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engineering
heat and mass transfer fundamentals and applications

Questions and Answers of Heat And Mass Transfer Fundamentals And Applications

An enclosure has an inside area of \(50 \mathrm{~m}^{2}\), and its inside surface is black and is maintained at a constant temperature. A small opening in the enclosure has an area of \(0.01
Approximations to Planck's law for the spectral emissive power are the Wien and RayleighJeans spectral distributions, which are useful for the extreme low and high limits of the product \(\lambda
The table below includes the four brightest single stars visible from Earth. The star temperature, star radius (one solar radius is equal to the radius of the sun), and distance between the star and
The spectral, directional emissivity of a diffuse material at \(2500 \mathrm{~K}\) has the following distribution:Determine the total, hemispherical emissivity at \(2500 \mathrm{~K}\). Determine the
A diffuse surface is characterized by the spectral hemispherical emissivity distribution shown. Considering surface temperatures over the range \(300 \leq T_{s} \leq 1000 \mathrm{~K}\), at what
Consider the diffuse surface of Problem 12.28. Determine the surface hemispherical emissivity and emissive power at \(T=300,500\), and \(700 \mathrm{~K}\). At what wavelength does the peak spectral
A small, opaque, diffuse object at \(T_{s}=500 \mathrm{~K}\) is suspended in a large furnace whose interior walls are at \(T_{f}=2500 \mathrm{~K}\). The walls are diffuse and gray and have an
One of two thin coatings may be applied to a metal plate, yielding the following spectral emissivities above and below a cutoff wavelength of \(\lambda_{c}=8 \mu \mathrm{m}\).If the plate temperature
An opaque surface, \(2 \mathrm{~m} \times 2 \mathrm{~m}\), is maintained at \(350 \mathrm{~K}\) and is simultaneously exposed to solar irradiation with \(G_{S}=1200 \mathrm{~W} / \mathrm{m}^{2}\).
A diffuse, opaque surface at \(680 \mathrm{~K}\) has spectral emissivities of \(\varepsilon_{\lambda}=0\) for \(0 \leq \lambda \leq 3 \mu \mathrm{m}, \varepsilon_{\lambda}=0.4\) for \(3 \mu
Consider a material that is gray, but directionally selective with \(\alpha_{\theta}(\theta, \phi)=0.8(1-\cos \phi)\). Determine the hemispherical absorptivity \(\alpha\) when collimated flux
Solar flux of \(1000 \mathrm{~W} / \mathrm{m}^{2}\) is incident on the top side of a plate whose surface has a solar absorptivity of 0.9 and an emissivity of 0.2 . The air and surroundings are at
Consider parallel surfaces that are opaque to thermal radiation. The horizontal surfaces are separated by a gap of thickness \(L=0.12 \mathrm{~m}\). The top surface is at temperature \(T_{2}\) and is
Consider an opaque, diffuse surface for which the spectral absorptivity and irradiation are as follows:What is the total absorptivity of the surface for the prescribed irradiation? If the surface is
Sheet steel emerging from the hot roll section of a steel mill has a temperature of \(1000 \mathrm{~K}\), a thickness of \(\delta=2.5 \mathrm{~mm}\), and the following distribution for the spectral,
Two special coatings are available for application to an absorber plate installed below the cover glass described in Example 12.9. Each coating is diffuse and is characterized by the spectral
A small disk \(4 \mathrm{~mm}\) in diameter is positioned at the center of an isothermal, hemispherical enclosure. The disk is diffuse and gray with an emissivity of 0.8 and is maintained at \(1000
Two plates, one with a black painted surface and the other with a special coating (chemically oxidized copper) are in earth orbit and are exposed to solar radiation. The solar rays make an angle of
The directional absorptivity of a gray surface varies with \(\theta\) as follows.(a) What is the ratio of the normal absorptivity \(\alpha_{n}\) to the hemispherical emissivity of the surface?(b)
The spectral absorptivity of aluminum coated with a thin layer of silicon dioxide may be approximated as \(\alpha_{\lambda, 1}=\) 0.98 for \(\lambda
A radiation thermometer measures irradiation reaching its sensor and is calibrated to indicate the temperature of a blackbody that produces the same flux. A steel billet having a diffuse, gray
Consider a two-color pyrometer such as in Problem 12.69 that operates at \(\lambda_{1}=0.65 \mu \mathrm{m}\) and \(\lambda_{2}=0.63 \mu \mathrm{m}\). Using Wien's law determine the temperature of a
Photovoltaic materials convert sunlight directly to electric power. Some of the photons that are incident upon the material displace electrons that are in turn collected to create an electric
A spherical satellite of diameter \(D\) is in orbit about the earth and is coated with a diffuse material for which the spectral absorptivity is \(\alpha_{\lambda}=0.6\) for \(\lambda \leq\) \(3 \mu
A spherical satellite in near-earth orbit is exposed to solar irradiation of \(1368 \mathrm{~W} / \mathrm{m}^{2}\). To maintain a desired operating temperature, the thermal control engineer intends
On an overcast day the directional distribution of the solar radiation incident on the earth's surface may be approximated by an expression of the form \(I_{i}=I_{n} \cos \theta\), where \(I_{n}\) is
Consider an opaque, gray surface whose directional absorptivity is 0.8 for \(0 \leq \theta \leq 30^{\circ}\) and 0.1 for \(\theta>30^{\circ}\). The surface is horizontal and exposed to solar
It is not uncommon for the night sky temperature in desert regions to drop to \(-40^{\circ} \mathrm{C}\). If the ambient air temperature is \(20^{\circ} \mathrm{C}\) and the convection coefficient
Growers use giant fans to prevent grapes from freezing when the effective sky temperature is low. The grape, which may be viewed as a thin skin of negligible thermal resistance enclosing a volume of
Consider a thin, opaque, horizontal plate with an electrical heater on its back side. The front side is exposed to ambient air that is at \(20^{\circ} \mathrm{C}\) and provides a convection heat
It is known that on clear nights a thin layer of water on the ground will freeze before the air temperature drops below \(0^{\circ} \mathrm{C}\). Consider such a layer of water on a clear night for
Fully developed conditions are known to exist for water flowing through a \(50-\mathrm{mm}\)-diameter tube at \(0.02 \mathrm{~kg} / \mathrm{s}\) and \(27^{\circ} \mathrm{C}\). What is the maximum
Water at \(35^{\circ} \mathrm{C}\) is pumped through a horizontal, \(200-\mathrm{m}\)-long, \(30-\mathrm{mm}\)-diameter tube at \(0.25 \mathrm{~kg} / \mathrm{s}\). Over time, a 2-mm-thick layer of
What is the pressure drop associated with water at \(27^{\circ} \mathrm{C}\) flowing with a mean velocity of \(0.1 \mathrm{~m} / \mathrm{s}\) through an \(800-\mathrm{m}-\) long cast iron pipe of
Dry, compressed air at \(T_{m, i}=75^{\circ} \mathrm{C}, p=10 \mathrm{~atm}\), with a mass flow rate of \(\dot{m}=0.001 \mathrm{~kg} / \mathrm{s}\), enters a \(30-\mathrm{mm}-\) diameter, 5 -m-long
Fluid enters a tube with a flow rate of \(0.020 \mathrm{~kg} / \mathrm{s}\) and an inlet temperature of \(20^{\circ} \mathrm{C}\). The tube, which has a length of \(8 \mathrm{~m}\) and diameter of
An oil preheater consists of a single tube of \(10-\mathrm{mm}\) diameter and 5-m length, with its surface maintained at \(180^{\circ} \mathrm{C}\) by swirling combustion gases. The engine oil (new)
Air at \(p=1 \mathrm{~atm}\) enters a thin-walled \((D=10-\mathrm{mm}\) diameter) long tube \((L=2 \mathrm{~m})\) at an inlet temperature of \(T_{m, i}=100^{\circ} \mathrm{C}\). A constant heat flux
Dry, compressed air at \(T_{m, i}=55^{\circ} \mathrm{C}, p=15 \mathrm{~atm}\), with a mass flow rate of \(\dot{m}=0.05 \mathrm{~kg} / \mathrm{s}\), enters a \(50-\mathrm{mm}-\) diameter,
Consider the conditions associated with the hot water pipe of Problem 7.42, but now account for the convection resistance associated with water flow at a mean velocity of \(u_{m}=0.4 \mathrm{~m} /
\(\mathrm{NaK}(56 \% / 44 \%)\), which is an alloy of sodium and potassium, is used to cool fast neutron nuclear reactors. The NaK flows at a rate of \(\dot{m}=0.8 \mathrm{~kg} / \mathrm{s}\) through
Liquid mercury at \(0.25 \mathrm{~kg} / \mathrm{s}\) is to be heated from 325 to \(375 \mathrm{~K}\) by passing it through a \(25-\mathrm{mm}\)-diameter tube whose surface is maintained at \(400
Compressed air at \(p=20\) atm enters a \(20-\mathrm{mm}\) diameter tube at \(T_{m, i}=20^{\circ} \mathrm{C}\) and a mass flow rate of \(\dot{m}=6 \times 10^{-4} \mathrm{~kg} / \mathrm{s}\). The air
Heated air required for a food-drying process is generated by passing ambient air at \(20^{\circ} \mathrm{C}\) through long, circular tubes \((D=50 \mathrm{~mm}, L=5 \mathrm{~m}\) ) housed in a steam
Refrigerant-134a is being transported at \(0.08 \mathrm{~kg} / \mathrm{s}\) through a Teflon tube of inside diameter \(D_{i}=20 \mathrm{~mm}\) and outside diameter \(D_{o}=25 \mathrm{~mm}\), while
Oil at \(150^{\circ} \mathrm{C}\) flows slowly through a long, thin-walled pipe of 35-mm inner diameter. The pipe is suspended in a room for which the air temperature is \(25^{\circ} \mathrm{C}\) and
Repeat Problem 8.52 for a circular tube of diameter \(D=2 \mathrm{~mm}\), an applied heat flux of \(q^{\prime \prime}=200,000 \mathrm{~W} / \mathrm{m}^{2}\), and a mass flow rate of \(\dot{m}=10
A thin-walled tube with a diameter of \(12 \mathrm{~mm}\) and length of \(25 \mathrm{~m}\) is used to carry exhaust gas from a smoke stack to the laboratory in a nearby building for analysis. The gas
A thin-walled, uninsulated 0.4-m-diameter duct is used to route chilled air at \(0.07 \mathrm{~kg} / \mathrm{s}\) through the attic of a large commercial building. The attic air is at \(37^{\circ}
Water at \(290 \mathrm{~K}\) and \(0.25 \mathrm{~kg} / \mathrm{s}\) flows through a Teflon tube \((k=0.35 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) of inner and outer radii equal to 10 and \(14
Air at \(4 \times 10^{-4} \mathrm{~kg} / \mathrm{s}\) and \(20^{\circ} \mathrm{C}\) enters a rectangular duct that is \(1 \mathrm{~m}\) long and \(4 \mathrm{~mm} \times 16 \mathrm{~mm}\) on a side. A
Air at \(1 \mathrm{~atm}\) and \(310 \mathrm{~K}\) enters a 2 -m-long rectangular duct with cross section \(80 \mathrm{~mm} \times 160 \mathrm{~mm}\). The duct is maintained at a constant surface
Rectangular flow channels are formed by milling long rectangular slots into flat metal plates, and brazing the plates together as shown below. Either large channels (Configuration A) or twice as many
For the conditions of Problem 8.70, how long must the annulus be if the water flow rate is \(0.35 \mathrm{~kg} / \mathrm{s}\) instead of \(0.02 \mathrm{~kg} / \mathrm{s}\) ?Data From Problem
Consider a concentric tube annulus for which the inner and outer diameters are 25 and \(50 \mathrm{~mm}\). Water enters the annular region at \(0.03 \mathrm{~kg} / \mathrm{s}\) and \(25^{\circ}
An ideal gas flows within a small diameter tube. Derive an expression for the transition density of the gas \(ho_{c}\) below which microscale effects must be accounted for. Express your result in
What is the convection mass transfer coefficient associated with fully developed atmospheric airflow at \(27^{\circ} \mathrm{C}\) and \(0.04 \mathrm{~kg} / \mathrm{s}\) through a
Air is forced through holes that are bored through a 0.5-m-thick block of solid (of molecular weight \(95 \mathrm{~kg} / \mathrm{kmol}\) ) that sublimates into the flowing air. Consider air at \(320
An object of characteristic length \(L=0.5 \mathrm{~m}\) is \(10^{\circ} \mathrm{C}\) warmer than the surrounding fluid, which is flowing at a velocity of \(0.5 \mathrm{~m} / \mathrm{s}\). Graph the
Consider an object of characteristic length \(0.015 \mathrm{~m}\) and a situation for which the temperature difference is \(10^{\circ} \mathrm{C}\). Evaluating thermophysical properties at the
Consider a large vertical plate with a uniform surface temperature of \(100^{\circ} \mathrm{C}\) suspended in quiescent air at \(25^{\circ} \mathrm{C}\) and atmospheric pressure.(a) Estimate the
For laminar free convection flow on a vertical plate, the recommended values of \(C\) and \(n\) for use in the correlation of Equation 9.24 are 0.59 and 1/4, respectively. Derive the values of \(C\)
A number of thin plates are to be cooled by vertically suspending them in a water bath at a temperature of \(20^{\circ} \mathrm{C}\). If the plates are initially at \(60^{\circ} \mathrm{C}\) and are
A square aluminum plate \(5 \mathrm{~mm}\) thick and \(150 \mathrm{~mm}\) on a side is heated while vertically suspended in quiescent air at \(75^{\circ} \mathrm{C}\). Determine the average heat
Consider a vertical plate of dimension \(0.25 \mathrm{~m} \times 0.50\mathrm{~m}\) that is at \(T_{s}=100^{\circ} \mathrm{C}\) in a quiescent environment at \(T_{\infty}=\) \(20^{\circ} \mathrm{C}\).
Show that the laminar, free convection correlations for a vertical, isothermal flat plate of height \(L\) can be applied to a vertical, isothermal cylinder of diameter \(D\) and height \(L\) if the
During a winter day, the window of a patio door with a height of \(1.8 \mathrm{~m}\) and width of \(1.0 \mathrm{~m}\) shows a frost line near its base. The room wall and air temperatures are
An electrical heater in the form of a horizontal disk of \(500-\mathrm{mm}\) diameter is used to heat the bottom of a tank filled with engine oil at a temperature of \(10^{\circ} \mathrm{C}\).
Consider a horizontal 5-mm-thick, 100-mm-long straight fin fabricated from plain carbon steel \((k=57\) \(\mathrm{W} / \mathrm{m} \cdot \mathrm{K}, \varepsilon=0.5)\). The base of the fin is
A hot, 0.5-m-diameter, 35 -mm-thick aluminum alloy disk is quenched from an initial temperature of \(T_{i}=\) \(400^{\circ} \mathrm{C}\) in a large oil bath of temperature \(T_{\infty}=35^{\circ}
A horizontal uninsulated steam pipe passes through a large room whose walls and ambient air are at \(300 \mathrm{~K}\). The pipe of \(125-\mathrm{mm}\) diameter has an emissivity of 0.85 and an outer
As discussed in Section 5.2, the lumped capacitance approximation may be applied if \(B_{i}
A long, uninsulated steam line with a diameter of \(100 \mathrm{~mm}\) and a surface emissivity of 0.8 transports steam at \(150^{\circ} \mathrm{C}\) and is exposed to atmospheric air and large
Consider Problem 8.38. A more realistic solution would account for the resistance to heat transfer due to free convection in the paraffin during melting. Assuming the tube surface to have a uniform
The concept of a critical insulation radius was introduced in Example 3.6. Consider the thin-walled copper tube and insulation of the example. Now, the tube temperature is \(-10^{\circ} \mathrm{C}\)
A sphere of \(30-\mathrm{mm}\) diameter contains an embedded electrical heater. Calculate the power required to maintain the surface temperature at \(89^{\circ} \mathrm{C}\) when the sphere is
Determined to reduce the \(\$ 7\) per week cost associated with heat loss through their patio window by convection and radiation, the tenants of Problem 9.15 cover the inside of the window with a
The front door of a dishwasher of width \(580 \mathrm{~mm}\) has a vertical air vent that is \(500 \mathrm{~mm}\) in height with a \(20-\mathrm{mm}\) spacing between the inner tub operating at
A solar collector design consists of an inner tube enclosed concentrically in an outer tube that is transparent to solar radiation. The tubes are thin walled with inner and outer diameters of 0.08
Graph the heat loss per unit length from the solar collector of Problem 9.76 over the range \(0.1 \leq D_{o} \leq 0.25\mathrm{~m}\) assuming (i) conduction heat transfer across the annular space and
According to experimental results for parallel airflow over a uniform temperature, heated vertical plate, the effect of free convection on the heat transfer convection coefficient will be \(5 \%\)
A horizontal, 25-mm-diameter cylinder is maintained at a uniform surface temperature of \(35^{\circ} \mathrm{C}\). Air at atmospheric pressure with a velocity of \(0.10 \mathrm{~m} / \mathrm{s}\) and
A \(205 \mathrm{~mm} \times 245 \mathrm{~mm}\) sheet of wetted fabric is hung up to dry on a warm, sunny day. The still air is at a temperature of \(30^{\circ} \mathrm{C}\) and relative humidity of
On a very still morning, the surface temperature of a lake used to cool the condenser of a power plant is \(30^{\circ} \mathrm{C}\) while the air temperature is \(23^{\circ} \mathrm{C}\) with a
Water at a temperature of \(T_{\infty}=25^{\circ} \mathrm{C}\) flows over one of the surfaces of a stainless steel wall (AISI 302) whose temperature is \(T_{s, 1}=40^{\circ} \mathrm{C}\). The wall is
A flat plate is of planar dimension \(1 \mathrm{~m} \times 0.75\mathrm{~m}\). For parallel laminar flow over the plate, calculate the ratio of the average heat transfer coefficients over the entire
Laminar flow normally persists on a smooth flat plate until a critical Reynolds number value is reached. However, the flow can be tripped to a turbulent state by adding roughness to the leading edge
A concentrating solar collector consists of a parabolic reflector and a collector tube of diameter \(D\), through which flows a working fluid that is heated with concentrated solar irradiation.
Helium at a free stream temperature of \(T_{\infty}=25^{\circ} \mathrm{C}\) is in parallel flow over a flat plate of length \(L=3 \mathrm{~m}\) and temperature \(T_{s}=85^{\circ} \mathrm{C}\).
A fan that can provide air speeds up to \(30 \mathrm{~m} / \mathrm{s}\) is to be used in a low-speed wind tunnel with atmospheric air at \(23^{\circ} \mathrm{C}\). If one wishes to use the wind
Consider the conditions of Example 6.4. A laminar boundary layer can be tripped to a turbulent condition at \(x=x_{r}\) by roughening the surface of the plate at \(x_{r}\). Calculate the minimum and
Consider laminar boundary layer flow over a flat plate. For identical flow conditions, determine the entries not shown in the table below, using the fact that \(\delta / \delta_{t}=P r^{n}\). The
An object of irregular shape has a characteristic length of \(L=0.5 \mathrm{~m}\) and is maintained at a uniform surface temperature of \(T_{s}=400 \mathrm{~K}\). When placed in atmospheric air at a
Atmospheric air is in parallel flow \(\left(u_{\infty}=10 \mathrm{~m} / \mathrm{s}, T_{\infty}=\right.\) \(15^{\circ} \mathrm{C}\) ) over a flat heater surface that is to be maintained at a
As a means of preventing ice formation on the wings of a small, private aircraft, it is proposed that electric resistance heating elements be installed within the wings. To determine representative
A circuit board with a dense distribution of integrated circuits (ICs) and dimensions of \(20 \mathrm{~mm} \times 20 \mathrm{~mm}\) on a side is cooled by the parallel flow of atmospheric air with a
On a summer day the air temperature is \(30^{\circ} \mathrm{C}\) and the relative humidity is \(55 \%\). Water evaporates from the surface of a lake at a rate of \(0.08 \mathrm{~kg} / \mathrm{h}\)
The dryer section of a paper mill consists of 30 hot, 1.5-m-diameter cylindrical rollers of length \(3 \mathrm{~m}\). A \(225^{\circ}\) arc of each roller is in contact with the moist paper sheet,
Photosynthesis, as it occurs in the leaves of a green plant, involves the transport of carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) from the atmosphere to the chloroplasts of the leaves. The rate
On a cool day in April a scantily clothed runner is known to lose heat at a rate of \(450 \mathrm{~W}\) when running on a level surface because of convection to the surrounding air at

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