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engineering
heat and mass transfer fundamentals and applications

Questions and Answers of Heat And Mass Transfer Fundamentals And Applications

An experiment involves the flow of air at atmospheric pressure and \(300 \mathrm{~K}\) over an object of characteristic length \(L=1 \mathrm{~m}\) that is coated with species A. The measured average
A strut is exposed to a hot airflow. It is necessary to run experiments to determine the average convection heat transfer coefficient \(\bar{h}\) from the air to the strut in order to be able to cool
Dry air at \(32^{\circ} \mathrm{C}\) flows over a wetted (water) plate of \(0.25 \mathrm{~m}^{2}\) area. The average convection coefficient is \(\bar{h}=22 \mathrm{~W} / \mathrm{m}^{2} \cdot
It is known that on clear nights the air temperature need not drop below \(0^{\circ} \mathrm{C}\) before a thin layer of water on the ground will freeze. Consider such a layer of water on a clear
A 1-mm-thick layer of water on an electrically heated plate is maintained at a temperature of \(T_{w}=340 \mathrm{~K}\), as dry air at \(T_{\infty}=300 \mathrm{~K}\) flows over the surface of the
Consider atmospheric air at \(20^{\circ} \mathrm{C}\) and a velocity of \(30 \mathrm{~m} / \mathrm{s}\) flowing over both surfaces of a 1-m-long flat plate that is maintained at \(130^{\circ}
Consider a flat plate subject to parallel flow (top and bottom) characterized by \(u_{\infty}=5 \mathrm{~m} / \mathrm{s}, T_{\infty}=20^{\circ} \mathrm{C}\).(a) Determine the average convection heat
Consider two cases involving parallel flow of dry air at \(V=1 \mathrm{~m} / \mathrm{s}, T_{\infty}=45^{\circ} \mathrm{C}\), and atmospheric pressure over an isothermal plate at \(T_{s}=20^{\circ}
In Example 7.2, it was determined that the sixth segment of the flat plate has the maximum power requirement. Which segment has the minimum power requirement if conditions are identical except the
The roof of a refrigerated truck compartment is of composite construction, consisting of a layer of foamed urethane insulation \(\left(t_{2}=50 \mathrm{~mm}, k_{i}=0.026 \mathrm{~W} / \mathrm{m}
The top surface of a compartment consists of very smooth (A) and highly roughened (B) portions, and the surface is placed in an atmospheric airstream. In the interest of minimizing total convection
The Weather Channel reports that it is a hot, muggy day with an air temperature of \(90^{\circ} \mathrm{F}\), a \(10 \mathrm{mph}\) breeze out of the southwest, and bright sunshine with a solar
Consider the concentrating photovoltaic apparatus of Problem 7.15. The apparatus is to be installed in a desert environment, so the space between the concentrating lens and top of the photovoltaic
A flat plate of width \(1 \mathrm{~m}\) and length \(0.2 \mathrm{~m}\) is maintained at a temperature of \(32^{\circ} \mathrm{C}\). Ambient fluid at \(22^{\circ} \mathrm{C}\) flows across the top of
Consider the following fluids, each with a velocity of \(V=3 \mathrm{~m} / \mathrm{s}\) and a temperature of \(T_{\infty}=20^{\circ} \mathrm{C}\), in cross flow over a \(10-\mathrm{mm}\)-diameter
Consider the conditions of Problem 7.36, but now allow for radiation exchange between the surface of the heating element \((\varepsilon=0.8)\) and the walls of the duct, which form a large enclosure
Determine the convection heat transfer coefficient, thermal resistance for convection, and the convection heat transfer rate that are associated with air at atmospheric pressure in cross flow over a
A long, thin metal plate is hung vertically after a heat treating process. The plate, of width \(W=0.2 \mathrm{~m}\), vertical dimension of \(3 \mathrm{~m}\), and an initial temperature of
Pin fins are to be specified for use in an industrial cooling application. The fins will be subjected to a gas in cross flow at \(V=10 \mathrm{~m} / \mathrm{s}\). The cylindrical fin has a diameter
Hot water at \(50^{\circ} \mathrm{C}\) is routed from one building in which it is generated to an adjoining building in which it is used for space heating. Transfer between the buildings occurs in a
To determine air velocity changes, it is proposed to measure the electric current required to maintain a platinum wire of \(0.25-\mathrm{mm}\) diameter at a constant temperature of \(77^{\circ}
A temperature sensor of \(10.5-\mathrm{mm}\) diameter experiences cross flow of water with a free stream temperature of \(80^{\circ} \mathrm{C}\) and variable velocity. Derive an expression for the
An aluminum transmission line with a diameter of \(20 \mathrm{~mm}\) has an electrical resistance of \(R_{\text {elec }}^{\prime}=\) \(2.636 \times 10^{-4} \Omega / \mathrm{m}\) and carries a current
Air at \(25^{\circ} \mathrm{C}\) flows over a 10 -mm-diameter sphere with a velocity of \(15 \mathrm{~m} / \mathrm{s}\), while the surface of the sphere is maintained at \(75^{\circ} \mathrm{C}\).(a)
A spherical, underwater instrument pod used to make soundings and to measure conditions in the water has a diameter of \(100 \mathrm{~mm}\) and dissipates \(400 \mathrm{~W}\).(a) Estimate the surface
Oil is cooled by spraying a mist of the hot liquid through cool air at \(T_{\infty}=27^{\circ} \mathrm{C}\). Two droplets, each of diameter \(D=100 \mu \mathrm{m}\) and temperature \(250^{\circ}
Worldwide, over a billion solder balls must be manufactured daily for assembling electronics packages. The uniform droplet spray method uses a piezoelectric device to vibrate a shaft in a pot of
For the conditions of Problem 7.60, what are the terminal velocity and the tank height if engine oil at \(315 \mathrm{~K}\), rather than water, is used as the coolant?Data From Problem 7.60:-Copper
Consider temperature measurement in a gas stream using the thermocouple junction described in Problem 7.66 ( \(D=2 \mathrm{~mm}, \varepsilon=0.60\) ). If the gas velocity and temperature are \(2
Consider the in-line tube bank of Problem \(7.69(D=\) \(10 \mathrm{~mm}, L=1 \mathrm{~m}\), and \(S_{T}=S_{L}=15 \mathrm{~mm}\) ), with condensing steam used to heat atmospheric air entering the tube
A tube bank uses an aligned arrangement of \(15-\mathrm{mm}-\) diameter tubes with \(S_{T}=S_{L}=30 \mathrm{~mm}\). There are 10 rows of tubes with 50 tubes in each row. Consider an application for
A tube bank uses an aligned arrangement of \(30-\mathrm{mm}\) diameter tubes with \(S_{T}=S_{L}=60 \mathrm{~mm}\) and a tube length of \(1 \mathrm{~m}\). There are 10 tube rows in the flow direction
A circular transistor of \(15-\mathrm{mm}\) diameter is cooled by impingement of an air jet exiting a 3-mm-diameter round nozzle with a velocity of \(20 \mathrm{~m} / \mathrm{s}\) and a temperature
A 25-mm-diameter hot surface at \(T_{s}=85^{\circ} \mathrm{C}\) is cooled by an air jet exiting a 5-mm-diameter round nozzle with a velocity of \(35 \mathrm{~m} / \mathrm{s}\) and temperature of
The use of rock pile thermal energy storage systems has been considered for solar energy and industrial process heat applications. A particular system involves a cylindrical container, \(2
Latent heat capsules consist of a thin-walled spherical shell within which a solid-liquid, phase-change material (PCM) of melting point \(T_{\mathrm{mp}}\) and latent heat of fusion \(h_{s f}\) is
Consider mass loss from a smooth wet flat plate due to forced convection at atmospheric pressure. The plate is \(0.4 \mathrm{~m}\) long and \(2 \mathrm{~m}\) wide. Dry air at \(300 \mathrm{~K}\) and
A van traveling \(60 \mathrm{~km} / \mathrm{h}\) has just passed through a thunderstorm that left a film of water \(0.05 \mathrm{~mm}\) thick on the top of the van. The top of the van can be assumed
An electric power plant generates \(500 \mathrm{MW}\) of electric power and operates at a thermal efficiency of 38 percent. The waste heat from the power plant is transferred to the environment from
A 20-mm-diameter, 1-m-long, thin-walled copper tube contains a material that generates thermal energy at a volumetric rate of \(\dot{q}=0.2 \mathrm{MW} / \mathrm{m}^{3}\). The rod is cooled by air at
Dry air at \(35^{\circ} \mathrm{C}\) and a velocity of \(20 \mathrm{~m} / \mathrm{s}\) flows over a long cylinder of \(25-\mathrm{mm}\) diameter. The cylinder is covered with a thin porous coating
In Section 5.5, the one-term approximation to the series solution for the temperature distribution was developed for a plane wall of thickness \(2 L\) that is initially at a uniform temperature and
Radiation heat transfer can occur within porous media in conjunction with conduction, as heat is radiatively transferred across pores of interstitial fluid. Under certain conditions, the effects of
An apparatus for measuring thermal conductivity employs an electrical heater sandwiched between two identical samples of diameter \(25 \mathrm{~mm}\) and length \(60 \mathrm{~mm}\), which are pressed
A thin stainless steel disk of thickness \(b\) and outer radius \(r_{o}\) has been heat treated to a high, uniform initial temperature of \(T_{i}\). The disk is then placed upon a small stand and
Steel balls \(10 \mathrm{~mm}\) in diameter are annealed by heating to \(1150 \mathrm{~K}\) and then slowly cooling to \(450 \mathrm{~K}\) in an air environment for which \(T_{\infty}=325
The heat transfer coefficient for hydrogen flowing over a sphere is to be determined by observing the temperature-time history of a sphere fabricated from pure copper. The sphere, which is \(20
A steel sphere (AISI 1010), \(100 \mathrm{~mm}\) in diameter, is coated with a dielectric material layer of thickness \(2 \mathrm{~mm}\) and thermal conductivity \(0.04 \mathrm{~W} / \mathrm{m} \cdot
A copper sheet of thickness \(2 L=2 \mathrm{~mm}\) has an initial temperature of \(T_{i}=118^{\circ} \mathrm{C}\). It is suddenly quenched in liquid water, resulting in boiling at its two surfaces.
A power transistor mounted on a finned heat sink can be modeled as a spatially isothermal object with internal heat generation and an external convection resistance.(a) Consider such a system of mass
A plane wall of a furnace is fabricated from plain carbon steel \(\left(k=60 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, ho=7850 \mathrm{~kg} / \mathrm{m}^{3}, c=430\right.\) \(\mathrm{J} /
In a manufacturing process, a spherical ceramic particle of diameter \(D=300 \mu \mathrm{m}\) and initial temperature \(T_{i}=1100 \mathrm{~K}\) is injected into a chamber containing a hot gas stream
In a tempering process, glass plate, which is initially at a uniform temperature \(T_{i}\), is cooled by suddenly reducing the temperature of both surfaces to \(T_{s}\). The plate is \(10
A plastic coating is applied to wood panels by first depositing molten polymer on a panel and then cooling the surface of the polymer by subjecting it to airflow at \(25^{\circ} \mathrm{C}\). As
A long plastic rod of \(20-\mathrm{mm}\) diameter \((k=0.3 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and \(ho c_{p}=1040 \mathrm{~kJ} / \mathrm{m}^{3} \cdot \mathrm{K}\) ) is uniformly heated in an
A \(D=100 \mathrm{~mm}\) diameter solid sphere, initially at a uniform temperature of \(T_{i}=50^{\circ} \mathrm{C}\), is placed in a flowing fluid at \(T_{\infty}=20^{\circ} \mathrm{C}\). The sphere
Consider the packed bed operating conditions of Problem 5.13, but with Pyrex ( \(ho=2225 \mathrm{~kg} / \mathrm{m}^{3}, c=835 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), \(k=1.4 \mathrm{~W} /
Two large blocks of different materials, such as aluminum and glass, have been sitting in a room \(\left(20^{\circ} \mathrm{C}\right)\) for a very long time. Which of the two blocks, if either, will
A generous amount of gel is applied to the surface of the window of an ultrasound probe prior to its use. The window is made of a polycarbonate material of density \(ho=\) \(1200 \mathrm{~kg} /
Special coatings are often formed by depositing thin layers of a molten material on a solid substrate. Solidification begins at the substrate surface and proceeds until the thickness \(S\) of the
Consider a packed bed of spheres, each of diameter \(D=2 \mathrm{~mm}\), at an initial temperature of \(T_{i}=90^{\circ} \mathrm{C}\). Cold water at \(T_{w}=5^{\circ} \mathrm{C}\) is poured onto the
During the cold winter months, an office building is partially heated by extracting thermal energy stored in soil beneath the building using a heat pump. During the summer, the building is partially
The \(\operatorname{Der}(T, t)\) function of \(I H T\) can be used to represent the temperature-time derivative of Equation 5.75. In this problem we will use the Der function to solve Example
Consider the solar collector of Problem 3.89. After reaching a steady-state operating condition with \(q_{\text {rad }}^{\prime \prime}=800 \mathrm{~W} / \mathrm{m}^{2}\), the net radiation flux to
Consider the nacelle of the wind turbine in Example 1.3. The nacelle is formed of a thermoplastic composite material of thickness \(L=20 \mathrm{~mm}\). The thermal conductivity, density, and
A flue passing hot exhaust gases has a square cross section, \(300 \mathrm{~mm}\) to a side. The walls are constructed of refractory brick \(150 \mathrm{~mm}\) thick with a thermal conductivity of
Small-diameter electrical heating elements dissipating \(50 \mathrm{~W} / \mathrm{m}\) (length normal to the sketch) are used to heat a ceramic plate of thermal conductivity \(2 \mathrm{~W} /
Free convection heat transfer is sometimes quantified by writing Equation 4.20 as \(q_{\text {conv }}=S k_{\text {eff }} \Delta T_{1-2}\), where \(k_{\text {eff }}\) is an effective thermal
Two parallel pipelines spaced \(2.0 \mathrm{~m}\) apart are buried in soil having a thermal conductivity of \(0.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). The pipes have outer diameters of 300
A small water droplet of diameter \(D=100 \mu \mathrm{m}\) and temperature \(T_{\mathrm{mp}}=0^{\circ} \mathrm{C}\) falls on a nonwetting metal surface that is at temperature \(T_{s}=-15^{\circ}
Pressurized steam at \(400 \mathrm{~K}\) flows through a long, thinwalled pipe of \(0.6-\mathrm{m}\) diameter. The pipe is enclosed in a concrete casing that is of square cross section and \(1.75
Hot water at \(80^{\circ} \mathrm{C}\) flows through a thin-walled copper tube of \(30-\mathrm{mm}\) diameter. The tube is enclosed by an eccentric cylindrical shell that is maintained at
A double-glazed window consists of two sheets of glass separated by an \(L=0.2-\mathrm{mm}\)-thick gap. The gap is evacuated, eliminating conduction and convection across the gap. Small cylindrical
A long power transmission cable is buried at a depth (ground-to-cable-centerline distance) of \(1 \mathrm{~m}\). The cable is encased in a thin-walled pipe of \(0.05-\mathrm{m}\) diameter, and, to
A small device is used to measure the surface temperature of an object. A thermocouple bead of diameter \(D=120 \mu \mathrm{m}\) is positioned a distance \(z=100 \mu \mathrm{m}\) from the surface of
A cubical glass melting furnace has exterior dimensions of width \(W=5 \mathrm{~m}\) on a side and is constructed from refractory brick of thickness \(L=0.35 \mathrm{~m}\) and thermal conductivity
Two thick walls are separated by a vacuum gap of thickness \(L\). A cylinder of diameter \(D\) runs between the walls. All surfaces are highly polished (their emissivity is small). The walls are at
An aluminum heat \(\operatorname{sink}(k=230 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\), used to cool an array of electronic chips, consists of a square channel of inner width \(w=30
A cylinder of diameter \(D=10 \mathrm{~mm}\) and temperature \(T_{1}=\) \(100^{\circ} \mathrm{C}\) is centrally located in an extruded square coating of bakelite of dimension \(w=11 \mathrm{~mm}\).
For a small heat source attached to a large substrate, the spreading resistance associated with multidimensional conduction in the substrate may be approximated by the expression [Yovanovich, M. M.,
In a two-dimensional cylindrical configuration, the radial \((\Delta r)\) and angular \((\Delta \phi)\) spacings of the nodes are uniform. The boundary at \(r=r_{i}\) is of uniform temperature
Consider the network for a two-dimensional system without internal volumetric generation having nodal temperatures shown below. If the grid spacing is \(100 \mathrm{~mm}\) and the thermal
Consider the square channel shown in the sketch operating under steady-state conditions. The inner surface of the channel is at a uniform temperature of \(600 \mathrm{~K}\), while the outer surface
Square channels of dimension \(L_{c}=\sqrt{2} \cdot 10 \mathrm{~mm}=\) \(14.14 \mathrm{~mm}\) are evenly spaced at \(S=25 \mathrm{~mm}\) along the centerline of a plate of thickness \(L_{p}=40
A flue passing hot exhaust gases has a square cross section, \(400 \mathrm{~mm}\) to a side. The walls are constructed of refractory brick \(200 \mathrm{~mm}\) thick with a thermal conductivity of
Consider the two-dimensional tube of a noncircular cross section formed by rectangular and semicylindrical subdomains patched at the common dashed control surfaces in a manner similar to that
A bar of thermal conductivity \(k=140 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) is of a trapezoidal cross section as shown in the schematic. The left and right faces are at temperatures \(T_{h}=\)
A long, solid cylinder of diameter \(D=25 \mathrm{~mm}\) is formed of an insulating core that is covered with a very thin \((t=50 \mu \mathrm{m})\), highly polished metal sheathing of thermal
Consider Problem 4.62. An engineer desires to measure the surface temperature of the thin sheathing by painting it black \((\varepsilon=0.98)\) and using an infrared measurement device to
A long bar of rectangular cross section, \(0.2 \mathrm{~m} \times 0.3\mathrm{~m}\) on a side and having a thermal conductivity of \(15 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), is subjected to the
A dormitory at a large university, built 50 years ago, has exterior walls constructed of \(L_{s}=30\)-mm-thick sheathing with a thermal conductivity of \(k_{s}=0.1 \mathrm{~W} / \mathrm{m} \cdot
A composite wall is composed of an insulating material of thermal conductivity \(k_{\text {ins }}=1.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) sandwiched between two 1-mm-thick stainless steel
Determine the thermal conductivity of the carbon nanotube of Example 3.4 when the heating island temperature is measured to be \(T_{h}=332.6 \mathrm{~K}\), without evaluating the thermal resistances
Consider the composite wall of Problem 3.11 under conditions for which the inside air is still characterized by \(T_{\infty, i}=20^{\circ} \mathrm{C}\) and \(h_{i}=30 \mathrm{~W} / \mathrm{m}^{2}
Consider a composite wall of overall height \(H=20\) \(\mathrm{mm}\) and thickness \(L=30 \mathrm{~mm}\). Section A has thickness \(L_{\mathrm{A}}=10 \mathrm{~mm}\), and sections \(\mathrm{B}\) and
The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, \(k_{\mathrm{A}}=25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) and \(k_{\mathrm{C}}=60
The \(t=4\)-mm-thick glass windows of an automobile have a surface area of \(A=2.6 \mathrm{~m}^{2}\). The outside temperature is \(T_{\infty, o}=32^{\circ} \mathrm{C}\) while the passenger
Consider the water of Example 1.5 to be initially liquid at its fusion temperature. The outer wall surface is suddenly reduced to \(T_{1}=-30^{\circ} \mathrm{C}\), resulting in solidification of the
A composite wall separates combustion gases at \(2400^{\circ} \mathrm{C}\) from a liquid coolant at \(100^{\circ} \mathrm{C}\), with gas and liquid-side convection coefficients of 25 and \(1000
Two AISI 304 stainless steel plates \(10 \mathrm{~mm}\) thick are subjected to a contact pressure of 1 bar under vacuum conditions for which there is an overall temperature drop of \(100^{\circ}

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