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engineering
mechanical engineering

Questions and Answers of Mechanical Engineering

Derive the transient, two-dimensional finite-difference equation for the temperature at nodal point 0 located on the boundary between two different materials.
A wall 0.12 m thick having a thermal diffusivity of 1.5 x 10-6 m2/s is initially at a uniform temperature of 85°C. Suddenly one face is lowered to a temperature of 20°C, while the other face is
A molded plastic product (p = 1200 kg/m3 ∙ c = 1500 J/kg ∙ K, k = 0.30 W/m ∙ K) is cooled by exposing one surface to an array of air jets, while the opposite surface is well insulated. The
The plane wall of Problem 2.48 (k = 50 W/m ∙ K, a = 1.5 X 10-6 m2/s) has a thickness of L = 40 mm and an initial uniform temperature of To = 25°C. Suddenly, the boundary at x = L experiences
Consider the fuel element of Example 5.9. Initially, the element is at a uniform temperature of 250°C with no heat generation. Suddenly, the element is inserted into the reactor core causing a
Consider the fuel element of Example 5.9, which operates at a uniform volumetric generation rate of q) = 10 7 W/m3, until the generation rate suddenly changes to q2 = 2 x 107 W/m3. Use the
(a) Calculate the temperature distribution 1.5 s after the change in operating power and compare your results with those tabulated in the example.(b) Use your FEHT model to plot temperature histories
In a thin-slab, continuous casting process, molten steel leaves a mold with a thin solid shell, and the molten material solidifies as the slab is quenched by water jets en route to a section of
A very thick plate 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
Referring to Example 5.10, Comment 4, consider a sudden exposure of the surface to large surroundings at an elevated temperature (Tsur) and to convection (T∞, h).(a) Derive the explicit,
Consider the thick slab of copper in Example 5.10, which is initially at a uniform temperature of 20oC and is suddenly exposed to a net radiant flux of 3 X 105 W/m2. Use the Finite-Difference
Consider the thick slab of copper in Example 5.10 which is initially at a uniform temperature of 20o0 and is suddenly exposed to large surroundings at 1000oC (instead of a prescribed heat flux).(a)
Consider the composite wall of Problem 2.53. In part (d), you are asked to sketch the temperature histories at x = 0, L during the transient period between cases 2 and 3. Calculate and plot these
In Section 5.5, the one-term approximation to the series solution for the temperature distribution was developed for a plane wan of thickness 2L that is initially at a uniform temperature and
Consider the bonding operation described in Problem 3.103, which was analyzed under steady-state conditions. In this case however, the laser will be used to heat the film for a prescribed period of
One end of a stainless steel (AISI 316) rod of diameter 10 mm and length 0.16 m is inserted into a fixture maintained at 200°C. The rod, covered with an insulating sleeve, reaches a uniform
A tantalum rod of diameter 3 mm and length 120 mm is supported by two electrodes within a large vacuum enclosure. Initially the rod is in equilibrium with the electrodes and its surroundings, which
A support rod (k = 15 W/m ∙ K, a = 4.0 X 10-6 m2/s) of diameter D = 15 mm and length L = 100 mm spans a channel whose walls are maintained at a temperature of Tb = 300 K. Suddenly, the rod is
Consider the acceleration-grid foil (k = 40 W/m ∙ K, a = 3 X 10-5 m2/s, F = 0.45) of Problem 4.72. Develop an implicit, finite-difference model of the foil, which can be used for the following
Circuit boards are treated by heating a stack of them under high pressure as illustrated in Problem 5.45 and described further in Problem 5.46. A finite-difference method of solution is sought with
Common transmission failures result from the glazing of clutch surfaces by deposition of oil oxidation and decomposition products. Both the oxidation and decomposition processes depend on temperature
Heat transfer is not an intuitive process muses the Curious Cook. Does doubling the thickness of a hamburger approximately double the cooking time? What effect does the initial temperature have on
A process mixture at 200Â°C flows at a rate of 207 kg/min onto a conveyor belt of 3-mm thickness, 1-m width, and 30-m length traveling with a velocity of 36 m/min. The underside of the belt is
A thin circular disk is subjected to induction heating from a coil the effect of which is to provide a uniform heat generation within a ring section as shown. Convection occurs at the upper surface,
An electrical cable, experiencing a uniform volumetric generation q, is half buried in an insulating material while the upper surface is exposed to a convection processes (T∞, h).(a) Derive the
Two very long (in the direction normal to the page) bars having the prescribed initial temperature distributions are to be soldered together. At time t = 0, the m = 3 face of the copper (pure) bar
1n a manufacturing process, stainless steel cylinders (AISI 304) initially at 600 K are quenched by submersion in an oil bath maintained at 300 K with h = 500 W/m2 ∙ K. Each cylinder is of length
Consider the system of Problem 4.55. Initially with no flue gases flowing, the walls (a = 5.5 X 10-7 m2/s) are at a uniform temperature of 25°C. Using the implicit, finite-difference method with a
Consider the system of Problem 4.73. Initially, the ceramic plate (a = 1.5 X 10-6 m2/s) is at a uniform temperature of 30°C, and suddenly the electrical heating elements are energized. Using the
Consider the thermal conduction module and operating conditions of Problem 4.76. To evaluate the transient response of the cold plate, which has a thermal diffusivity of a = 75 X 10-6 m2/s. assume
The operations manager for a metals processing plant anticipates the need to repair a large furnace and has come to you for an estimate of the time required for the furnace interior to cool to a safe
The door panel of an automobile is fabricated by a plastic hot-extrusion process resulting in the ribbed cross section shown schematically. Following a process involving air-cooling, painting and
In flow over a surface velocity and temperature profiles are of the forms u(y) = Ay + By2 – Cy3 and T(y) = D + Ey + Fy2- Gy3 where the coefficients A through G are constants. Obtain expressions for
Water at a temperature of T∞ = 25°C flows over one of the surfaces of a steel wall (AISI 1010) whose temperature is Ts,1 = 40°C. The wal1 is 0.35 m thick, and its other surface temperature is Ts,
In a particular application involving airflow over a heated surface, the boundary layer temperature distribution may be approximated as where y is the distance normal to the surface and thePrandtl
For laminar flow over a flat plate, the local heat transfer coefficient h. is known to vary as x–1/2, where x is the distance from the leading edge (x = 0) of the plate. What is the ratio of the
For laminar free convection from a heated vertical surface, the local convection coefficient may be expressed as hx = Cx-1/4, where h, is the coefficient at a distance x from the leading edge of the
A circular, hot gas jet at T∞ is directed normal to a circular plate that has radius ro and is maintained at a uniform temperature Ts. Gas flow over the plate is axisymmetric, causing the local
Parallel flow of atmospheric air over a flat plate of length L = 3 m is disrupted by an array of stationary rods placed in the flow path over the plate.Laboratory measurements of the local convection
Air at a free stream temperature of T∞ = 20°C is in parallel flow over a flat plate of length L = 5 m and temperature Ts = 90°C. However, obstacles placed in the flow intensify mixing with
The heat transfer rate per unit width (normal to the page) from a longitudinal section, x2 â€“ x1, can be expressed as q'12 = h12 (x2 â€“ xl)(Ts â€“ T∞), where h12 is the average
Experiments have been conducted to determine local heat transfer coefficients for flow perpendicular to a long, isothermal bar of rectangular cross section. The bar is of width c, parallel to the
Experiments to determine the local convection heat transfer coefficient for uniform flow normal to a heated circular disk have yielded a radial Nusselt number distribution of the form where both n
An experimental procedure for validating results of the foregoing problem involves preheating a copper disk to an initial elevated temperature T; and recording its temperature history T(t) as it is
If laminar flow is induced at the surface of a disk due to rotation about its axis, the local convection coefficient is known to be a constant, h = C, independent of radius. Consider conditions for
Consider airflow over a flat plate of length L = 1 m under conditions for which transition occurs at xc = 0.5 m based on the critical Reynolds number, Re xc = 5 x 105.(a) Evaluating the thermo
A fan that can provide air speeds up to 50 m/s is to be used in a low-speed wind tunnel with atmospheric air at 25°C. If one wishes to use the wind tunnel to study flat-plate boundary layer behavior
Assuming a transition Reynolds number of 5 x 105, determine the distance from the leading edge of a flat plate at which transition will occur for each of the following fluids when u∞; = 1 m/s:
To a good approximation the dynamic viscosity μ, the thermal conductivity k, and the specific heat c p are independent of pressure. In what manner do the kinematic viscosity v and thermal
An object of irregular shape has a characteristic length of L = 1 m and is maintained at a uniform surface temperature of Ts = 400 K. When placed in atmospheric air at a temperature of T∞ = 300 K
Experiments have shown that, for airflow at T∞ = 35°C and V1 = 100 m/s, the rate of heat transfer from a turbine blade of characteristic length L1 = 0.15 m and surface temperature Ts, 1 = 300°C
Experimental measurements of the convection heat transfer coefficient for a square bar in cross flow yielded the following values:Assume that the functional form of the Nusselt number is Nu = C Rem
Experimental results for heat transfer over a flat plate with an extremely rough surface were found to be correlated by an expression of the form Nu x = 0.04Rex0.9 Pr1/3 where Nu x is the local value
Consider conditions for which a fluid with a free stream velocity of V = I m/s flows over a surface with a characteristic length of L = I m, providing an average convection heat transfer coefficient
For flow over a flat plate of length L, the local heat transfer coefficient hx is known to vary as x-1/2, where x is the distance from the leading edge of the plate. What is the ratio of the average
For laminar boundary layer flow over a flat plate with air at 20°C and 1 atm, the thermal boundary layer thickness 8r is approximately 13% larger than the velocity boundary layer thickness 8.
Sketch the variation of the velocity and thermal boundary layer thicknesses with distance from the leading edge of a flat plate for the laminar flow of air, water engine oil and mercury. For each
Forced air at T∞ = 25Â°C and V = 10 m/s is used to cool electronic elements on a circuit board. One such element is a chip, 4 mm by 4 mm. located 120 mm from the leading edge of the board.
Consider the electronic elements that are cooled by forced convection in Problem 6.26. The cooling system is designed and tested at sea level (P = I atm), but the circuit board is sold to a customer
Consider the chip on the circuit board of Problem 6.26. To ensure reliable operation over extended periods, the chip temperature should not exceed 85°C. Assuming the availability of forced air at
A major contributor to product defects in electronic modules relates to stresses induced during thermal cycling (intermittent heating and cooling). For example, in circuit cards having active and
To assess the efficacy of different liquids for cooling an object of given size and shape by forced convection it is convenient to introduce figure of merit, FF, which combines the influence of an
Gases are often used instead of liquids to cool electronics in avionics applications because of weight considerations. The cooling systems are often closed so that coolants other than air may be
The defroster of an automobile functions by discharging warm air on the inner surface of the windshield. To prevent condensation of water vapor on the surface, the temperature of the air and the
A micro scale detector monitors a steady flow (T∞ = 27Â°C, V = 10 m/s) of air for the possible presence of small hazardous particulate matter that may be suspended in the room. The sensor is
A thin, flat plate that is 0.2 m by 0.2 m on a side is oriented parallel to an atmospheric airstream having a velocity of 40 m/s. The air is at a temperature of T∞ = 20°C, while the plate is
Atmospheric air is in parallel flow (u∞ = 15 m/s, T∞ = 15°C) over a flat heater surface that is to be maintained at a temperature of 140°C. The heater surface area is 0.25 m2, and the airflow
For flow over a flat plate with an extremely rough surface, convection heat transfer effects are known to be correlated by the expression of Problem 6.21. For airflow at 50 m/s, what is the surface
A thin, flat plate that is 0.2 m by 0.2 m on a side with extremely rough top and bottom surfaces is placed in a wind tunnel so that its surfaces are parallel to an atmospheric air stream having 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 120 mm by 120 mm on a side is cooled by the parallel flow of atmospheric air with a velocity of 2 m/s.From
On a summer day the air temperature is 27°C and the relative humidity is 30%. Water evaporates from the surface of a lake at a rate of 0.10 kg/h per square meter of water surface area. The
It is observed that a 230-mm-diameter pan of water at 23°C has a mass loss rate of 1.5 X 10-5 kg/s when the ambient air is dry and at 23°C.(a) Determine the convection mass transfer coefficient for
The rate at which water is lost because of evaporation from the surface of a body of water may be determined by measuring the surface recession rate. Consider a slimmer day for which the temperature
Photosynthesis, as it occurs in the leaves of a green plant, involves transport of carbon dioxide (C02) from the atmosphere to the chloroplasts of the leaves and the rate of photosynthesis may be
Species A is evaporating from a flat surface into species B. Assume that the concentration profile for species A in the concentration boundary layer is of the form CA(y) = Dy2 + Ey + F, where D, E,
Consider cross flow of gas X over an object having a characteristic length of L = 0.1 m. For a Reynolds number of I x 104, the average heat transfer coefficient is 25 W/m2 ∙ K. The same object is
Consider conditions for which a fluid with a free stream velocity of V = 1 m/s flows over an evaporating or subliming surface with a characteristic length of L = 1 m, providing an average mass
An object of irregular shape has a characteristic length of L = 1 m and is maintained at a uniform surface temperature of Ts = 325 K. It is suspended in an airstream that is at atmospheric pressure
On a cool day in April a scantily clothed runner is known to lose heat at a rate of 500 W because of convection to the surrounding air at T∞ = 10oC. The runner's skin remains dry and at a
An object of irregular shape 1 m long maintained at a constant temperature of 100°C is suspended in an airstream having a free stream temperature of O°C, pressure of I atm, and a velocity of 120
An industrial process involves the evaporation of water from a liquid film that forms on a contoured surface. Dry air is passed over the surface and from laboratory measurements the convection heat
The naphthalene sublimation technique involves use of a mass transfer experiment coupled with an analysis based on the heat and mass transfer analogy to obtain local or average convection heat
Consider application of the naphthalene sublimation technique (Problem 6.51) to a gas turbine blade that is coated with naphthalene and has a surface area of As = 0.05 m2To determine the average
A manufacturer of ski equipment wishes to develop headgear that will offer enhanced thermal protection for skiers on cold days at the slopes. Headgear can be made with good thermal insulating
A streamlined strut supporting a bearing housing is exposed to a hot airflow from an engine exhaust. It is necessary to run experiments to determine the average convection heat transfer coefficient h
Consider the conditions of Problem 6.3, but with a thin film of water on the surface. If the air is dry and the Schmidt number Se is 0.6, what is the evaporative mass flux? Is there net energy
Consider the conditions of Problem 6.7, for which a heat transfer experiment yielded the prescribed distribution of the local convection coefficient, hx(x). The experiment was performed for surface
Using the naphthalene sublimation technique, the radial distribution of the local convection mass transfer coefficient for uniform flow normal to a circular disk has been correlated by an expression
To reduce the threat of predators, the sand grouse, a bird of Kenya, will lay its eggs in locations well removed from sources of groundwater. To bring water to its chicks, the grouse will then fly to
A laboratory experiment involves simultaneous heat and mass transfer from a water-soaked towel experiencing irradiation from a bank of radiant lamps and parallel flow of air over its surface. Using a
In the spring, concrete surfaces such as sidewalks and driveways are sometimes very wet in the morning, even when it has not rained during the night. Typical night-time conditions are shown in the
Dry air at 32°C flows over a wetted (water) plate of 0.2 m2 area. The average convection coefficient is h = 20 W/m2 ∙ K, and the heater power required to maintain the plate at a temperature of
Dry air at 32Â°C flows over a wetted plate of length 200 mm and width 1 m (case A). An imbedded electrical heater supplies 432 Wand the surface temperature is 27Â°C.(a) What is the evaporation
A 20-mm diameter sphere is suspended in a dry air stream with a temperature of 22°C. The power supplied to an embedded electrical heater within the sphere is 2.51 W when the surface temperature is
A successful California engineer has installed a circular hot tub in his back yard and finds that for the typical operating conditions prescribed below, water must be added at a rate of 0.00 I kg/s
It is known that on clear nights the air temperature need not drop below 0°C before a thin layer of water on the ground will freeze. Consider such a layer of water on a clear night for which the
An expression for the actual water vapor partial pressure in terms of wet-bulb and dry-bulb temperatures, referred to as the Carrier equation, is given as where.Pv, Pgw, and P are the actual partial
A wet-bulb thermometer consists of a mercury-in-glass thermometer covered with a wetted (water) fabric. When suspended in a stream of air, the steady-state thermometer reading indicates the wet-bulb
An industrial process involves evaporation of a thin water film from a contoured surface by heating it from below and forcing air across it. Laboratory measurements for this surface have provided the

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