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engineering
mechanical engineering

Questions and Answers of Mechanical Engineering

A truncated solid cone is of circular cross section, and its diameter is related to the axial coordinate by an expression of the form D = ax 3/2, where a = 1.0 m-1/2.The sides are well insulated,
From Figure it is evident that, over a wide temperature range, the temperature dependence of the thermal conductivity of many solids may be approximated by a linear expression of the form k = ko +
Consider a tube wall of inner and outer radii r; and ro, whose temperatures are maintained at Ti and To, respectively. The thermal conductivity of the cylinder is temperature dependent and may be
Measurements show that steady-state conduction through a plane wall without heat generation produced a convex temperature distribution such that the mid- point temperature was 6.To higher than
A device used to measure the surface temperature of an object to within a spatial resolution of approximately 50 nm is shown in the schematic. It consists of an extremely sharp-tipped stylus and an
A steam pipe of 0.12-m outside diameter is insulated with a layer of calcium silicate.(a) If the insulation is 20 mm thick and its inner and outer surfaces are maintained at Ts,1 = 800 K and Ts.2 =
Consider the water heater described in Problem 1.37. We now wish to determine the energy needed to compensate for heat losses incurred while the water is prescribed temperature of 55°C. The
A thin electrical heater is wrapped around the outer surface of a long cylindrical tube whose inner surface is maintained at a temperature of 5°C. The tube wall has inner and outer radii of 25 and
In the previous problem, the electrical power required to maintain the heater at To = 25°C depends on the thermal conductivity of the wall material k, the thermal contact resistance Rt,c, and the
A stainless steel (AISI 304) tube used to transport a chilled pharmaceutical has an inner diameter of 36 mm and a wall thickness of 2 mm. The pharmaceutical and ambient air are at temperatures of
Superheated steam at 575°C is routed from a boiler to the turbine of an electric power plant through steel tubes (k = 35 W/m ∙ K) of 300 mm inner diameter and 30 mm wall thickness. To reduce heat
A thin electrical heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm. The rod (A) has a thermal conductivity of k A = 0.15 W/m. K, while
A wire of diameter D = 2 mm and uniform temperature T has an electrical resistance of 0.01 n/m and a current flow of 20 A.(a) What is the rate at which heat is dissipated per unit length of wire?
A 2-mm-diameter electrical wire is insulated by a 2-mm-thick rubberized sheath (k = 0.13 W/m ∙ K), and the wire/sheath interface is characterized by a thermal contact resistance of R c = 3 X 10-4
Electric current flows through a long rod generating thermal energy at a uniform volumetric rate of q = 2 X 106 W/m3. The rod is concentric with a hollow ceramic cylinder, creating an enclosure that
The evaporator section of a refrigeration unit consists of thin-walled, 10-mm-diarneter tubes through which refrigerant passes at a temperature of - 18°C. Air is cooled as it flows over the tubes,
A composite cylindrical wall is composed of two materials of thermal conductivity k A and k B, which are separated by a very thin, electric resistance heater for which interfacial contact resistances
An electrical current of 700 A flows through a stainless steel cable having a diameter of 5 mm and an electrical resistance of 6 X 10-4 Ω/m (i.e., per meter of cable length). The cable is in an
A 0.20-m-diameter, thin-walled steel pipe is used to transport saturated steam at a pressure of 20 bars in a room for which the air temperature is 25°C and the convection heat transfer coefficient
Steam at a temperature of 250°C flows through a steel pipe (AISI 1010) of 60-mm inside diameter and 75-mm outside diameter. The convection coefficient between the steam and the inner surface of the
We wish to determine the effect of adding a layer of magnesia insulation to the steam pipe of the foregoing problem. The convection coefficient at the outer surface of the insulation may be assumed
An uninsulated, thin-walled pipe of 100-mm diameter is used to transport water to equipment that operates outdoors and uses the water as a coolant. During particularly harsh winter conditions, the
Steam flowing through a long, thin-walled pipe maintains the pipe wall at a uniform temperature of 500 K. The pipe is covered with an insulation blanket comprised of two different materials, A and
A Bakelite coating is to be used with a 10-mm-diameter conducting rod, whose surface is maintained at 200°C by passage of an electrical current. The rod is in a fluid at 25°C, and the convection
A storage tank consists of a cylindrical section that has a length and inner diameter of L = 2 m and Di = 1 m, respectively, and two hemispherical end sections. The tank is constructed from
Consider the liquid oxygen storage system and the laboratory environmental conditions of Problem 1.49. To reduce oxygen loss due to vaporization, an insulating layer should be applied to the outer
In Example 3.5, an expression was derived for the critical insulation radius of an insulated, cylindrical tube. Derive the expression that would be appropriate for an insulated sphere.
A hollow aluminum sphere, with an electrical heater in the center, is used in tests to determine the thermal conductivity of insulating materials. The inner and outer radii of the sphere are 0.15 and
A spherical tank for storing liquid oxygen on the space shuttle is to be made from stainless steel of 0.80-m outer diameter and 5-mm wall thickness. The boiling point and latent heat of vaporization
A spherical cryosurgical probe may be imbedded in diseased tissue for the purpose of freezing, and thereby destroying, the tissue. Consider a probe of 3-mm diameter whose surface is maintained at -
A spherical vessel used as a reactor for producing pharmaceuticals has a 10-mm-thick stainless steel wall (k = 17 W/m ∙ K) and an inner diameter of I m. The exterior surface of the vessel is
The wall of a spherical tank of 1-m diameter contains an exothermic chemical reaction and is at 200°C when the ambient air temperature is 25°C. What thickness of urethane foam is required to reduce
A composite spherical shell of inner radius r1 = 0.25 m is constructed from lead of outer radius r2 = 0.30 m and AISI 302 stainless steel of outer radius r3 = 0.31 m. The cavity is filled with
As an alternative to storing radioactive materials in oceanic waters, it is proposed that the system of Problem 3.62 be placed in a large tank for which the flow of water, and hence the convection
The energy transferred from the anterior chamber of the eye through the cornea varies considerably depending on whether a contact lens is worn. Treat the eye as a spherical system and assume the
The outer surface of a hollow sphere of radius r2 is subjected to a uniform heat flux q2. The inner surface at r1 is held at a constant temperature T∞.1.(a) Develop an expression for the
A spherical shell of inner and outer radii ri and r0, respectively, is filled with a heat-generating material that provides for a uniform volumetric generation rate (W/m3) of q. The outer surface of
A spherical tank of 3-m diameter contains a liquefied petroleum gas at -60°C. Insulation with a thermal conductivity of 0.06 W/m. K and thickness 250 mm is applied to the tank to reduce the heat
A transistor, which may be approximated as a hemispherical heat source of radius r0 = 0.1 mm. is embedded in a large silicon substrate (k = 125 W/m ∙ K) and dissipates heat at a rate q. All
One modality for destroying malignant tissue involves imbedding a small spherical heat source of radius ro within the tissue and maintaining local temperatures above a critical value Tc for an
Consider cylindrical and spherical shells with inner and outer surfaces at r1 and r2 maintained at uniform temperatures Ts.1 and Ts.2 respectively. If there is uniform heat generation within the
The steady-state temperature distribution in a composite plane wall of three different materials, each of constant thermal conductivity, is shown as follows.(a) Comment on the relative magnitudes of
A plane wall of thickness 0.1 m and thermal conductivity 25 W/m ∙ K having uniform volumetric heat generation of 0.3 MW/m3 is insulated on one side, while the other side is exposed to a fluid at
Consider one-dimensional conduction in a plane composite wall. The outer surfaces are exposed to a fluid at 25°C and a convection heat transfer coefficient of 1000 W/m2 ∙ K. The middle wall B
Consider a plane composite wall that is composed of three materials (materials A, B, and C are arranged left to right) of thermal conductivities kA = 0.24 W/m ∙ K, kB = 0.13 W/m ∙ K, and kC =
Consider the composite wall of Example 3.7. In the Comments section, temperature distributions in the wall were determined assuming negligible contact resistance between materials A and B. Compute
A plane wall of thickness 2L and thermal conductivity k experiences a uniform volumetric generation rate q. As shown in the sketch for Case I, the surface at x = - L is perfectly insulated, while the
A nuclear fuel element of thickness 2L is covered with a steel cladding of thickness b. Heat generated within the nuclear fuel at a rate q is removed by a fluid at T∞, which adjoins one surface and
Consider the clad fuel element of Problem 3.77.(a) Using appropriate relations from Tables C.1 and C.2, obtain an expression for the temperature distribution T(x) in the fuel element. For kf = 60 W/m
The air inside a chamber at T∞,i = 50°C is heated convectively with h; = 20 W/m2 ∙ K by a 200-mm-thick wall having a thermal conductivity of 4 W/m ∙ K and a uniform heat generation of 1000
In the previous problem, the strip heater acts to guard against heat losses from the wall to the outside, and the required heat flux q”o depends on chamber operating conditions such as q and
The exposed surface (x = 0) of a plane wall of thermal conductivity k is subjected to microwave radiation that causes volumetric heating to vary as where q"0(W/m3) is a constant. The boundary at x =
A quartz window of thickness L serves as a viewing port in a furnace used for annealing steel. The inner surface (x = 0) of the window is irradiated with a uniform heat flux q;: due to emission from
For the conditions described in Problem 1.44, determine the temperature distribution, T(r), in the container, expressing your result in terms of qo, ro, T∞, h, and the thermal conductivity k of the
A cylindrical shell of inner and outer radii, ri and r0, respectively, is filled with a heat-generating material that provides a uniform volumetric generation rate (W/m3) of q. The inner surface is
Consider the solid tube of Example 3.8. Using Equation (7) with Equation (10) in the IHT workspace, calculate and plot the temperature distributions for a tube of inner and outer radii, 50 mm and 100
An air heater may be fabricated by coiling Nichrome wire and passing air in cross flow over the wire. Consider a heater fabricated from wire of diameter D = 1 mm, electrical resistivity Pe = 10-6 Ω
The cross section of a long cylindrical fuel element in a nuclear reactor is shown. Energy generation occurs uniformly in the thorium fuel rod, which is of diameter D = 25 mm and is wrapped in a thin
A nuclear reactor fuel element consists of a solid cylindrical pin of radius r1 and thermal conductivity kf. The fuel pin is in good contact with a cladding material of outer radius r2 and thermal
Consider the configuration of Example 3.8, where uniform volumetric heating within a stainless steel tube is induced by an electric current and heat is transferred by convection to air flowing
A homeowner, whose water pipes have frozen during a period of cold weather, decides to melt the ice by passing an electric current I through the pipe wall. The inner and outer radii of the wall are
A high-temperature, gas-cooled nuclear reactor consists of a composite cylindrical wall for which a thorium fuel element (k = 57 W/m ∙ K) is encased in graphite (k ≈ 3 W/m ∙ K) and gaseous
A long cylindrical rod of diameter 200 mm with thermal conductivity of 0.5 W/m. K experiences uniform volumetric heat generation of 24,000 W/m3. The rod is encapsulated by a circular sleeve having an
A radioactive material of thermal conductivity k is cast as a solid sphere of radius ro and placed in a liquid bath for which the temperature T∞ and convection coefficient h are known. Heat is
Radioactive wastes are packed in a thin-walled spherical container. The wastes generate thermal energy non-uniformly according to the relation q = qo[1 â€“ (r/r0)2], where q is the local rate of
Radioactive wastes (krw = 20 W/m ∙ K) are stored in a spherical, stainless steel (kss, = 15 W/m ∙ K) container of inner and outer radii equal to ri = 0.5 m and ro = 0.6 m. Heat is generated
Unique characteristics of biologically active materials such as fruits, vegetables, and other products require special care in handling. Following harvest and separation from producing plants,
Consider the plane wall, long cylinder, and sphere shown schematically, each with the same characteristic length a. thermal conductivity k, and uniform volumetric energy generation rate q.(a) On the
The radiation heat gage shown in the diagram is made from constantan metal foil, which is coated black and is in the form of a circular disk of radius R and thickness t. The gage is located in an
Copper tubing is joined to the absorber of a flat-plate solar collector as shown.The aluminum alloy (2024- T6) absorber plate is 6 mm thick and well insulated on its bottom. The top surface of the
Copper tubing is joined to the absorber of a flat-plate solar collector as shown.The aluminum alloy (2024- T6) absorber plate is 6 mm thick and well insulated on its bottom. The top surface of the
A thin flat plate of length L, thickness t, and width W > L is thermally joined to two large heat sinks that are maintained at a temperature To. The bottom of the plate is well insulated, while the
Consider the flat plate of Problem 3.101, but with the heat sinks at different temperatures, T(0) = To and T(L) = T L , and with the bottom surface no longer insulated. Convection heat transfer is
A bonding operation utilizes a laser to provide a constant heat flux, q"0, across the top surface of a thin adhesive-backed, plastic film to be affixed to a metal strip as shown in the sketch. The
A thin metallic wire of thermal conductivity k, diameter D, and length 2L is annealed by passing an electrical current through the wire to induce a uniform volumetric heat generation q. The ambient
A motor draws electric power Pelec from a supply line and delivers mechanical power Pmech to a pump through a rotating copper shaft of thermal conductivity ks, length L, and diameter D. The motor is
Consider the fuel cell stack of Problem 1.58. The t = 0.42 rum thick membranes have a nominal thermal conductivity of k = 0.79 W/m ∙ K that can be increased to keff,x = 15.1 W/m ∙ K by loading
The thermocouple (TC) installation on a snowmobile engine cylinder head is shown in the schematic. The TC wire leads are attached to the upper and lower surfaces of the cylindrically shaped solder
Consider a rod of diameter D, thermal conductivity k, and length 2L that is perfectly insulated over one portion of its length, - L
A probe of overall length L = 200 mm and diameter D = 12.5 mm is inserted through a duct wall such that a portion of its length, referred to as the immersion length L i , is in contact with the water
A rod of diameter D = 25 mm and thermal conductivity k = 60 W/m. K protrudes normally from a furnace wall that is at Tw = 200Â°C and is covered by insulation of thickness L ins = 200 mm. The rod is
A metal rod of length 2L, diameter D, and thermal conductivity k is inserted into a perfectly insulating wall, exposing one-half of its length to an air stream that is of temperature T∞ and
A very long rod of 5-mm diameter and uniform thermal conductivity k = 25 W/m. K is subjected to a heat treatment process. The center, 30-mm-Iong portion of the rod within the induction heating coil
From Problem 1.71 consider the wire leads connecting the transistor to the circuit board. The leads are of thermal conductivity k, thickness t. width w, and length L. One end of a lead is maintained
A disk-shaped electronic device of thickness Ld, diameter D, and thermal conductivity kd dissipates electrical power at a steady rate Pe along one of its surfaces. The device is bonded to a cooled
Turbine blades mounted to a rotating disc in a gas turbine engine are exposed to a gas stream that is at T∞ = 1200Â°C and maintains a convection coefficient of h = 250 W/m2 ∙ K over the
In a test to determine the friction coefficient, μ, associated with a disk brake, one disk and its shaft are rotated at a constant angular velocity w, while an equivalent disk/shaft assembly is
Consider an extended surface of rectangular cross section with heat flow in the longitudinal direction.In this problem we seek to determine conditions for which the transverse (y-direction)
A long, circular aluminum rod is attached at one end to a heated wall and transfers heat by convection to a cold fluid.(a) If the diameter of the rod is tripled, by how much would the rate of heat
A brass rod 100 mm long and 5 mm in diameter extends horizontally from a casting at 200°e. The rod is in an air environment with T∞ = 20°C and h = 30 W/m2 ∙ K. What is the temperature of the
The extent 10 which the tip condition affects the thermal performance of a fin depends on the fin geometry and thermal conductivity, as well as the convection coefficient. Consider an alloyed
The extent to which the tip condition affects the thermal performance of a fin depends on the fin geometry and thermal conductivity, as well as the convection coefficient. Consider an alloyed
A straight fin fabricated from 2024 aluminum alloy (k = 185 W/m ∙ K) has a base thickness of t = 3 mm and a length of L = 15 mm. Its base temperature is Tb = 100°C, and it is exposed to a fluid
Two long copper rods of diameter D = 10 mm are soldered together end to end, with solder having a melting point of 650°e. The rods are in air at 25°C with a convection coefficient of l0W/m2 ∙ K.
Circular copper rod of diameter D = 1 mm and length L = 25 mm are used to enhance heat transfer from a surface that is maintained at Ts.1 = 100°C. One end of the rod is attached to this surface (at
During the initial stages of the growth of the nanowire of Problem 3.109, a slight perturbation of the liquid catalyst droplet can cause it to be suspended on the top of the nanowire in an off-center
Consider two long slender rods of the same diameter but different materials. One end of each rod is attached to a base surface maintained at 100°C, while the surfaces of the rods are exposed to
A 40-mm-Iong, 2-mm-diameter pin fin is fabricated of an aluminum alloy (k = 140 W/m2 ∙ K).(a) Determine the fin heat transfer rate for Th = 50°C, T∞. = 25°C, h = 1000 W/m2 ∙ K. and an
An experimental arrangement for measuring the thermal conductivity of solid materials involves the use of two long rods that are equivalent in every respect, except that one is fabricated from a
Finned passages are frequently formed between parallel plates to enhance convection heat transfer in compact heat exchanger cores. An important application is in electronic equipment cooling, where

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