Questions and Answers of Fundamentals Thermal Fluid

Two infinitely long parallel plates of width w are located at w distance apart, as shown in Fig. P21€“95. The two plates behave as black surfaces, where surface 1 has a temperature of
Consider two rectangular surfaces perpendicular to each other with a common edge which is 1.6 m long. The horizontal surface is 0.8 m wide and the vertical surface is 1.2 m high. The horizontal
A furnace is shaped like a long equilateral-triangular duct where the width of each side is 2 m. Heat is supplied from the base surface, whose emissivity is ε1 = 0.8, at a rate of 800 W/m2 while the
Reconsider Prob. 21–97. Using an appropriate software, investigate the effects of the rate of the heat transfer at the base surface and the temperature of the side surfaces on the temperature of
Consider a long semicylindrical duct of diameter 1.0 m. Heat is supplied from the base surface, which is black, at a rate of 1200 W/m2, while the side surface with an emissivity of 0.4 is maintained
Consider a 20-cm-diameter hemispherical enclosure. The dome is maintained at 600 K and heat is supplied from the dome at a rate of 50 W while the base surface with an emissivity of 0.55 is maintained
Two very large parallel plates are maintained at uniform temperatures of T1 = 600 K and T2 = 400 K and have emissivities ε1 = 0.5 and ε2 = 0.9, respectively. Determine the net rate of radiation
Reconsider Prob. 21–101. Using an appropriate software, investigate the effects of the temperature and the emissivity of the hot plate on the net rate of radiation heat transfer between the plates.
Air is flowing between two infinitely large parallel plates. The upper plate is at 500 K and has an emissivity of 0.7, while the lower plate is a black surface with temperature at 330 K. If the air
Liquid nitrogen is stored in a spherical tank of 1m diameter, where tank surface is maintained uniformly at 80K. The spherical tank is encosed by a 1.6m diameter concentric sphere with a uniform
Two very long concentric cylinders of diameters D1 = 0.35 m and D2 = 0.5 m are maintained at uniform temperatures of T1 = 950 K and T2 = 500 K and have emissivities ε1 = 1 and ε2 = 0.55,
Two-phase gas-liquid oxygen is stored in a spherical tank of 1-m diameter, where it is maintained at its normal boiling point. The spherical tank is enclosed by a 1.6-m diameter concentric spherical
Two concentric spheres of diameters D1 = 0.3 m and D2 = 0.4 m are maintained at uniform temperatures T1 = 700 K and T2 = 500 K and have emissivities ε1 = 0.5 and ε2 = 0.7, respectively. Determine
A spherical tank of diameter D = 2 m that is filled with liquid nitrogen at 100 K is kept in an evacuated cubic enclosure whose sides are 3 m long. The emissivities of the spherical tank and the
Repeat Prob. 21€“108 by replacing the cubic enclosure by a spherical enclosure whose diameter is 3 m.Repeat Prob. 21€“108A spherical tank of diameter D = 2 m that is filled with
Reconsider Prob. 21€“108. Using an appropriate software, investigate the effects of the side length and the emissivity of the cubic enclosure, and the emissivity of the spherical tank on
A 9-ft-high room with a base area of 12 ft × 12 ft is to be heated by electric resistance heaters placed on the ceiling, which is maintained at a uniform temperature of 90°F at all times. The floor
Consider a 4-m × 4-m × 4-m cubical furnace whose floor and ceiling are black and whose side surfaces are reradiating. The floor and the ceiling of the furnace are maintained at temperatures of 550
Consider a circular grill whose diameter is 0.3 m. The bottom of the grill is covered with hot coal bricks at 950 K, while the wire mesh on top of the grill is covered with steaks initially at
Consider a 10-ft × 10-ft × 10-ft cubical furnace whose top and side surfaces closely approximate black surfaces and whose base surface has an emissivity ε = 0.7. The base, top, and side surfaces
Reconsider Prob. 21–114E. Using an appropriate software, investigate the effect of base surface emissivity on the net rates of radiation heat transfer between the base and the side surfaces,
A 1-m-diameter spherical cavity is maintained at a uniform temperature of 600 K. Now a 5-mm-diameter hole is drilled. Determine the maximum rate of radiation energy streaming through the hole. What
Daylight and incandescent light may be approximated as a blackbody at the effective surface temperatures of 5800 K and 2800 K, respectively. Determine the wavelength at maximum emission of radiation
Two parallel concentric disks, 20 cm and 40 cm in diameter, are separated by a distance of 10 cm. The smaller disk (ε = 0.80) is at a temperature of 300°C. The larger disk (ε = 0.60) is at a
The human skin is “selective” when it comes to the absorption of the solar radiation that strikes it perpendicularly. The skin absorbs only 50 percent of the incident radiation with wavelengths
The spectral emissivity of an opaque surface at 1500 K is approximated asDetermine the total emissivity and the emissive flux of thesurface. for λ6 μη =0 ε
The spectral absorptivity of an opaque surface is as shown on the graph. Determine the absorptivity of the surface for radiation emitted by a source at(a) 1000 K(b) 3000 K. 0.8 0.1 2, um 0.3 1.2
The surface in Prob. 21€“120 receives solar radiation at a rate of 470 W/m2. Determine the solar absorptivity of the surface and the rate of absorption of solar radiation.In ProbThe
The spectral transmissivity of a glass cover used in a solar collector is given asSolar radiation is incident at a rate of 950 W/m2, and the absorber plate, which can be considered to be black, is
Solar radiation is incident on the front surface of a thin plate with direct and diffuse components of 300 and 250 W/m2, respectively. The direct radiation makes a 30° angle with the normal of
A horizontal opaque flat plate is well insulated on the edges and the lower surface. The top surface has an area of 5 m2, and it experiences uniform irradiation at a rate of 5000 W. The plate absorbs
Consider two diffuse surfaces A1and A2oriented on a spherical surface as shown in the figure. Determine(a) The expression for the view factor F12 in terms of A2 and L,(b) The value of the view factor
Consider an enclosure consisting of eight surfaces. How many view factors does this geometry involve? How many of these view factors can be determined by the application of the reciprocity and the
Consider a cylindrical enclosure with A1, A2, and A3representing the internal base, top, and side surfaces, respectively. Using the length to diameter ratio, K = L/D, determine(a) The expression for
Two parallel back disks are positioned coaxially with a distance of 0.25 m apart. The lower disk is 0.2 m in diameter and the upper disk is 0.4 m in diameter. If the lower disk is heated electrically
A dryer is shaped like a long semicylindrical duct of diameter 1.5 m. The base of the dryer is occupied with water soaked materials to be dried, and maintained at a temperature of 370 K and
A large number of long tubes, each of diameter D, are placed parallel to each other and at a center-to-center distance of s. Since all of the tubes are geometrically similar and at the same
Consider the two parallel coaxial disks of diameters a and b, shown in Fig. P21€“132. For this geometry, the view factor from the smaller disk to the larger disk can be calculated
Two square plates, with the sides a and b (and b > a), are coaxial and parallel to each other, as shown in Fig. P21€“133, and they are separated by a center-to-center distance of L. The
A vertical 2-m-high and 5-m-wide double-pane window consists of two sheets of glass separated by a 3-cm-thick air gap. In order to reduce heat transfer through the window, the air space between the
A 2-m-internal-diameter double-walled spherical tank is used to store iced water at 0°C. Each wall is 0.5 cm thick, and the 1.5-cm-thick air space between the two walls of the tank is evacuated
Two concentric spheres of diameters D1 = 15 cm and D2 = 25 cm are separated by air at 1 atm pressure. The surface temperatures of the two spheres enclosing the air are T1 = 350 K and T2 = 275 K,
Consider a cubical furnace with a side length of 3 m. The top surface is maintained at 700 K. The base surface has an emissivity of 0.90 and is maintained at 950 K. The side surface is black and is
A furnace is of cylindrical shape with a diameter of 1.2 m and a length of 1.2 m. The top surface has an emissivity of 0.70 and is maintained at 500 K. The bottom surface has an emissivity of 0.50
Consider a thin 16-cm-long and 20-cm-wide horizontal plate suspended in air at 20°C. The plate is equipped with electric resistance heating elements with a rating of 20 W. Now the heater is
Repeat Prob. 20€“34 for an aluminum plate painted flat black (solar absorptivity 0.98 and emissivity 0.98) and also for a plate painted white (solar absorptivity 0.26 and emissivity 0.90).
A circular grill of diameter 0.25 m has an emissivity of 0.8. If the surface temperature is maintained at 150°C, determine the required electrical power when the room air and surroundings are at
A can of engine oil with a length of 150 mm and a diameter of 100 mm is placed vertically in the trunk of a car. In a hot summer day, the temperature in the trunk is 43°C. If the surface temperature
Flue gases from an incinerator are released to atmosphere using a stack that is 0.6 m in diameter and 10.0 m high. The outer surface of the stack is at 40°C and the surrounding air is at 10°C.
In a plant that manufactures canned aerosol paints, the cans are temperature-tested in water baths at 55°C before they are shipped to ensure that they withstand temperatures up to 55°C during
Reconsider Prob. 20€“39. In order to reduce the heating cost of the hot water, it is proposed to insulate the side and bottom surfaces of the container with 5-cm-thick fiberglass insulation
Consider a cylinder with a length of 15 cm and a diameter of 10 cm. The cylinder has a surface temperature of 43°C, while the room air temperature is 17°C. Determine whether placing the cylinder
An aluminum soda can of 150 mm in length and 60 mm in diameter is placed horizontally inside a refrigerator compartment that maintains a temperature of 4°C. If the surface temperature of the can is
Thermal energy generated by the electrical resistance of a 5-mm-diameter and 4-m-long bare cable is dissipated to the surrounding air at 20°C. The voltage drop and the electric current across the
A 10-m-long section of a 6-cm-diameter horizontal hot-water pipe passes through a large room whose temperature is 27°C. If the temperature and the emissivity of the outer surface of the pipe are
A 3-mm-diameter and 12-m-long electric wire is tightly wrapped with a 1.5-mm-thick plastic cover whose thermal conductivity and emissivity are k = 0.20 W/m·K and ε = 0.9. Electrical measurements
Hot water is being transported in a horizontal pipe (k = 0.15 W/m∙K, Di = 2.5 cm, Do = 4.5 cm), where the pipe inner surface temperature is at 100°C. A length of 2 m of the pipe outer surface is
Flat-plate solar collectors are often tilted up toward the sun in order to intercept a greater amount of direct solar radiation. The tilt angle from the horizontal also affects the rate of heat loss
A vertical 4-ft-high and 6-ft-wide double-pane window consists of two sheets of glass separated by a 1-in air gap at atmospheric pressure. If the glass surface temperatures across the air gap are
Consider a vertical plate with length L, placed in quiescent air. If the film temperature is 20°C and the average Nusselt number in natural convection is of the form Nu = CRanL, show that the
Repeat Prob. 20–28 assuming the circuit board to be positioned horizontally with (a) chips facing up and (b) chips facing down.Repeat Prob. 20–28A 50-cm × 50-cm circuit board that contains 121
Consider a 15-cm Ã— 20-cm printed circuit board (PCB) that has electronic components on one side. The board is placed in a room at 20°C. The heat loss from the back surface of the
Reconsider Prob. 20€“30. Using an appropriate software, investigate the effects of the room temperature and the emissivity of the board on the temperature of the hot surface of the board
A 50-cm × 50-cm circuit board that contains 121 square chips on one side is to be cooled by combined naturalconvection and radiation by mounting it on a vertical surface in a room at 25°C. Each
The side surfaces of a 3-m-high cubic industrial furnace burning natural gas are not insulated, and the temperature at the outer surface of this section is measured to be 110°C. The temperature
Reconsider Prob. 20–25E. Using an appropriate software, plot the rate of natural convection heat transfer for different orientations of the plate as a function of the plate temperature as the
Consider a 2-ft × 2-ft thin square plate in a room at 75°F. One side of the plate is maintained at a temperature of 130°F, while the other side is insulated. Determine the rate of heat transfer
Consider a 1.2-m-high and 2-m-wide glass window with a thickness of 6 mm, thermal conductivity k = 0.78 W/m·K, and emissivity Îµ = 0.9. The room and the walls that face the window
Reconsider Prob. 20€“22. Using an appropriate software, evaluate the effect of the uniform surface heat flux on the plate midpoint temperature for(a) The highly polished surface(b) The
A 0.5-m-long thin vertical copper plate is subjected to a uniform heat flux of 1000 W/m2on one side, while the other side is exposed to air at 5°C. Determine the plate midpoint temperature for(a)
A 0.5-m-long thin vertical plate is subjected to a uniform heat flux of 1200 W/m2 on one side, while the other side is exposed to hydrogen gas at 5°C. Assuming that the properties of the hydrogen
A 0.5-m-long thin vertical plate is subjected to uniform heat flux on one side, while the other side is exposed to cool air at 5°C. The plate surface has an emissivity of 0.73, and its midpoint
A long 2-in-diameter rod with surface temperature of 200°F is submerged in a bath of fluid. Determine the Grashof and Rayleigh numbers if the fluid is(a) Liquid water at 40°F,(b) Liquid ammonia at
In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why?
What is natural convection? How does it differ from forced convection? What force causes natural convection currents?
A 300-W cylindrical resistance heater is 0.75 m long and 0.5 cm in diameter. The resistance wire is placed horizontally in a fluid at 20°C. Determine the outer surface temperature of the resistance
Thick fluids such as asphalt and waxes and the pipes in which they flow are often heated in order to reduce the viscosity of the fluids and thus to reduce the pumping costs. Consider the flow of such
Reconsider Prob. 20€“47. To reduce the heating cost of the pipe, it is proposed to insulate it with sufficiently thick fiberglass insulation (k = 0.035 W/m·K) wrapped with aluminum
During a visit to a plastic sheeting plant, it was observed that a 60-m-long section of a 2-in nominal (6.03-cm-outer-diameter) steam pipe was extended from one end of the plant to the other with no
Reconsider Prob. 20€“50. Using an appropriate software, investigate the effect of the surface temperature of the steam pipe on the rate of heat loss from the pipe and the annual cost of
Reconsider Prob. 20€“50. In order to reduce heat losses, it is proposed to insulate the steam pipe with 5-cmthick fiberglass insulation (k = 0.038 W/m·K) and to wrap it with aluminum
A 1.5-m-diameter, 4-m-long cylindrical propane tank is initially filled with liquid propane, whose density is 581 kg/m3. The tank is exposed to the ambient air at 25°C in calm weather. The outer
Hot engine oil is being transported in a horizontal pipe (k = 15 W/m∙K, Di = 5 cm) with a wall thickness of 5 mm. The pipe is covered with a 5-mm-thick layer of insulation (k = 0.15 W/m∙K). A
Reconsider Prob. 20–55. Using an appropriate software, evaluate the effect of the insulation layer thickness on the outer surface temperature. By varying the insulation layer thickness from 5 to 15
A hot fluid (kfluid = 0.72 W/m∙K) is flowing as a laminar fully-developed flow inside a pipe with an inner diameter of 35 mm and a wall thickness of 5 mm. The pipe is 10 m long and the outer
A hot liquid (cp = 1000 J/kg∙K) flows at a flow rate of 0.05 kg/s inside a copper pipe with an inner diameter of 45 mm and a wall thickness of 5 mm. At the pipe exit, the liquid temperature
An average person generates heat at a rate of 240 Btu/h while resting in a room at 70°F. Assuming onequarter of this heat is lost from the head and taking the emissivity of the skin to be 0.9,
An incandescent lightbulb is an inexpensive but highly inefficient device that converts electrical energy into light. It converts about 10 percent of the electrical energy it consumes into light
The water in a 40-L tank is to be heated from 15°C to 45°C by a 6-cm-diameter spherical heater whose surface temperature is maintained at 85°C. Determine how long the heater should be kept on.
A 2-m-diameter thin-walled stainless steel spherical tank is filled with chemicals undergoing a reaction. The reaction releases heat through the tank, where the tank outer surface temperature is
A hot liquid is filled in a spherical tank with an inner diameter of 3 m and a wall thickness of 3 cm. The tank wall is made of a material with a thermal conductivity of 0.15 W/m∙K. The hot liquid
The upper and lower compartments of a well-insulated container are separated by two parallel sheets of glass with an air space between them. One of the compartments is to be filled with a hot fluid
Someone claims that the air space in a double-pane window enhances the heat transfer from a house because of the natural convection currents that occur in the air space and recommends that the
Consider a double-pane window consisting of two glass sheets separated by a 1-cm-wide air space. Someone suggests inserting a thin vinyl sheet in the middle of the two glasses to form two 0.5-cm-wide
What does the effective conductivity of an enclosure represent? How is the ratio of the effective conductivity to thermal conductivity related to the Nusselt number?
Show that the thermal resistance of a rectangular enclosure can be expressed as R = Lc /(Ak Nu), where k is the thermal conductivity of the fluid in the enclosure.
Consider a 3-m-high rectangular enclosure consisting of two surfaces separated by a 0.1-m air gap at 1 atm. If the surface temperatures across the air gap are 30°C and €“10°C,
A vertical 1.5-m-high and 3.0-m-wide enclosure consists of two surfaces separated by a 0.4-m air gap at atmospheric pressure. If the surface temperatures across the air gap are measured to be 280 K
A vertical 1.5-m-high, 2.8-m-wide double-pane window consists of two layers of glass separated by a 2.0-cm air gap at atmospheric pressure. The room temperature is 26°C while the inner glass
Reconsider Prob. 20€“73E. Using an appropriate software, investigate the effect of the air gap thickness on the rates of heat transfer by natural convection and radiation, and the R-value

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