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physics
thermodynamics

Questions and Answers of Thermodynamics

Rework Problem 3-64 with the surface marked at a constant 100ºC now absorbing a constant heat flux of 500 W/m2. Add nodes as necessary.Problem 3-64The two-dimensional solid shown in Figure P3-64
The tapered aluminum pin fin shown in Figure P3-72 is circular in cross section with a base diameter of 1 cm and a tip diameter of 0.5 cm. The base is maintained at 200ºC and loses heat by
Write the nodal equations 1 through 7 for the symmetrical solid shown in Figure P3-73. ˆ†x = ˆ†y = 1 cm.Figure P3-73
Obtain the temperature for nodes 1 through 6 shown in Figure P3-74. ˆ†x = ˆ†y = 1 cm.
Write the nodal equations for nodes 1 through 9 shown in Figure P3-75.ˆ†x = ˆ†y = 1 cm.
Write the nodal equation for nodes 1 through 12 shown in Figure P3-76. Express the equations in a format for Gauss-Seidel iteration.
Sometimes a square grid is desired even for a circular system. Consider the quadrant of a circle shown in Figure P3-77 with r = 10 cm. ˆ†x = ˆ†y = 3 cm and k = 10W/m·
A furnace of 70- by 60- by 90-cm inside dimensions is constructed of a material having a thermal conductivity of 0.5 Btu/h · ft · ºF. The wall thickness is 6 in. The inner and outer surface
The slanted intersection shown in Figure P3-81 involves materials A and B. Write steady state nodal equations for nodes 3, 4, 5, and 6 using Table 3-2(f and g) as a guide.
A horizontal plate, 25 by 50 cm, is maintained at a constant temperature of 78ºC and buried in a semi-infinite medium at a depth of 5 m. The medium has an isothermal surface maintained at 15ºC and
A cube 20 cm on a side is maintained at 80ºC and buried in a large medium at 10ºC with a thermal conductivity of 2.3 W/m· ºC. Calculate the heat lost by the cube. How does this compare with the
A long horizontal cylinder having a diameter of 10 cm is maintained at a temperature of 100ºC and centered in a 30-cm-thick slab of material for which k = W/m· ºC. The outside of the slab is at
A horizontal plate 20 by 150 cm is buried in a large medium at a depth of 2.0 m and maintained at 50ºC. The surface of the medium is at 10ºC and has k = 1.5W/m· ºC. Calculate the heat lost by the
A thin disk 10 cm in diameter is maintained at 75ºC and placed on the surface of a large medium at 15ºC with k = 3 W/m· ºC. Calculate the heat conducted into the medium.
Repeat Problem 3-87 for a square 10 cm on a side. Compare the heat transfers on a per unit area basis. Problem 3-87 A thin disk 10 cm in diameter is maintained at 75ºC and placed on the surface of a
A hot steam pipe 10 cm in diameter is maintained at 200ºC and centered in a square mineral-fiber insulation 20 cm on a side. The outside surface temperature of the insulation is 35ºC. Calculate the
A cube 35 cm on each external side is constructed of fireclay brick. The wall thickness is 5.0 cm. The inner surface temperature is 500ºC, and the outer surface temperature is 80ºC. Compute the
A pipe having a diameter of 10 cm passes through the center of a concrete slab having a thickness of 70 cm. The surface temperature of the pipe is maintained at 100ºC by condensing steam while the
Consider a circumferential fin of rectangular profile as shown in Figure 2-12. Set up nodal equations for a fin of thickness t, heat transfer coefficient h, thermal conductivity k, and heat
Set up a nodal equation for the geometry of Problem 2-123, using increments in the height of the truncated cone as the one-dimensional variable. Then work the problem with the numerical method and
Set up nodal equations for the geometry of Problem 2-122, using increments in an angle θ as the one-dimensional variable. Then work the problem using the numerical method and compare with the
A cube 30 cm on a side is buried in an infinite medium with a thermal conductivity of 1.8 W/m· ºC. The surface temperature of the cube is 30ºC while the temperature of the medium is 10ºC.
A thin horizontal disk having a diameter of 15 cm is maintained at a constant surface temperature of 87ºC and buried at a depth of 20 cm in a semi-infinite medium with an adiabatic surface. The
A copper rod has an internal heater that maintains its surface temperature at 50ºC while it is buried vertically in a semi-infinite medium. The rod is 2 cm in diameter and 40 cm long and the
Rework Problem 2-122, using a numerical approach with five nodes operating in increments of the radial angle Î¸, and compare with the analytical results of Problem 2-122.Problem 2-122The
A basement for a certain home is 4 × 5 m with a ceiling height of 3 m. The walls are concrete having a thickness of 10 cm. In the winter the convection coefficient on the inside is 10 W/m2 ∙ ºC
A copper sphere initially at a uniform temperature T0 is immersed in a fluid. Electric heaters are placed in the fluid and controlled so that the temperature of the fluid follows a periodic variation
A stainless-steel rod (18% Cr, 8% Ni) 6.4 mm in diameter is initially at a uniform temperature of 25ºC and is suddenly immersed in a liquid at 150ºC with h = 120 W/m2·ºC. Using the
The plate in Problem 3-63 is initially uniform in temperature at 100ºC and suddenly exposed to the convection boundary. Select a value for ∆τ and calculate the nodal temperatures after 10 time
The solid shown in Problem 3-64 is initially uniform in temperature at 100ºC and suddenly exposed to the convection boundary and heat generation while the right face is kept at 100ºC. Select a
A steel rod 12.5 mm in diameter and 20 cm long has one end attached to a heat reservoir at 250ºC. The bar is initially maintained at this temperature throughout. It is then subjected to an airstream
The two-dimensional body of Figure 3-6 has the initial surface and internal temperatures as calculated. At time zero the 500ºC face is suddenly lowered to 30ºC. Taking ∆x = ∆y = 15 cm and α =
A 5-cm-diameter copper sphere is initially at a uniform temperature of 200ºC. It is suddenly exposed to an environment at 20ºC having a heat-transfer coefficient h = 28W/m2·ºC. Using the
A fireproof safe is constructed of loosely packed asbestos contained between thin sheets of stainless steel. The safe is built in the form of a cube with inside and outside dimensions of 0.5 and 1.0
A large slab of brick [k = 1.07W/m · ºC, α = 5.4 × 10−7m2/s] is initially at a uniform temperature of 20ºC. One surface is suddenly exposed to a uniform heat flux of 4500 W/m2. Calculate and
A granite sphere having a diameter of 15 cm and initially at a uniform temperature of 120ºC is suddenly exposed to a convection environment with h = 350 W/m2 · ºC and T = 30ºC. Calculate the
The solid of Problem 3-74 is initially uniform in temperature at 100ºC, but suddenly the two surfaces are lowered to 0 and 40ºC. If the solid has k = 20 W/m·ºC and α = 5 × 10−6 m2/s, find the
A copper sphere having a diameter of 3.0 cm is initially at a uniform temperature of 50ºC. It is suddenly exposed to an airstream of 10ºC with h = 15 W/m2·ºC. How long does it take the sphere
Apply the lumped-capacity criterion of Equation (4-6) [h(V/A)/k < 0.1] to each of the geometries treated with the Heisler charts. Approximately what percent error would result for each geometry in
Because of symmetry, the temperature gradient ∂T/∂x at the centerline of an infinite plate will be zero when both sides are subjected to the same boundary condition in a cooling process. This may
Rework Problem 4-135 for the surface temperature suddenly lowered to 25ºC. This is equivalent to h→∞. Problem 4-135
Rework Problem 4-135, assuming the plate behaves as a lumped capacity. Problem 4-135
Rework Problem 4-135, assuming the aluminum plate behaves as a semi-infinite solid with the desired temperature occurring at x = 5 cm. Perform the same kind of calculation for Problem 4-136. Problem
A concrete driveway having a thickness of 18 cm attains an essentially uniform temperature of 30ºC on a warm November day in Texas. A "blue norther" arrives, which suddenly subjects the driveway to
An aluminum sphere, 5.0 cm in diameter, is initially at a uniform temperature of 50ºC. It is suddenly exposed to an outer-space radiation environment at 0 K (no convection). Assuming the surface of
A 5-lb roast initially at 70ºF is placed in an oven at 350ºF. Assuming that the heat-transfer coefficient is 2.5 Btu/h · ft2 · ºF and that the thermal properties of the roast may be approximated
Oranges with a diameter of about 3 in are to be cooled from room temperature of 25ºC to 3ºC using an air-convection environment with h = 45 W/m2 · ºC and T∞ = 0ºC. Assuming that the oranges
A cold-storage building 16 × 35 m is built on a concrete slab having a thickness of 15 cm, which is placed on a suitable insulating material in contact with the ground. During the start-up period
A 2.0-mm-thick sheet of polyethylene covers a 10-cm-thick slab of high-density particle board that is perfectly insulated on the back side. The assembly is initially uniform in temperature at 20ºC.
An aluminum can having a volume of about 350 cm3 contains beer at 1ºC. Using a lumped-capacity analysis, estimate the time required for the contents to warm to 15ºC when the can is placed in a room
Free convection in air at atmospheric pressure is found to experience a convection heat-transfer coefficient that varies as h = A(∆T)n, where ∆T is the temperature difference between the surface
A 12-mm-diameter aluminum sphere is heated to a uniform temperature of 400ºC and then suddenly subjected to room air at 20ºC with a convection heat-transfer coefficient of 10 W/m2·ºC. Calculate
A 4-cm-diameter copper sphere is initially at a uniform temperature of 200ºC. It is suddenly exposed to a convection environment at 30ºC with h = 20 W/m2·ºC. Calculate the time necessary for the
When a sine-wave temperature distribution is impressed on the surface of a semi-infinite solid, the temperature distribution in the solid is given bywhere Tx,Ï„ = temperature at depth x and
Using the temperature distribution of Problem 4-18, show that the time lag between maximum points in the temperature wave at the surface and at a depth x is given byProblem 4-18 When a sine-wave
An infinite plate having a thickness of 2.5 cm is initially at a temperature of 150ºC, and the surface temperature is suddenly lowered to 30ºC. The thermal diffusivity of the material is 1.8 ×
A thick concrete wall having a uniform temperature of 54ºC is suddenly subjected to an airstream at 10ºC. The heat-transfer coefficient is 10 W/m2·ºC. Calculate the temperature in the concrete
A very large slab of copper is initially at a temperature of 300ºC. The surface temperature is suddenly lowered to 35ºC. What is the temperature at a depth of 7.5 cm 4 min after the surface
On a hot summer day a concrete driveway may reach a temperature of 50ºC. Suppose that a stream of water is directed on the driveway so that the surface temperature is suddenly lowered to 10ºC. How
A semi-infinite slab of copper is exposed to a constant heat flux at the surface of 0.5 MW/m2. Assume that the slab is in a vacuum, so that there is no convection at the surface. What is the surface
A large slab of copper is initially at a uniform temperature of 90ºC. Its surface temperature is suddenly lowered to 30ºC. Calculate the heat-transfer rate through a plane 7.5 cm from the surface
A large slab of aluminum at a uniform temperature of 30ºC is suddenly exposed to a constant surface heat flux of 15 kW/m2. What is the temperature at a depth of 2.5 cm after 2 min?
What error would result from using the first four terms of Equation (4-3) to compute the temperature at τ = 0 and x = L?
An aluminum sphere having a diameter of 5.6 cm is initially at a uniform temperature of 355ºC and is suddenly exposed to a convection environment at T = 23ºC with a convection heat transfer
A large thick layer of ice is initially at a uniform temperature of −20ºC. If the surface temperature is suddenly raised to −1ºC, calculate the time required for the temperature at a depth of
A large slab of concrete (stone 1-2-4 mix) is suddenly exposed to a constant radiant heat flux of 900W/m2. The slab is initially uniform in temperature at 20ºC. Calculate the temperature at a depth
A very thick plate of stainless steel (18% Cr, 8% Ni) at a uniform temperature of 300ºC has its surface temperature suddenly lowered to 100ºC. Calculate the time required for the temperature at a
A large slab has properties of common building brick and is heated to a uniform temperature of 40ºC. The surface is suddenly exposed to a convection environment at 2ºC with h = 25 W/m2 · ºC.
A large block having the properties of chrome brick at 200ºC is at a uniform temperature of 30ºC when it is suddenly exposed to a surface heat flux of 3 × 104 W/m2. Calculate the temperature at a
A slab of copper having a thickness of 3.0 cm is initially at 300ºC. It is suddenly exposed to a convection environment on the top surface at 80ºC while the bottom surface is insulated. In 6 min
A large slab of aluminum has a thickness of 10 cm and is initially uniform in temperature at 400ºC. Suddenly it is exposed to a convection environment at 90ºC with h = 1400 W/m2 · ºC. How long
A horizontal copper plate 10 cm thick is initially uniform in temperature at 250ºC. The bottom surface of the plate is insulated. The top surface is suddenly exposed to a fluid stream at 80ºC.
A large slab of aluminum has a thickness of 10 cm and is initially uniform in temperature at 400ºC. It is then suddenly exposed to a convection environment at 90ºC with h = 1400 W/m2 · ºC. How
A plate of stainless steel (18% Cr, 8% Ni) has a thickness of 3.0 cm and is initially uniform in temperature at 500ºC. The plate is suddenly exposed to a convection environment on both sides at
A steel cylinder 10 cm in diameter and 10 cm long is initially at 300ºC. It is suddenly immersed in an oil bath that is maintained at 40ºC, with h = 280 W/m2 · ºC. Find (a) the temperature at the
Derive an expression for the heat flux per unit area at depth x and time τ when a semi-infinite solid is suddenly exposed to an instantaneous energy pulse at the surface of strength Q0/A.
Buildings of various constructions exhibit different responses to thermal changes in climate conditions. Consider a 10-cm-thick wall of normal weight structural concrete (c = 0.9 kJ/kg · ºC)
A semi-infinite solid of aluminum is coated with a special chemical material that reacts suddenly to ultraviolet radiation and releases energy in the amount of 1.0 MJ/m2. If the solid is initially
A semi-infinite solid of stainless steel (18% Cr, 8% Ni) is initially at a uniform temperature of 0ºC. The surface is pulsed with a laser with 10 MJ/m2 instantaneous energy. Calculate the
What strength pulse would be necessary to produce the same temperature effect at a depth of 1.2 cm as that experienced at a depth of 1.0 cm?
A semi-infinite solid of aluminum is to be pulsed with a laser at the surface such that a temperature of 600ºC will be attained at a depth of 2 mm, 0.2 s after the pulse. The solid is initially at
A slab of polycrystalline aluminum oxide is to be pulsed with a laser to produce a temperature of 900ºC at a depth of 0.2 mm after a time of 0.2 s. The solid is initially at 40ºC. Calculate the
A 20 by 20 cm slab of copper 5 cm thick at a uniform temperature of 260ºC suddenly has its surface temperature lowered to 35ºC. Using the concepts of thermal resistance and capacitance and the
Repeat Problem 4-49 for window glass. Problem 4-49 A slab of polycrystalline aluminum oxide is to be pulsed with a laser to produce a temperature of 900ºC at a depth of 0.2 mm after a time of 0.2 s.
An aluminum bar has a diameter of 11 cm and is initially uniform in temperature at 300ºC. If it is suddenly exposed to a convection environment at 50ºC with h = 1200 W/m2 · ºC, how long does it
A fused-quartz sphere has a thermal diffusivity of 9.5 × 10−7 m2/s, a diameter of 2.5 cm, and a thermal conductivity of 1.52 W/m· ºC. The sphere is initially at a uniform temperature of 25ºC
Lead shot may be manufactured by dropping molten-lead droplets into water. Assuming that the droplets have the properties of solid lead at 300ºC, calculate the time for the center temperature to
A steel sphere 10 cm in diameter is suddenly immersed in a tank of oil at 10ºC. The initial temperature of the sphere is 220ºC; h = 5000 W/m2 · ºC. How long will it take the center of the sphere
A boy decides to place his glass marbles in an oven at 200ºC. The diameter of the marbles is 15 mm. After a while he takes them from the oven and places them in room air at 20ºC to cool. The
A lead sphere with d = 1.5 mm and initial temperature of 200ºC is suddenly exposed to a convection environment at 100ºC and h = 5000 W/m2 · ºC. Calculate the time for the center temperature to
A long steel bar 5 by 10 cm is initially maintained at a uniform temperature of 250ºC. It is suddenly subjected to a change such that the environment temperature is lowered to 35ºC. Assuming a
A steel bar 2.5 cm square and 7.5 cm long is initially at a temperature of 250ºC. It is immersed in a tank of oil maintained at 30ºC. The heat-transfer coefficient is 570 W/m2 · ºC. Calculate the
A cube of aluminum 10 cm on each side is initially at a temperature of 300ºC and is immersed in a fluid at 100ºC. The heat-transfer coefficient is 900 W/m2 · ºC. Calculate the temperature at the
A piece of aluminum weighing 6 kg and initially at a temperature of 300ºC is suddenly immersed in a fluid at 20ºC. The convection heat-transfer coefficient is 58W/m2 · ºC. Taking the aluminum as
A short concrete cylinder 15 cm in diameter and 30 cm long is initially at 25ºC. It is allowed to cool in an atmospheric environment in which the temperature is 0ºC. Calculate the time required for
Assume that node m in Problem 3-39 occurs along a circular rod having a diameter of 2 cm with ∆x = 1 cm. The material is glass with k = 0.8 W/m· ºC, ρ = 2700 kg/m3, c = 0.84 kJ/kg · ºC. The
A 4.0-cm cube of aluminum is initially at 450ºC and is suddenly exposed to a convection environment at 100ºC with h = 120 W/m2 · ºC. How long does it take the cube to cool to 250ºC?
A cube of aluminum 11 cm on each side is initially at a temperature of 400ºC. It is suddenly immersed in a tank of oil maintained at 85ºC. The convection coefficient is 1100 W/m2 · ºC. Calculate
An aluminum cube 5 cm on a side is initially at a uniform temperature of 100ºC and is suddenly exposed to room air at 25ºC. The convection heat-transfer coefficient is 20 W/m2 · ºC. Calculate the
A stainless steel cylinder (18% Cr, 8% Ni) is heated to a uniform temperature of 200ºC and then allowed to cool in an environment where the air temperature is maintained constant at 30ºC. The

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