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engineering
mechanical engineering

Questions and Answers of Mechanical Engineering

Show that the rate of heat conduction per unit length through a long hollow cylinder of inner radius ri and outer radius ro, made of a material whose thermal conductivity varies linearly with
A long, hollow cylinder is constructed from a material whose thermal conductivity is a function of temperature according to k = 0.060 + 0.00060 T, where T is in ?F and k is in Btu/h ?F. The inner and
A plane wall 15 cm thick has a thermal conductivity given by the relationk = 2.0 + 0.0005 T W/(m K)where T is in degrees Kelvin. If one surface of this wall is maintained at 150 ?C and the other at
A plane wall 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90?C. The convective heat transfer
A small dam, which may be idealized by a large slab 1.2 m thick, is to be completely poured in a short period of time. The hydration of the concrete results in the equivalent of a distributed source
Two large steel plates at temperatures of 90? and 70?C are separated by a steel rod 0.3 m long and 2.5 cm in diameter. The rod is welded to each plate. The space between the plates is filled with
The shield of a nuclear reactor can be idealized by a large 10 in. thick flat plate having a thermal conductivity of 2 Btu/(h ft ?F). Radiation from the interior of the reactor penetrates the shield
Derive an expression for the temperature distribution in an infinitely long rod of uniform cross section within which there is uniform heat generation at the rate of 1 W/m. Assume that the rod is
Derive an expression for the temperature distribution in a plane wall in which there are uniformly distributed heat sources which vary according to the linear relationqG = qw [1 ?? β(T ?? Tw)]where
A plane wall of thickness 2L has internal heat sources whose strength varies according toqG = q0 cos (ax)where q0 is the heat generated per unit volume at the center of the wall (x = 0) and
Heat is generated uniformly in the fuel rod of a nuclear reactor. The rod has a long, hollow cylindrical shape with its inner and outer surfaces at temperatures of Ti and To, respectively. Derive an
Show that the temperature distribution in a sphere of radius ro, made of a homogeneous material in which energy is released at a uniform rate per unit volume qG , is GIVENA homogeneous sphere
In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where qg = local rate of heat generation per unit volume at rro = outside radiusq1 =
wAn electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire, having an electrical resistivity of 80 × 10??6 ohm-centimeter. The
The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section,
The tip of a soldering iron consists of a 0.6-cm-OD copper rod, 7.6 cm long. If the tip must be 204?C, what is the required minimum temperature of the base and the heat flow, in Btu??s per hour and
One end of a 0.3 m long steel rod is connected to a wall at 204?C. The other end is connected to a wall which is maintained at 93?C. Air is blown across the rod so that a heat transfer coefficient of
Both ends of a 0.6 cm copper U-shaped rod, as shown in the accompanying sketch, are rigidly affixed to a vertical wall, the temperature of which is maintained at 93?C. The developed length of the rod
A circumferential fin of rectangular cross section, 3.7 cm OD and 0.3 cm thick surrounds a 2.5 cm diameter tube. The fin is constructed of mild steel. Air blowing over the fin produces a heat
A turbine blade 6.3 cm long (see sketch on p. 156), with cross-sectional area A = 4.6 ×10??4 m2 and perimeter P = 0.12 m, is made of stainless steel (k = 18 W/(m K). The temperature of the root, Ts,
To determine the thermal conductivity of a long, solid 2.5 cm diameter rod, one half of the rod was inserted into a furnace while the other half was projecting into air at 27?C. After steady state
Heat is transferred from water to air through a brass wall (k = 54 W/(m K)). The addition of rectangular brass fins, 0.08 cm thick and 2.5 cm long, spaced 1.25 cm apart, is contemplated. Assuming a
The wall of a liquid-to-gas heat exchanger has a surface area on the liquid side of 1.8 m2 (0.6m × 3m) with a heat transfer coefficient of 255 W/(m2 K). On the other side of the heat exchanger wall
The top of a 12 in. I-beam is maintained at a temperature of 500?F, while the bottom is at 200?F. The thickness of the web is 1/2 in. Air at 500?F is blowing along the side of the beam so that h = 7
The handle of a ladle used for pouring molten lead is 30 cm long. Originally the handle was made of 1.9 × 1.25 cm mild steel bar stock. To reduce the grip temperature, it is proposed to form the
A 0.3-cm thick aluminum plate has rectangular fins on one side, 0.16 × 0.6 cm, spaced 0.6 cm apart. The finned side is in contact with low pressure air at 38?C and the average heat transfer
Compare the rate of heat flow from the bottom to the top in the aluminum structure shown in the sketch with the rate of heat flow through a solid slab. The top is at ??10?C, the bottom at 0?C. The
Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.GIVENThe sketch belowASSUMPTIONSSteady state conditionsTwo
Use a flux plot to estimate the rate of heat flow through the object shown in the sketch. The thermal conductivity of the material is 15 W/(m K). Assume no heat is lost from the sides.GIVENThe shape
Determine the rate of heat transfer per unit length from a 5-cm-OD pipe at 150?C placed eccentrically within a larger cylinder of 85% Magnesia wool as shown in the sketch. The outside diameter of the
Determine the rate of heat flow per foot length from the inner to the outer surface of the molded insulation in the accompanying sketch. Use k = 0.1 Btu/(h ft ?F).GIVENThe object with a cross section
A long 1-cm-diameter electric copper cable is embedded in the center of a 25 cm square concrete block. If the outside temperature of the concrete is 25?C and the rate of electrical energy dissipation
A large number of 1.5-in.-OD pipes carrying hot and cold liquids are embedded in concrete in an equilateral staggered arrangement with center line 4.5 in. apart as shown in the sketch. If the pipes
A long 1-cm-diameter electric cable is imbedded in a concrete wall (k = 0.13 W/(m K)) which is 1 m by 1 m, as shown in the sketch below. If the lower surface is insulated, the surface of the cable is
Determine the temperature distribution and heat flow rate per meter length in a long concrete block having the shape shown below. The cross-sectional area of the block is square and the hole is
A 30-cm-OD pipe with a surface temperature of 90?C carries steam over a distance of 100 m. The pipe is buried with its center line at a depth of 1 m, the ground surface is ?? 6?C, and the mean
Two long pipes, one having a 10-cm-OD and a surface temperature of 300?C, the other having a 5-cm-OD and a surface temperature of 100?C, are buried deeply in dry sand with their centerlines 15 cm
A radioactive sample is to be stored in a protective box with 4 cm thick walls having interior dimensions 4 by 4 by 12 cm. The radiation emitted by the sample is completely absorbed at the inner
A 6-in.-OD pipe is buried with its centerline 50 in. below the surface of the ground [k of soil is 0.20 Btu/(h ft ?F)]. An oil having a density of 6.7 lb/gal and a specific heat of 0.5 Btu/(lb ?F)
A 2.5-cm-OD hot steam line at 100?C runs parallel to a 5.0 cm OD cold water line at 15?C. The pipes are 5 cm center to center and deeply buried in concrete with a thermal conductivity of 0.87 W/(m
Calculate the rate of heat transfer between a 15-cm-OD pipe at 120?C and a 10-cm-OD pipe at 40?C. The two pipes are 330 m long and are buried in sand [k = 0.33W/(m K)] 12 m below the surface (Ts =
A 0.6-cm-diameter mild steel rod at 38?C is suddenly immersed in a liquid at 93?C with hc = 110W/(m2 K). Determine the time required for the rod to warm to 88?C.GIVENA mild steel rod is suddenly
A spherical shell satellite (3-m-OD, 1.25-cm-wall thickness, made of stainless steel) reenters the atmosphere from outer space. If its original temperature is 38?C, the effective average temperature
A thin-wall cylindrical vessel (1 m in diameter) is filled to a depth of 1.2 m with water at an initial temperature of 15?C. The water is well stirred by a mechanical agitator. Estimate the time
A thin-wall jacketed tank, heated by condensing steam at one atmosphere contains 91 kg of agitated water. The heat transfer area of the jacket is 0.9 m2 and the overall heat transfer coefficient U =
The heat transfer coefficients for the flow of 26.6?C air over a 1.25 cm diameter sphere are measured by observing the temperature-time history of a copper ball of the same dimension. The temperature
A spherical stainless steel vessel at 93?C contains 45 kg of water initially at the same temperature. If the entire system is suddenly immersed in ice water, determine (a) the time required for the
A copper wire, 1/32-in.-OD, 2 in. long, is placed in an air stream whose temperature rises at Tair = (50 + 25t)?F, where t is the time in seconds. If the initial temperature of the wire is 50?F,
A large 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on the one side is 28 W/(m2 K) and on the other side is 57 W/(m2 K). If the temperature of both
A 1.4-kg aluminum household iron has a 500 W heating element. The surface area is 0.046 m2. The ambient temperature is 21?C and the surface heat transfer coefficient is 11 W/(m2 K). How long after
Estimate the depth in moist soil at which the annual temperature variation will be 10% of that at the surface. GIVEN Moist soil ASSUMPTIONS Conduction is one dimensional The soil has uniform and
A small aluminum sphere of diameter D, initially at a uniform temperature To, is immersed in a liquid whose temperature, T??, varies sinusoidally according toT?? ?? Tm = A sin (ωt)where: Tm =
A wire of perimeter P and cross-sectional area A emerges from a die at a temperature T above ambient and with a velocity U. Determine the temperature distribution along the wire in the steady state
Ball bearings are to be hardened by quenching them in a water bath at a temperature of 37?C. Suppose you are asked to devise a continuous process in which the balls could roll from a soaking oven at
Estimate the time required to heat the center of a 1.5-kg roast in a 163?C over to 77?C. State your assumptions carefully and compare your results with cooking instructions in a standard
A stainless steel cylindrical billet [k = 14.4 W/(m K), α = 3.9 ×10??6m2/s] is heated to 593?C preparatory to a forming process. If the minimum temperature permissible for forming is 482?C, how
In the vulcanization of tires, the carcass is placed into a jig, and steam at 149?C is admitted suddenly to both sides. If the tire thickness is 2.5 cm, the initial temperature is 21?C, the heat
A long copper cylinder 0.6 m in diameter and initially at a uniform temperature of 38?C is placed in a water bath at 93?C. Assuming that the heat transfer coefficient between the copper and the water
A steel sphere with a diameter of 7.6 cm is to be hardened by first heating it to a uniform temperature of 870?C and then quenching it in a large bath of water at a temperature of 38?C. The following
A 2.5-cm-thick sheet of plastic initially at 21°C is placed between two heated steel plates that are maintained at 138°C. The plastic is to be heated just long enough for its mid-plane temperature
A monster turnip (assumed spherical) weighing in at 0.45 kg is dropped into a cauldron of water boiling at atmospheric pressure. If the initial temperature of the turnip is 17?C, how long does it
An egg, which for the purposes of this problem can be assumed to be a 5-cm-diameter sphere having the thermal properties of water, is initially at a temperature of 4?C. It is immersed in boiling
A long wooden rod at 38?C with a 2.5 cm diameter is placed into an airstream at 600?C. The heat transfer coefficient between the rod and air is 28.4 W/(m2 K). If the ignition temperature of the wood
In the inspection of a sample of meat intended for human consumption, it was found that certain undesirable organisms were present. In order to make the meat safe for consumption, it is ordered that
A frozen-food company freezes its spinach by first compressing it into large slabs and then exposing the slab of spinach to a low-temperature cooling medium. The large slab of compressed spinach is
In the experimental determination of the hat transfer coefficient between a heated steel ball and crushed mineral solids, a series of 1.5% carbon steel balls were heated to a temperature of 700?C and
A mild-steel cylindrical billet, 25-cm in diameter, is to be raised to a minimum temperature of 760?C by passing it through a 6-m long strip type furnace. If the furnace gases are at 1538?C and the
A solid lead cylinder 0.6-m in diameter and 0.6-m long, initially at a uniform temperature of 121?C, is dropped into a 21?C liquid bath in which the heat transfer coefficient hc is 1135 W/(m2 K).
A long 0.6-m-OD 347 stainless steel (k = 14 W/(m K) cylindrical billet at 16?C room temperature is placed in an oven where the temperature is 260?C. If the average heat transfer coefficient is 170
Repeat Problem 2.85(a), but assume that the billet is only 1.2-m long and the average heat transfer coefficient at both ends is 136 W/(m2 K).A long, 0.6 m OD 347 stainless steel (k = 14 W/(m K))
A large billet of steel initially at 260?C is placed in a radiant furnace where the surface temperature is held at 1200?C. Assuming the billet is infinite in extent, compute the temperature at point
Show that in the limit ??x ?? 0, the difference equation for one-dimensional steady conduction with heat generation, Equation (3.1), is equivalent to the differential equation, Equation
?What is the physical significance of the statement that the temperature of each node is just the average of its neighbors if there is no heat generation? [with reference to Equation (3.2)]?
Give an example of a practical problem in which the variation of thermal conductivity with temperature is significant and for which a numerical solution is therefore the only viable solution method.
Discuss advantages and disadvantages of using a large control volume.
For one-dimensional conduction, why are the boundary control volumes half the size of interior control volumes?GIVENOne-dimensional conductionEXPLAIN(a) Why the boundary control volume is half the
Discuss advantages and disadvantages of two methods for solving one-dimensional steady conduction problems.
Solve the system of equations 2T1 + T2 – T3 = 30T1 – T2 + 7T3 = 270T1 + 6T2 – T3 = 160by Jacobi and Gauss-Seidel iteration. Use as a convergence criterion | T2 (p) – T2 (p – 1) | <
Develop the control volume difference equation for one-dimensional steady conduction in a fin with variable cross-sectional area A(x) and perimeter P(x). The heat transfer coefficient from the fin to
Using your results from Problem 3.8, find the heat flow at the base of the fin for the following conditions:k = 20 Btu/(h ft ?F)L = 2 in. ho = 20 Btu/(h ft2 ?F)To = 200?FT?? = 80?FUse a grid spacing
Consider a pin fin with variable conductivity k(T), constant cross sectional area Ac and constant perimeter, P. Develop the difference equations for steady one-dimensional conduction in the fin and
How would you treat a radiation heat transfer boundary condition for a one-dimensional steady problem? Develop the difference equation for a control volume near the boundary and explain how to solve
How should the control volume method be implemented at an interface between two materials with different thermal conductivities? Illustrate with a steady, one-dimensional example. Neglect contact
How would you include contact resistance between the two materials in Problem 3.12? Derive the appropriate difference equations. GIVEN Interface between two materials with different thermal
A turbine blade 5-cm long, with cross-sectional area A = 4.5 cm2 and perimeter P = 12 cm, is made of a high-alloy steel [k = 25 W/(m K)]. The temperature of the blade attachement point is 500?C and
Determine the difference equations applicable to the centerline and at the surface of an axisymmetric cylindrical geometry with volumetric heat generation and convective boundary condition. Assume
Determine the appropriate difference equations for an axisymmetric, steady, spherical geometry with volumetric heat generation. Explain how to solve the equations.GIVENAxisymmetric, steady, spherical
Show that in the limit ??x ?? 0 and ??t ?? 0, the difference Equation (3.12) is equivalent to the differential Equation (2.5). GIVENThe difference equation for one-dimensional transient
Determine the largest permissible time step for a one-dimensional transient conduction problem to be solved by an explicit method if the node spacing is 1 mm and the material is (a) carbon steel 1C,
Consider one-dimensional transient conduction with a convective boundary condition in which the ambient temperature near the surface is a function of time. Determine the energy balance equation for
What are the advantages and disadvantages of using explicit and implicit difference equations?EXPLAIN(a) Advantages and disadvantages of explicit and implicit methods
Equation (3.15) is often called the fully-implicit form of the one-dimensional transient conduction difference equation because all quantities in the equation, except for the temperatures in the
A 3-m-long steel rod (k = 43 W/(mK), α = 1.17 \ 10–5 m2/s) is initially at 20°C and insulated completely except for its end faces. One end is suddenly exposed to the flow of combustion gases at
A Trombe wall is a masonry wall often used in passive solar homes to store solar energy. Suppose such a wall, fabricated from 20 cm thick solid concrete blocks (k = 0.13 W/(mK), α = 0.05 \
To more accurately model the energy input from the sun, suppose the absorbed flux in Problem 3.23 is given byqabs (t) = t (375 – 46.875 t)where t is in hours and qabs is in W/m2. (This time
An interior wall of a cold furnace, initially at 0°C, is suddenly exposed to a radiant flux of 15 kW/m2 when the furnace is brought on line. The outer surface of the wall is exposed to ambient air
A long cylindrical rod, 8 cm in diameter, is initially at a uniform temperature of 20°C. At time t = 0, the rod is exposed to an ambient temperature of 400°C through a heat transfer coefficient of
Develop a reasonable layout of nodes and control volumes for the geometry shown in the sketch below. Provide a scale drawing showing the problem geometry overlaid with the nodes and control
Develop a reasonable layout of nodes and control volumes for the geometry shown in the sketch below. Provide a scale drawing showing the problem geometry overlaid with the nodes and control volumes.
Determine the temperature at the four nodes shown in the figure. Assume steady conditions and two-dimensional heat conduction. The four faces of the square shape are each at different temperatures as

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