Questions and Answers of Fundamentals Momentum Heat

A cylindrical nuclear fuel element is 10.16 cm long and 10.77 cm in diameter. The fuel generates heat uniformly at a rate of 51.7 × 103 kJ/s · m3. The fuel is placed in an environment having a
Radioactive waste (k = 20 W/m · K) is stored in a cylindrical stainless steel (k = 15W/m · K) container with inner and outer diameters of 1.0 and 1.2 m, respectively. Thermal energy is generated
T(rauses volumetric heating to vary according toq̇(x) = q̇0[1 - (x/L)]where q̇0 has a constant value of 180 kW/m3 and the slab thickness, L, is 0.06 m. The thermal conductivity of the slab
What additional thickness of insulation will be necessary to reduce the boil-off rate of liquid nitrogen to one-half of the rate corresponding to Problem 17.23? All values and dimensions in Problem
Liquid nitrogen at 77 K is stored in an insulated spherical container that is vented to the atmosphere. The container is made of a thin-walled material with an outside diameter of 0.5 m; 25 mm of
Work Problem 17.20 for the case of aluminium rather than copper. The resistivity of aluminum is 2.83 × 10-6 ohm – cm.Data From Problem 17.20Copper wire having a diameter of 3/16 in. is insulated
What would be the result of Problem 17.20 if the fluid surrounding the insulated wire was maintained at 70°F with a convective heat-transfer coefficient between the insulation and the fluid of 4
Copper wire having a diameter of 3/16 in. is insulated with a 4-in. layer of material having a thermal conductivity of 0.14 Btu/h ft °F. The outer surface of the insulation is maintained at 70°F.
A computer IC chip consumes 10 W of power, which is dissipated as heat. The chip measures 4 cm by 4 cm on a side and is 0.5-cm thick. Currently, the IC chip is packaged into an electronic device as
A computer IC chip consumes 10 W of power, which is dissipated as heat. The chip measures 4 cm by 4 cm on a side and is 0.5-cm thick. Currently the IC chip is packaged into an electronic device as
Saturated steam at 40 psia flows at 5 fps through a schedule-40, 1½-in. steel pipe. The convective heat-transfer coefficient by condensing steam on the inside surface may be taken as 1500 Btu/h ft2
A 2-in. schedule-40 steel pipe carries saturated steam at 60 psi through a laboratory that is 60 ft long. The pipe is insulated with 1.5 in. of 85% magnesia that costs $0.75 per foot. How long must
A cross section of a typical home ceiling is depicted below. Given the properties listed for the materials of construction, determine how much heat is transferred through the insulation and through
A composite wall is to be constructed of ¼ in. of stainless steel (k = 10 Btu/h ft °F), 3 in. of cork board (k = 0.025 Btu/h ft °F), and ½ in. of plastic (k = 1.5 Btu/h ft °F). Determine the
A 2.5-cm thick sheet of plastic (k = 2.42 W/m · K) is to be bonded to a 5-cm thick aluminum plate. The glue that will accomplish the bonding is to be held at a temperature of 325 K to achieve the
Determine the percent in heat flux if, in addition to the conditions specified in Problem 17.11, there are two 3/4-in.- diameter steel bolts extending through the wall per square foot of wall area (k
A heater composed of Nichrome wire wound back and forth and closely spaced is covered on both sides with 1/8 - in. thickness of asbestos (k = 0.15 Btu/h ft °F) and then with a 1/8 -in. thickness of
Given the conditions of Problem 17.9, except that the outside temperature of the masonry brick cannot exceed 325 K, by how much must the thickness of kaolin be adjusted to satisfy this
A furnace wall consisting of 0.25 m of fire clay brick, 0.20 m of kaolin, and a 0.10-m outer layer of masonry brick is exposed to furnace gas at 1370 K with air at 300 K adjacent to the outside wall.
A furnace wall is to be designed to transmit a maximum heat flux of 200 Btu/h ft2 of wall area. The inside and outside wall temperatures are to be 2000°F and 300°F, respectively. Determine the most
A double-pane insulated window unit consists of two 1-cm-thick pieces of glass separated by a 1.8 cm layer of air. The unit measures 4 m in width and is 3 m wide. Under conditions where the extreme
A stainless steel plate 1.6 cm thick rests on top of a hot plate, which is maintained at 250°C. Air flows over the top surface of the plate to provide a convective heat-transfer coefficient of h
It is desired to transport liquid metal through a pipe embedded in a wall at a point where the temperature is 650 K. A 1.2-m-thick wall constructed of a material having a thermal conductivity varying
Evaluate the appropriate €œmean€ area for steady-state heat conduction in a hollow sphere that satisfies an equation of the formRepeat part (b) of Problem 17.2 for the spherical
The steady-state expression for heat conduction through a plane wall is q =(kA/L) Î”T as given by equation (17-4). For steady-state heat conduction through a hollow cylinder, anexpression
One-dimensional steady-state conduction, with no internal heat generation, occurs across a plane wall having a constant thermal conductivity of 30 W/m · K. The material is 30 cm thick. For each case
Heat is generated in a spherical fuel element according to the relationshipwhere qÌ‡ is the volumetric heat-generation rate, kW/m3, and ro is the radius of the sphere. Develop the
Heat is generated in a cylindrical fuel rod in a nuclear reactor according to the relationship where qÌ‡ is the volumetric heat generation rate, kW/m3, and ro is the outside cylinder
Heat is transferred by conduction (assumed to be one dimensional) along the axial direction through the truncated conical section shown in the figure. The two base surfaces are maintained at constant
A spherical shell with inner and outer dimensions of ro, and ri, respectively, has surface temperatures Ti (ri) and To (ro). Assuming constant properties and one-dimensional (radial) conduction,
In a boundary layer where the velocity profile is given by where Î´ is the velocity boundary-layer thickness, plot the dimensionless dissipation function,
Use the relation T ds = dh - dP/ρ to show that the effect of the dissipation function, Φ, is to increase the entropy, S. Is the effect of heat transfer the same as the dissipation function?
Solve Problem 16.5 for the same conditions, except that at x = L, dT/dx = Î¾ (a constant).Data From Problem 16.5Solve equation (16-19) for the temperature distribution in a plane wall if
Solve Problem 16.5 for the same conditions, except that the boundary condition at x = L is dT/dx = 0.Data From Problem 16.5Solve equation (16-19) for the temperature distribution in a plane wall if
Solve equation (16-19) for the temperature distribution in a plane wall if the internal heat generation per unit volume varies according to qÌ‡ = qÌ‡0e-Î²x/L. The
Show that equation (16-10) reduces to the form DT V ·kVT + ġ + A = pcy- +v•µV?v Dt
Starting with the Fourier field equation in cylindrical coordinates,a. Reduce this equation to the applicable form for steady-state heat transfer in the Î¸ direction.b. For the conditions
Perform the same operations as in parts (a), (b), and (c) of Problem 16.1 with respect to a spherical system.Data From Problem 16.1The Fourier field equation in cylindrical coordinates isa. What form
The Fourier field equation in cylindrical coordinates isa. What form does this equation reduce to for the case of steady-state, radial heat transfer?b. Given the boundary conditionsT = Ti at r =
Liquid nitrogen at 77 K is stored in a cylindrical container having an inside diameter of 25 cm. The cylinder is made of stainless steel and has a wall thickness of 1.2 cm. Insulation is to be added
If, for the conditions of Problem 15.29, ho in Btu/h ft °F varies according to h0 = 0.575/D10/4, where D0 is the outside diameter of the insulation in feet, determine the thickness of insulation
A 1-in.-nominal-diameter steel pipe with its outside surface at 400°F is located in air at 90°F with the convective heat-transfer coefficient between the surface of the pipe and the air equal to
Water at 40°F is to flow through a 11/2-in. schedule 40 steel pipe. The outside surface of the pipe is to be insulated with a 1-in.-thick layer of 85% magnesia and a 1-in.-thick layer of packed
A 4 in-OD pipe is to be used to transport liquid metals and will have an outside surface temperature of 1400F under operating conditions. Insulation is 6 in. thick and has a thermal conductivity
Given the furnace wall and other conditions as specified in Problem 15.25, what thickness of celotex (k = 0.065W/m · K) must be added to the furnace wall in order that the outside surface
Determine the heat-transfer rate per square meter of wall area for the case of a furnace with inside air at 1340 K. The furnace wall is composed of a 0.106-m layer of fireclay brick and a 0.635-cm
Solve Problem 15.23 if instead of the surface temperatures being known, the air temperatures outside and inside are 30 and 75°F, respectively, and the convective heat-transfer coefficients are 7 and
The outside walls of a house are constructed of a 4-in. layer of brick, 1/2 in. of celotex, an air space 35/8 in. thick, and 1/4 in. of wood paneling. If the outside surface of the brick is at 30°F
Compare the heat loss through the storm window described in Problem 15.21 with the same conditions existing except that the window is a single pane of glass 0.32 cm thick.Data From Problem 15.21The
The cross section of a storm window is shown in the sketch. How much heat will be lost through a window measuring 1.83 m by 3.66 m on a cold day when the inside and outside air temperatures are,
Evaluate the required thickness of styrofoam for the freezer compartment in the previous problem when the inside wall is exposed to air at -10°C through a surface coefficient of 16 W/m2 · K and the
The freezer compartment in a conventional refrigerator can be modeled as a rectangular cavity 0.3 m high and 0.25 m wide with a depth of 0.5 m. Determine the thickness of styrofoam insulation (k =
If in Problem 15.17, the lower surface of the plate is exposed to air with a convective heat-transfer coefficient of 3 Btu/h ft °F, what steady-state temperature will be reacheda. If radiant
The solar radiation incident on a steel plate 2 ft square is 400 Btu/h. The plate is 1.4 in. thick and lying horizontally on an insulating surface, its upper surface being exposed to air at 90°F. If
Solve for the inside surface temperature of the brick wall described in Problem 15.15, but with the additional consideration of radiation from the outside surface to surroundings at 25°C.Data From
A 0.20-m-thick brick wall (k = 1.3W/m · K) separates the combustion zone of a furnace from its surroundings at 25°C. For an outside wall surface temperature of 100°C, with a convective
If, in Problem 15.13, the plate is made of asbestos, k = 0.10 Btu/h ft °F, what will be the temperature of the top of the asbestos if the hot plate is rated at 800 W?Data From Problem 15.13A
A 1-in.-thick steel plate measuring 10 in. in diameter is heated from below by a hot plate, its upper surface exposed to air at 80°F. The heat-transfer coefficient on the upper surface is 5 Btu/h ft
If, in the previous problem, the convective heat-transfer coefficients at the inner (steel) and outer surfaces are 40 and 5 Btu/h ft °F, respectively, determinea. The heat flux if the gases are at
A composite wall is to be constructed of 1/4-in. stainless steel (k = 10 Btu/h ft °F), 3 in. of cork board (k = 0.025 Btu/hft °F) and 1/2 in. of plastic (k = 1.5 Btu/h ft °F).a. Draw the thermal
If, in the previous problem, a 3-in.-thick layer of kaolin brick (k = 0.07 Btu/h ft °F) is added to the outside of the asbestos, what heat flux will result if the outside surface of the kaolin is
The heat loss from a boiler is to be held at a maximum of 900 Btu/h ft2 of wall area. What thickness of asbestos (k = 0.10 Btu/h ft °F) is required if the inner and outer surfaces of the insulation
Solve Problem 15.7 if all specified conditions remain the same but radiant energy exchange from glass to the surroundings at the air temperature is also considered.Data From 15.7Plate glass, k = 1.35
Plate glass, k = 1.35 W/m · K, initially at 850 K, is cooled by blowing air past both surfaces with an effective surface coefficient of 5 W/m2 · K. It is necessary, in order that the glass not
For the sheet of insulation specified in Problem 15.5, with a heat rate of 4 kW, evaluate the temperature at both surfaces if the cool side is exposed to air at 30°C with a surface coefficient of
A sheet of insulating material, with thermal conductivity of 0.22 W/m · K, is 2 cm thick and has a surface area of 2.97 m2. If 4 kW of heat are conducted through this sheet and the outer (cooler)
Solve Problem 15.1 if the asbestos pad has a 1.905-cm steel bolt running through its centerData From Problem 15.1An asbestos pad is square in cross section, measuring 5 cm on a side at its small end,
Solve Problem 15.1 if, in addition to a varying cross- sectional area, the thermal conductivity varies according to k = k0 (1 + /βT), where k0 = 0.138, β = 1.95 × 10-4, T = temperature in Kelvin,
Solve Problem 15.1 for the case of the larger cross section exposed to the higher temperature and the smaller end held at 300 K.Data From Problem 15.1An asbestos pad is square in cross section,
An asbestos pad is square in cross section, measuring 5 cm on a side at its small end, increasing linearly to 10 cm on a side at the large end. The pad is 15 cm high. If the small end is held at 600
A pump operating at 2400 rpm delivers 3.2 m3/s of water against a head of 21 m. Is this pump an axial-flow, mixed-flow, or radial-flow machine?
A pump operating at 520 rpm has the capability of producing 3.3 m3/s of water flow against a head of 16 m. What type of pump is this?
An axial-flow pump has a specified specific speed of 6.0. The pump must deliver 2400 gpm against a head of 18 m. Determine the required operating rpm of the pump.
A pump is required to deliver 60,000 gpm against a head of 300 m when operating at 2000 rpm. What type of pump should be specified?
Pumps used in an aqueduct operate at 400 rpm and deliver a flow of 220 m3/s against a head of 420 m. What types of pumps are they?
A centrifugal pump with an impeller diameter of 0.18 m is to be used to pump water (Ï = 1000 kg/m3) with the pump inlet located 3.8 m above the surface of the supply reservoir. At a flow
For the pumping system described in Problem 14.23, how will the maximum elevation above the surface of the reservoir change if the water temperature is 80°C(Pv = 47.35 kPa)?Data From Problem 14.23A
A 0.25 m pump delivers 20°C water (Pv = 2.34 kPa) at 0.065 m3/s and 2000 rpm. The pump begins to cavitate when the inlet pressure is 82.7 kPa and the inlet velocity is 6.1 m/s. Determine the
Water at 20°C is to be pumped through the system shown. The operating data for this motor-driven pump data are as follows:The inlet pipe to the pump is 0.06 m diameter commercial steel, 8.5 m in
For the same pump and system operation described in Problem 14.20 determine (a) the discharge rate and (b) power required when the pump operates at 900 rpm.
A pump whose operating characteristics are described in Problem 14.14 is to be used in the system depicted below. Determine (a) the discharge rate and (b) power required.Data From Problem
The pump having the characteristics shown in Problem 14.14 is used to pump water from one reservoir to another that is 95 m higher in elevation. The water will flow through a steel pipe that is 0.28
If the pump having the characteristics shown in Problem 14.14 is tripled in size but halved in rotational speed,what will be the discharge rate and head when operating at maximum efficiency?Data From
The pump having the characteristics shown in Problem 14.14 is to be operated at 800 rpm. What discharge rate is to be expected if the head developed is 410 m?Data From Problem 14.14Performance curves
For the pump having the characteristics shown in Problem 14.14, operating at maximum efficiency with the speed increased to 1000 rpm, what will be (a) the new discharge flow rate and (b) the power
The pump having the characteristics shown in Problem 14.14 was used as a model for a prototype that is to be six times larger. If this prototype operates at 400 rpm, what (a) power; (b) head; and (c)
Performance curves for an operating centrifugal pump are shown below in both conventional units and in dimensionless form. The pump is used to pump water at maximum efficiency at a head of 90 m.
Rework Problem 14.9 for a desired flow rate of 0.201 m3/s at 1800 rpm.Data From Problem 14.9A pump having the characteristics described in the previous problem is to be built that will deliver water
Rework Problem 14.9 for a desired flow rate of 0.30 m3/s at 1800 rpm.Data From Problem 14.9A pump having the characteristics described in the previous problem is to be built that will deliver water
Rework Problem 14.8 for a pump diameter of 0.35 m operating at 2400 rpm.Data From Problem 14.8The figure below represents performance, in non-dimensional form, for a family of centrifugal pumps. For
Rework Problem 14.8 for a pump diameter of 0.40 m operating at 2200 rpm.Data From Problem 14.8The figure below represents performance, in non-dimensional form, for a family of centrifugal pumps. For
A pump having the characteristics described in the previous problem is to be built that will deliver water at a rate of 0.2 m3/s when operating at best efficiency and a rotational speed of 1400 rpm.
The figure below represents performance, in non-dimensional form, for a family of centrifugal pumps. For a pump from this family with a characteristic diameter of 0.45 m operating at maximum
A centrifugal water pump operates at 1500 rpm. The dimensions follow: r1 = 12 cm...........β1 = 32o r2 = 20 cm...........β2 = 20oL = 4.2 cmDetermine (a) the design point discharge rate,
A centrifugal pump having the dimensions shown develops a flow rate of 0.032 m3/s when pumping gasoline (Ï = 680 kg/m3). The inlet flow may be assumed to be radial. Estimate (a) the
A centrifugal pump is being used to pump water at a flow rate of 0.018 m3/s and the required power is measured to be 4.5 kW. If the pump efficiency is 63%, determine the head generated by the pump.
A centrifugal pump has the configuration and dimensions shown below. For water flowing at a rate of 0.0071 m3/s and an impeller speed of 1020 rpm, determine the power required to drive the pump. The
A centrifugal pump has the following dimensions: d2 = 42 cm, L = 5 cm, and β2 = 33°. It rotates at 1200 rpm, and the head generated is 52 m of water. Assuming radial entry flow, determine the
A centrifugal pump is used with gasoline (ρ = 680 kg/m3). Relevant dimensions are as follows: d1 = 15 cm, d2 = 28 cm, L = 9 cm, β1 = 25°, and β2 = 40°. The gasoline enters the pump parallel to
A centrifugal pump delivers 0.2 m3/s of water when operating at 850 rpm. Relevant impeller dimensions are as follows: outside diameter = 0.45 m, blade length = 50 cm, and blade exit angle = 24°.

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