container. The wastes generate thermal energy nonuniformly according to the relation \(\dot{q}=\dot{q}_{o}\left[1-\left(r /
Radioactive wastes \(\left(k_{\mathrm{rw}}=20 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\right)\) are stored in a spherical, stainless steel \(\left(k_{\mathrm{ss}}=15 \mathrm{~W} / \mathrm{m} \cdot
Consider the manufacture of photovoltaic silicon, as described in Problem 1.37. The thin sheet of silicon is pulled from the pool of molten material very slowly and is subjected to an ambient
A stainless steel rod (AISI 304) of length \(L=100 \mathrm{~mm}\) and triangular cross section is attached between two isothermal heat sinks at \(T_{o}=50^{\circ} \mathrm{C}\). The rod perimeter is
A long, circular aluminum rod is attached at one end to a heated wall and transfers heat by convection to a cold fluid.(a) If the diameter of the rod is doubled, by how much would the rate of heat
A pin fin of uniform, cross-sectional area is fabricated of an aluminum alloy \((k=160 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\). The fin diameter is \(D=4 \mathrm{~mm}\), and the fin is exposed
Two long copper rods of diameter \(D=8 \mathrm{~mm}\) are soldered together end to end, with solder having a melting point of \(250^{\circ} \mathrm{C}\). The rods are in air at \(30^{\circ}
An experimental arrangement for measuring the thermal conductivity of solid materials involves the use of two long rods that are equivalent in every respect, except that one is fabricated from a
Determine the percentage increase in heat transfer associated with attaching aluminum fins of rectangular profile to a plane wall. The fins are \(45 \mathrm{~mm}\) long, \(0.5 \mathrm{~mm}\) thick,
An aluminum tube of inner diameter \(D_{i}=1 \mathrm{~mm}\) and wall thickness \(0.1 \mathrm{~mm}\) is used to transport a warm biological fluid. The tube is coated with \(N=500\) alternating layers
Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity \(k=50 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and a thickness \(L=0.35
Consider a plane wall \(120 \mathrm{~mm}\) thick and of thermal conductivity \(120 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Steady-state conditions are known to exist with \(T_{1}=500
Consider a \(400 \mathrm{~mm} \times 400 \mathrm{~mm}\) window in an aircraft. For a temperature difference of \(90^{\circ} \mathrm{C}\) from the inner to the outer surface of the window, calculate
Calculate the thermal conductivity of air, hydrogen, and carbon dioxide at \(300 \mathrm{~K}\), assuming ideal gas behavior. Compare your calculated values to values from Table A.4.Data From Table
The thermal conductivity of helium at a certain temperature is \(0.15 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). Calculate the helium temperature assuming ideal gas behavior, and compare it to the
A method for determining the thermal conductivity \(k\) and the specific heat \(c_{p}\) of a material is illustrated in the sketch. Initially the two identical samples of diameter \(D=50
Consider the temperature distributions associated with a \(d x\) differential control volume within the one-dimensional plane walls shown below.(a) Steady-state conditions exist. Is thermal energy
Consider a one-dimensional plane wall of thickness \(2 L\) that experiences uniform volumetric heat generation. The surface temperatures of the wall are maintained at \(T_{s, 1}\) and \(T_{s, 2}\) as
Uniform internal heat generation at \(\dot{q}=6 \times 10^{7} \mathrm{~W} / \mathrm{m}^{3}\) is occurring in a cylindrical nuclear reactor fuel rod of \(60-\mathrm{mm}\) diameter, and under
A plane wall of thickness \(2 L=60 \mathrm{~mm}\) and thermal conductivity \(k=5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) experiences uniform volumetric heat generation at a rate \(\dot{q}\),
A composite rod consists of two different materials, A and B, each of length \(0.5 L\).The thermal conductivity of Material A is half that of Material B, that is, \(k_{\mathrm{A}} /
A one-dimensional plane wall of thickness \(2 L=\) \(80 \mathrm{~mm}\) experiences uniform thermal energy generation of \(\dot{q}=1000 \mathrm{~W} / \mathrm{m}^{3}\) and is convectively cooled at\(x=
The steady-state temperature distribution in a onedimensional wall of thermal conductivity \(k\) and thickness \(L\) is of the form \(T=a x^{2}+b x+c\). Derive expressions for the heat fluxes at the
One-dimensional, steady-state conduction with no energy generation is occurring in a plane wall of constant thermal conductivity.(a) Is the prescribed temperature distribution possible? Briefly
A plane layer of coal of thickness \(L=1 \mathrm{~m}\) experiences uniform volumetric generation at a rate of \(\dot{q}=10 \mathrm{~W} / \mathrm{m}^{3}\) due to slow oxidation of the coal particles.
Consider the steady-state temperature distribution in a radial wall (cylinder or sphere) of inner and outer radii \(r_{i}\) and \(r_{o}\), respectively. The temperature distribution is\[T(r)=C_{1}
Two-dimensional, steady-state conduction occurs in a hollow cylindrical solid of thermal conductivity \(k=22 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), outer radius \(r_{o}=1.5 \mathrm{~m}\), and
Consider the steady-state temperature distributions within a composite wall composed of Material A and Material B for the two cases shown. There is no internal generation, and the conduction process
A long cylindrical rod, initially at a uniform temperature \(T_{i}\), is suddenly immersed in a large container of liquid at \(T_{\infty}
A composite one-dimensional plane wall is of overall thickness \(2 L\). Material A spans the domain \(-L \leq x
Consider the fireclay brick wall of Example 1.1 that is operating under different thermal conditions. The temperature distribution, at an instant in time, is \(T(x)=a+\) \(b x\) where \(a=1400
The thermal conductivity of a sheet of rigid, extruded insulation is reported to be \(k=0.029 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). The measured temperature difference across a 25 -mm-thick
The heat flux that is applied to the left face of a plane wall is \(q^{\prime \prime}=20 \mathrm{~W} / \mathrm{m}^{2}\). The wall is of thickness \(L=10\) \(\mathrm{mm}\) and of thermal conductivity
The concrete slab of a basement is \(11 \mathrm{~m}\) long, \(8 \mathrm{~m}\) wide, and \(0.20 \mathrm{~m}\) thick. During the winter, temperatures are nominally \(17^{\circ} \mathrm{C}\) and
The heat flux through a wood slab \(50 \mathrm{~mm}\) thick, whose inner and outer surface temperatures are 40 and \(20^{\circ} \mathrm{C}\), respectively, has been determined to be \(40 \mathrm{~W}
The inner and outer surface temperatures of a glass window \(5 \mathrm{~mm}\) thick are 15 and \(5^{\circ} \mathrm{C}\). The thermal resistance of the glass window due to conduction is \(R_{t, \text
The heat flux that is applied to one face of a plane wall is \(q^{\prime \prime}=20 \mathrm{~W} / \mathrm{m}^{2}\). The opposite face is exposed to air at temperature \(30^{\circ} \mathrm{C}\), with
A wall is made from an inhomogeneous (nonuniform) material for which the thermal conductivity varies through the thickness according to \(k=a x+b\), where \(a\) and \(b\) are constants. The heat flux
The 8-mm-thick bottom of a 220-mm-diameter pan may be made from aluminum \((k=240 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) or copper \((k=390 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\). When
You've experienced convection cooling if you've ever extended your hand out the window of a moving vehicle or into a flowing water stream. With the surface of your hand at a temperature of
The free convection heat transfer coefficient on a thin hot vertical plate suspended in still air can be determined from observations of the change in plate temperature with time as it cools.
A cartridge electrical heater is shaped as a cylinder of length \(L=300 \mathrm{~mm}\) and outer diameter \(D=30 \mathrm{~mm}\). Under normal operating conditions, the heater dissipates \(2
A one-dimensional plane wall is exposed to convective and radiative conditions at \(x=0\). The ambient and surrounding temperatures are \(T_{\infty}=20^{\circ} \mathrm{C}\) and \(T_{\text {sur
An overhead 25 -m-long, uninsulated industrial steam pipe of \(100-\mathrm{mm}\) diameter is routed through a building whose walls and air are at \(25^{\circ} \mathrm{C}\). Pressurized steam
A vacuum system, as used in sputtering electrically conducting thin films on microcircuits, is comprised of a baseplate maintained by an electrical heater at \(400 \mathrm{~K}\) and a shroud within
Energy storage is necessary to, for example, allow solar-derived electricity to be generated around the clock. For a given mass of storage medium, show that the ratio of sensible thermal energy
An electrical resistor is connected to a battery, as shown schematically. After a brief transient, the resistor assumes a nearly uniform, steady-state temperature of \(95^{\circ} \mathrm{C}\), while
Pressurized water ( \(p_{\text {in }}=10 \mathrm{bar}, T_{\text {in }}=110^{\circ} \mathrm{C}\) ) enters the bottom of an \(L=12\)-m-long vertical tube of diameter \(D=110 \mathrm{~mm}\) at a mass
Approximately 40 percent of the water that is pumped in the United States is used to cool power plants. Sufficient quantities of water may not be available in arid regions, necessitating use of
Chips of width \(L=15 \mathrm{~mm}\) on a side are mounted to a substrate that is installed in an enclosure whose walls and air are maintained at a temperature of \(T_{\text {sur }}=25^{\circ}
One method for growing thin silicon sheets for photovoltaic solar panels is to pass two thin strings of high melting temperature material upward through a bath of molten silicon. The silicon
In one stage of an annealing process, 304 stainless steel sheet is taken from \(300 \mathrm{~K}\) to \(1250 \mathrm{~K}\) as it passes through an electrically heated oven at a speed of \(V_{s}=12
A freezer compartment is covered with a 3-mm-thick layer of frost at the time it malfunctions. If the compartment is in ambient air at \(20^{\circ} \mathrm{C}\) and a coefficient of \(h=\) \(2
An experiment to determine the convection coefficient associated with airflow over the surface of a thick stainless steel casting involves the insertion of thermocouples into the casting at distances
Consider the diffusion of urea in an agar gel discussed in Example 1.26. In this case the gel, containing a uniform initial urea concentration of \(50 \mathrm{~g} / \mathrm{L}\), is molded in the
Consider the ternary mixture of Example 6.2 and Problem 6.3. It is desired to recover in the vapor \(75 \%\) of the benzene in the feed, and to recover in the liquid \(70 \%\) of the \(o\)-xylene in
Consider the binary batch distillation of Example 6.3. For this system, \(n\)-heptane with \(n\)-octane at \(1 \mathrm{~atm}\), the average relative volatility is \(\alpha=2.16\) (Treybal, 1980).
Consider the differential distillation of Example (6.3. For this system, \(n\)-heptane with \(n\)-octane at \(1 \mathrm{~atm}\), the average relative volatility is \(\alpha=2.16\) (Treybal, 1980).
Consider the extraction process of Problem 7.3. Calculate the total amount of solvent required if the extraction is done in a crosscurrent cascade consisting of 5 ideal stages. Use equation (3-89)
Larson (1964) measured the diffusivity of chloroform in air at \(298 \mathrm{~K}\) and a pressure of \(1 \mathrm{~atm}\) and reported its value as \(0.093 \mathrm{~cm}^{2} / \mathrm{s}\). Estimate
If one or both components of a binary gas mixture are polar, a modified Lennard-Jones relation is often used. Brokaw (equation (1969) has suggested an alternative method for this case. 1-49) is used,
A wetted-wall experimental setup consists of a glass pipe, \(50 \mathrm{~mm}\) in diameter and \(1.0 \mathrm{~m}\) long. Water at \(300 \mathrm{~K}\) flows down the inner wall. Dry air enters the
(a) In studying rates of diffusion of naphthalene into air, an investigator replaced a \(30.5-\mathrm{cm}\) section of the inner pipe of an annulus with a naphthalene rod. The annulus was composed of
During the experiment described in Problem 2.3, the air velocity was measured at \(6 \mathrm{~m} / \mathrm{s}\), parallel to the longest side of the pan. Estimate the mass-transfer coefficient
During the experiment described in Problem 2.2, the air velocity was measured at \(10 \mathrm{~m} / \mathrm{s}\). Estimate the mass-transfer coefficient predicted by equation (2-64) and compare it to
Water flows through a thin tube, the walls of which are lightly coated with benzoic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2}\right)\). The water flows slowly, at \(298 \mathrm{~K}\)
In studying the sublimation of naphthalene into an airstream, an investigator constructed a 3-m-long annular duct. The inner pipe was made from a \(25-\mathrm{mm}-\mathrm{OD}\), solid naphthalene
The interfacial surface area per unit volume, \(a\), in many types of packing materials used in industrial towers is virtually impossible to measure. Both \(a\) and the mass-transfer coefficient
Cavatorta et al. (1999) studied the electrochemical reduction of ferricyanide ions, \(\left\{\mathrm{Fe}(\mathrm{CN})_{6}\right\}^{-3}\), to ferrocyanide,
Design a packed-bed air humidifier to process \(9.12 \mathrm{~kg} / \mathrm{h}\) of dry air. Assume that conditions are like those of Example 2.13. The packing will consist of spherical glass beads
At a different point in the packed distillation column of Example 3.10, the methanol content of the bulk of the gas phase \(76.2 \mathrm{~mol} \%\); that of the bulk of the liquid phase is \(60
Consider a countercurrent mass-transfer device for which the equilibrium distribution relation consists of a set of discrete values \(\left\{X_{i D}, Y_{i D}\right\}\) instead of a continuous model
The drying and liquid–liquid extraction operations described in Problems 3.20 and 3.21, respectively, are examples of a flow configuration called a cross-flow cascade. Figure 3.30 is a schematic
Repeat the calculations of Examples 4.6, 4.7, 4.8, and 4.9 for a column diameter corresponding to \(50 \%\) of flooding.Data From Example 4.6:-Design a sieve-tray column for the ethanol absorber of
Repeat the calculations of Example 9.5, but for a total solution normality of 0.5.Data From Example 9.5:-For the Cu2+/Na+ exchange with a strong-acid resin, show how the fraction CuR2 in the resin
In the benzene adsorber of Example 9.7, the flow rate is increased to \(0.25 \mathrm{~m}^{3} / \mathrm{s}\). Calculate the breakthrough time and the fraction of the bed adsorption capacity that has
Redesign the VOCs adsorber of Example 9.15 for a breakthrough time of \(4.0 \mathrm{~h}\). The pressure drop through the bed [calculated using the Ergun equation (2-95)] should not exceed \(1.0

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