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engineering
mechanical engineering
Questions and Answers of
Mechanical Engineering
Consider one-dimensional conduction in a plane composite wall. The exposed surfaces of materials A and B are maintained at T1 = 600 K and T2 = 300 K respectively. Material A, of thickness La = 20 mm,
A platen of thermal conductivity k = 15 W/m ∙ K is heated by flow of a hot fluid through channels of width L = 20mm, with T∞,i = 200°C and hi = 500W/m2 ∙ K. The upper surface of the platen is
Consider the cooling arrangement for the very large-scale integration (VLSI) chip of Problem 4.75. Use the finite-element method of FEHT to obtain the following results.(a) Determine the temperature
Consider a thin electrical heater attached to a plate and backed by insulation. Initially, the heater and plate are at the temperature of the ambient air, T∞. Suddenly, the power to the heater is
The inner surface of a plane wall is insulated while the outer surface is exposed to an airstream at T∞. The wall is at a uniform temperature corresponding to that of the airstream. Suddenly, a
A microwave oven operates on the principle that application of high-frequency field causes electrically polarized molecules in food to oscillate. The net effect is a nearly uniform generation of
A plate of thickness 2L, surface area As, mass M, and specific heat c p ' initially at a uniform temperature T∞, is suddenly heated on both surfaces by a convection process (T∞, h) for a period
Steel balls 12 mm in diameter are annealed by heating to 1150 K and then slowly cooling to 400 K in an air environment for which T∞, = 325 K and h = 20 W/m2 ∙ K. Assuming the properties of the
Consider the steel balls of Problem 5.5, except now the air temperature increases with time as T∞,(t) = 325 K + at where a = 0.1875 K/s.(a) Sketch the ban temperature versus time for 0 < t <
The heat transfer coefficient for air 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 12.7 mm in
A solid steel sphere (AISI 1010), 300 mm in diameter, is coated with a dielectric material layer of thickness 2 mm and thermal conductivity 0.04 W/m' K. The coated sphere is initially at a uniform
The base plate of an iron has a thickness of L = 7 mm and is made from an aluminum alloy (p = 2800 kg/m3 ∙c = 900 J/kg ∙ K, k = 180 W/m ∙ K, ε = 0.80). An electric resistance heater is
Carbon steel (AISI 1010) shafts of 0.1-m diameter are heat treated in a gas-fired furnace whose gases are at 1200 K and provide a convection coefficient of 100 W/m2 ∙ K. If the shafts enter the
A thermal energy storage unit consists of a large rectangular channel, which is well insulated on its outer surface and encloses alternating layers of the storage material and the flow passage.Each
Thermal energy storage systems commonly involve a packed bed of solid spheres, through which a hot gas flows if the system is being charged, or a cold gas if it is being discharged. In a charging
A tool used for fabricating semiconductor devices consists of a chuck (thick metallic, cylindrical disk) onto which a very thin silicon wafer (p = 2700 kg/m3 ∙ c = 875 J/kg ∙ K, k = 177 W/m
A spherical vessel used as a reactor for producing pharmaceuticals has a 5-mm-thick stainless steel wall (k = 17 W/m ∙ K) and an inner diameter of D j = 1.0 m. During production, the vessel is
Batch processes are often used in chemical and pharmaceutical operations to achieve a desired chemical composition for the final product and typically involve a transient heating operation to take
A plane wall of a furnace is fabricated from plain carbon steel (k = 60 W/m ∙ K, p = 7850 kg/m3, c = 430 J/kg ∙ K) and is of thickness L = 10 mm. To protect it from the corrosive effects of the
A steel strip of thickness 8 = 12 mm is annealed by passing it through a large furnace whose walls are maintained at a temperature Tw corresponding to that of combustion gases flowing through the
A long wire of diameter D = 1 mm is submerged in an oil bath of temperature T∞ = 25°C. The wire has an electrical resistance per unit length of R = 0.01Ω/m. If a current of I = 100 A flows
Consider the system of Problem 5.1 where the temperature of the plate is space wise isothermal during the transient process.(a) Obtain an expression for the temperature of the plate as a function of
An electronic device, such as 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)
Before being injected into a furnace, pulverized coal is preheated by passing it through a cylindrical tube whose surface is maintained at Tsur = 1000°C. The coal pellets are suspended in an airflow
A metal sphere of diameter D, which is at a uniform temperature Tj, is suddenly removed from a furnace and suspended from a fine wire in a large room with air at a uniform temperature T∞ and the
As permanent space stations increase in size, there is an attendant increase in the amount of electrical power they dissipate. To keep station compartment temperatures from exceeding prescribed
In a material processing experiment conducted aboard the space shuttle, a coated niobium sphere of l0-mm diameter is removed from a furnace at 900°C and cooled to a temperature of 300°C. Although
Plasma spray-coating processes are often used to provide surface protection for materials exposed to hostile environments, which induce degradation through factors such as wear, corrosion, or
Thin film coatings characterized by high resistance to abrasion and fracture may be formed by using micro-scale composite particles in a plasma spraying process. A spherical particle typically
A chip that is of length L = 5 mm on a side and thickness t = 1 mm is encased in a ceramic substrate, and its exposed surface is convectively cooled by a dielectric liquid for which h = 150 W/m2 ∙
Consider the conditions of Problem 5.27. In addition to treating heat transfer by convection directly from the chip to the coolant, a more realistic analysis would account for indirect transfer from
Thermal stress testing is a common procedure used to assess the reliability of an electronic package. Typically, thermal stresses are induced in soldered or wired connections to reveal mechanisms
The objective of this problem is to develop thermal models for estimating the steady-state temperature and the transient temperature history of the electrical transformer shown below.The external
In thermo mechanical data storage, a processing head, consisting of M heated cantilevers, is used to write data onto an underlying polymer storage medium. Electrical resistance heaters are micro
The melting of water initially at the fusion temperature, Tf = 0°C, was considered in Example 1.5. Freezing of water often occurs at 0°C. However, pure liquids that undergo a cooling process can
As noted in Problem 5.3, microwave ovens operate by rapidly aligning and reversing water molecules within the food, resulting in volumetric energy generation and, in turn, cooking of the food. When
Consider the series solution, Equation 5.39, for the plane wall with convection. Calculate mid plane (x* = 0) and surface (x* = 1) temperatures θ* for Fo = 0.1 and I, using Bi = 0.1, 1, and 10.
Consider the one-dimensional wall shown in the sketch, which is initially at a uniform temperature T j and is suddenly subjected to the convection boundary condition with a fluid at T∝.For a
Referring to the semiconductor processing tool of Problem 5.13, it is desired at some point in the manufacturing cycle to cool the chuck, which is made of aluminum alloy 2024. The proposed cooling
Annealing is a process by which steel is reheated and then cooled to make it less brittle. Consider the reheat stage for a 100-mm-thick steel plate (p = 7830 kg/m3, c = 550 J/kg ∙ K, k = 48 W/m ∙
Consider the heavily insulated pipe of Example 5.4, which is suddenly subjected to the flow of hot oil. Use the Transient Conduction, Plane Wall model of IHT to obtain the following solutions.(a)
The 150-mm-thick wall of a gas-fired furnace is constructed of fire-day brick (k = 1.5 W/m ∙ K. p = 2600 kg/m ∙ c p = 1000 J/kg ∙ K) and is well insulated at its outer surface. The wall is at a
Steel is sequentially heated and cooled (annealed) to relieve stresses and to make it less brittle. Consider a 100-mm-thick plate (k = 45 W/m ∙ K. p = 7800 kg/m3 ∙ cp = 500J/kg ∙ K) that
A plate of thickness 2L = 25 mm at a temperature of 600°C is removed from a hot pressing operation and must be cooled rapidly in order to achieve the required physical properties. The process
During transient operation the steel nozzle of a rocket engine must not exceed a maximum allowable operating temperature of 1500 K when exposed to combustion gases characterized by a temperature of
In a tempering process, glass plate, which is initially at a uniform temperature Ti, is cooled by suddenly reducing the temperature of both surfaces to Ts. The plate is 20 mm thick, and the glass has
The strength and stability of tires may be enhanced by heating both sides of the rubber (k = 0.14 W/m ∙ K. a = 6.35 x 10-8 m2/s) in a steam chamber for which T∝ = 200°C. In the heating process,
Copper-coated, epoxy-fi1led fiberglass circuit boards are treated by heating a stack of them under high pressure as shown in the sketch. The purpose of the pressing-heating operation is to cure the
Circuit boards are treated by heating a stack of them under high pressure as illustrated in Problem 5.45. The platens at the top and bottom of the stack are maintained at a uniform temperature by a
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 air flow at 25°C. As first approximations,
A long rod of 60-mm diameter and thermo physical properties P = 8000 kg/m3, c = 500 J/kg ∙ K, and k = 50 W/m ∙ K is initially at a uniform temperature and is heated in a forced convection furnace
A long cylinder of 30-mm diameter, initia1ly at a uniform temperature of 1000 K. is suddenly quenched in a large, constant-temperature oil bath at 350 K. The cylinder properties are k = 1.7 W/m ∙
A long pyroceram rod of diameter 20 mm is clad with a very thin metallic tube for mechanical protection. The bonding between the rod and the tube has a thermal contact resistance of Rt.c = 0.12 m ∙
A long rod 40 mm in diameter, fabricated from sapphire (aluminum oxide) and initially at a uniform temperature of 800 K, is suddenly cooled by a fluid at 300 K having a heat transfer coefficient of
A long plastic rod of 30-mm diameter (k = 0.3 W/m ∙ K and pcp = 1040kJ/m3 ∙ K) is uniformly heated in an oven as preparation for a pressing operation. For best results, the temperature in the rod
In a manufacturing process, long rods of different diameters are at a uniform temperature of 400°C in a curing oven, from which they are removed and cooled by forced convection in air at 25°C. One
The density and specific heat of a particular material are known (p = 1200 kg/m3 ∙ c p = 1250 J/kg ∙ K), but its thermal conductivity is unknown. To determine the thermal conductivity, a long
In Section 5.2 we noted that the value of the Biot number significantly influences the nature of the temperature distribution in a solid during a transient conduction process. Reinforce your
In heat treating to harden steel ban bearings (c = 500 J/kg ∙ K p = 7800 kg/m3, k = 50 W/m ∙ K), it is desirable to increase the surface temperature for a short time without significantly warming
A cold air chamber is proposed for quenching steel ball bearings of diameter D = 0.2 m and initial temperature Ti = 400°C. Air in the chamber is maintained at – 15°C by a refrigeration system,
Stainless steel (AISI 304) ball bearings, which have uniformly been heated to 850°C, are hardened by quenching them in an oil bath that is maintained at 40°C. The ball diameter is 20 mm, and the
As part of a heat treatment process cylindrical, 304 stainless steel rods of 100-mm diameter are cooled from an initial temperature of 500°C by suspending them in an oil bath at 30°e. If a
A sphere 30 mm in diameter initially at 800 K is quenched in a large bath having a constant temperature of 320 K with a convection heat transfer coefficient of 75 W/m2 ∙ K. The thermo physical
Spheres A and B are initially at 800 K, and they are simultaneously quenched in large constant temperature baths, each having a temperature of 320 K. The following parameters are associated with each
Spheres of 40-mm diameter heated to a uniform temperature of 400°C are suddenly removed from the oven and placed in a forced-air bath operating at 25°C with a convection coefficient of 300 W 1m:!.
Consider the packed bed operating conditions of Problem 5.12, but with Pyrex (p = 2225 kg/m3 ∙ c = 835 J/kg ∙ K. k = 1.4 W/m ∙ K) used instead of aluminum. How long does it take a sphere near
The convection coefficient for flow over a solid sphere may be determined by submerging the sphere which is initial1y at 25°C, into the flow, which is at 75°C, and measuring its surface temperature
Consider the sphere of Example 5.5, which is initially at a uniform temperature when it is suddenly removed from the furnace and subjected to a two-step cooling process. Use the Transie1l1
Two large blocks of different materials, such as copper and concrete have been sitting in a room (23°C) for a very long time. Which of the two blocks if either will feel colder to the touch? Assume
A plane wal1 of thickness 0.6 m (L = 0.3 m) is made of steel (k = 30 W/m ∙ K. p = 7900 kg/m3, c = 640 J/kg ∙ K). It is initially at a uniform temperature and is then exposed to air on both
Asphalt pavement may achieve temperatures as high as 50°C on a hot summer day. Assume that such a temperature exists throughout the pavement, when suddenly a rainstorm reduces the surface
A thick steel slab (p = 7800 kg/m3, c = 480 J/kg ∙ K, k = 50 W/m ∙ K) is initially at 300°C and is cooled by water jets impinging on one of its surfaces. The temperature of the water is 25°C,
Consider the water main of Example 5.6, which is buried in soil initially at 20°C and is suddenly subjected to a constant surface temperature of -15°C for 60 days. Use the Transient
A tile-iron consists of a massive plate maintained at 150°C by an imbedded electrical heater. The iron is placed in contact with a tile to soften the adhesive, allowing the tile to be easily lifted
The manufacturer of a heat flux gage like that illustrated in Problem 1 12 claims the time constant for a 63.2% response to be τ = (4d2 pc p) π2k where p, c p, and k are the thermo physical
A simple procedure for measuring surface convection heat transfer coefficients involves coating the surface with a thin layer of material having a precise melting point temperature. The surface is
An insurance company has hired you as a consultant to improve their understanding of burn injuries. They are especially interested in injuries induced when a portion of a worker's body comes into
A procedure for determining the thermal conductivity of a solid material involves embedding a thermocouple in a thick slab of the solid and measuring the response to a prescribed change in
The density and specific heat of a plastic material are known (p = 950 kg/m3, cp = 1100 J/kg ∙ K), but its thermal conductivity is unknown. To determine the thermal conductivity, an experiment is
A very thick slab with thermal diffusivity 5.6 x 10-6 m2/s and thermal conductivity 20 W/m ∙ K is initially at a uniform temperature of 325°C. Suddenly, the surface is exposed to a coolant at
A thick oak wall, initially at 25°C, is suddenly exposed to combustion products for which T∞ = 800°C and h=20W/m2 ∙ K.(a) Determine the time of exposure required for the surface to reach
Standards for firewalls may be based on their thermal response to a prescribed radiant heat flux. Consider a 0.25-m-thick concrete wall (p = 2300 kg/m3 ∙ c = 880 J/kg. K, k = 1.4 W/m ∙ K), which
It is well known that, although two materials are at the same temperature, one may feel cooler to the touch than the other. Consider thick plates of copper and glass, each at an initial temperature
Two stainless steel plates (p = 8000 kg/m3, c = 500 J/kg ∙ K, k = 15 W/m ∙ K), each 20 mm thick and insulated on one surface, are initially at 400 and 300 K when they are pressed together at
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 solid
When a molten metal is cast in a mold that is a poor conductor, the dominant resistance to heat flow is within the mold wall. Consider conditions for which a liquid metal is solidifying in a
Joints of high quality can be formed by friction welding. Consider the friction welding of two 4O-mm-diameter Inconel rods. The bottom rod is stationary, while the top rod is forced into a
An above-ground circular swimming pool is heated so that it can be used in cool weather. The ground has a temperature of 10°C far from the pool. The heater is turned on and quickly brings the pool
A rewritable optical disc (DVD) is formed by sandwiching a 15-nm-thick binary compound storage material between two I-mm-thick polycarbonate sheets. Data are written to the opaque storage medium by
To enable cooking a wider range of foods in microwave ovens, thin, metallic packaging materials have been developed that will readily absorb microwave energy. As the packaging material is heated by
The structural components of modern aircraft are commonly fabricated of high-performance composite materials. These materials are fabricated by impregnating mats of extremely strong fibers that are
Problem 4.9 addressed radioactive wastes stored underground in a spherical container. Because of uncertainty in the thermal properties of the soil, it is desired to measure the steady-state
A thermal storage medium consists of a large mass of limestone. Ambient air is pumped through a 30-mm-high, 5-m-long 5-m-wide fissure within the limestone at a velocity of 2m/s. providing a heat
Consider the experimental measurement of Example 5.8. It is desired to measure the thermal conductivity of an extremely thin sample of the same nanostructured material having the same length and
The stability criterion for the explicit method requires that the coefficient of the term of the one-dimensional, finite-difference equation be zero or positive. Consider the situation for
A thin rod of diameter D is initially in equilibrium with its surroundings, a large vacuum enclosure at temperature Tsur. Suddenly an electrical current I (A) is passed through the rod having an
A one-dimensional slab of thickness 2L is initially at a uniform temperature Ti. Suddenly, electric current is passed through the slab causing a uniform volumetric heating q (W/m3). At the same time,
A plane wall (p = 4000 kg/m3, c p = 500 J/kg ∙ K, k = 10 W/m ∙ K) of thickness L = 20 mm initially has a linear, steady-state temperature distribution with boundaries maintained at T1 = 0°C and
A round solid cylinder made of a plastic material (a = 6 x 10-7 m2/s) is initially at a uniform temperature of 20oC and is well insulated along its lateral surface and at one end. At time t = 0, heat
Derive the explicit finite-difference equation for an interior node for three-dimensional transient conduction. Also determine the stability criterion. Assume constant properties and equal grid
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