Question: An electric furnace is to be used
An electric furnace is to be used for batch heating a certain material with a specific heat of 670 J/kg K from 20°C to 760°C. The material is placed on the furnace floor, which is 2 m * 4 m in area as shown in the accompanying sketch. The side walls of the furnace are made of a refractory material. A grid of round resistor rods is installed parallel to the plane of the roof but several inches below it. The resistors are 13 ïm in diameter and are spaced 5 cm center-to-center. The resistor temperature is to be maintained at 1100°C; under these conditions the emissivity of the resistor surface is 0.6. If the top surface of the stock is assumed to have an emissivity of 0.9, estimate the time required for heating a 6-metric-ton batch. External heat losses from the furnace can be neglected, the temperature gradient through the stock can be considered negligibly small, and steady-state conditions can be assumed.
> A small dam, which is 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 of constant strength of 100 W/m3. If both dam surfaces are
> The rate of heat flow per unit length q/L through a hollow cylinder of inside radius ri and outside radius ro is where /Determine the per- cent error in the rate of heat flow if the arithmetic mean area / is used instead of the logarithmic mean area / ra
> Estimate the rate of heat loss per unit length from a 5-cm ID, 6-cm OD steel pipe covered with high- temperature insulation having a thermal conductivity of 0.11 W/(m K) and a thickness of 1.2 cm. Steam flows in the pipe. It has a quality of 99% and is a
> Steam having a quality of 98% at a pressure of 1.37 3 105 N/m2 is flowing at a velocity of 1 m/s through a steel pipe of 2.7-cm OD and 2.1-cm ID. The heat transfer coefficient at the inner surface, where condensation occurs, is 567 W/m2 K. A dirt
> A solution with a boiling point of 828C boils on the outside of a 2.5-cm tube with a No. 14 BWG gauge wall. On the inside of the tube flows saturated steam at 420 kPa (abs). The convection heat transfer coefficients are 8.5 kW/(m2 K) on the steam side an
> Heat is transferred at a rate of 0.1 kW through glass wool insulation (density 5 100 kg/m3) with a 5-cm thickness and 2-m2 area. If the hot surface is at 70°C, determine the temperature of the cooler surface.
> Suppose that a pipe carrying a hot fluid with an external temperature of Ti and outer radius ri is to be insulated with an insulation material of thermal conductivity k and outer radius ro. Show that if the convection heat transfer coefficient on the out
> Calculate the rate of heat loss per foot and the thermal resistance for a 15-cm schedule 40 steel pipe covered with a 7.5-cm-thick layer of 85% magnesia. Superheated steam at 150oC flows inside the pipe / and still air at 168C is on the outside /
> The heat conduction equation in cylindrical coordinates is (a) Simplify this equation by eliminating terms equal to zero for the case of steady-state heat flow without sources or sinks around a right-angle corner such as the one in the accompanying sket
> Exhaust gases from a power plant are used to pre- heat air in a cross-flow heat exchanger. The exhaust gases enter the heat exchanger at 450°C and leave at 200°C. The air enters the heat exchanger at 70°C, leaves at 250&A
> Nomads in the desert make ice by exposing a thin water layer to cold air during the night. This icing or freezing of thin layers of water is often also referred to as ice making by nocturnal (or night time) cooling, where the surface temperature of water
> For the design of a novel type of nuclear power plant, it is necessary to determine the temperature distribution in a large slab-type nuclear fuel element. Volumetric heat is generated uniformly in the fuel element at the rate of 2 * 107 W/m3. This slab
> The conversion of solar energy into electric power by means of photovoltaic panels will be an important part of the transition from fossil fuels to sustainable energy sources. As described in detail in Principles of Sustainable Energy [14], a typical PV
> 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 908C. The convection heat transfer coefficient between the wall and the environment is 50
> Discuss the modes of heat transfer that determine the equilibrium temperature of the space shuttle Endeavour when it is in orbit. What happens when it reenters the earth’s atmosphere?
> A person wearing a heavy parka is standing in a cold wind. Describe the modes of heat transfer determining heat loss from the person’s body.
> Describe and compare the modes of heat loss through the single-pane and double-pane window assemblies shown in the sketch below.
> With increasing emphasis on energy conservation, the heat loss from buildings has become a major concern. The typical exterior surface areas and R-factors (area 3 thermal resistance) for a small tract house are listed below: (a) Calculate the rate of hea
> Consider the cooling of (a) a personal computer with a separate CPU and (b) a laptop computer. The reliable functioning of these machines depends on their effective cooling. Identify and briefly explain all modes of heat transfer involved in the cool
> What are the important modes of heat transfer for a person sitting quietly in a room? What if the person is sitting near a roaring fireplace?
> Water is heated by hot air in a heat exchanger. The flow rate of the water is 12 kg/s and that of the air is 2 kg/s. The water enters at 40°C, and the air enters at 460°C. The overall heat transfer coefficient of the heat exchanger is 275 W/m2 K based o
> Explain each in your own words. (a) What is the mode of heat transfer through a large steel plate that has its surfaces at specified temperatures? (b) What are the modes when the temperature on one surface of the steel plate is not specified, but the s
> Explain a fundamental characteristic that differentiates conduction from convection and radiation.
> Referring to Problem 1.74, how many kilograms of ice can a 3-ton refrigeration unit produce in a 24-h period? The heat of fusion of water is 330 kJ/kg.
> A manufacturer in the United States wants to sell a refrigeration system to a customer in Germany. The standard measure of refrigeration capacity used in the United States is the ton (T); a 1 T capacity means that the unit is capable of making abou
> Estimate the R-values for a 5-cm-thick fiberglass board and a 2.5-cm-thick polyurethane foam layer. Then, compare their respective conductivity- times-density products if the density for fiberglass is 50 kg/m3 and the density of polyurethane is 30 kg/m
> An ice chest (see sketch) is to be constructed from styro foam 1 k 5 0.033 W/m K 2 . If the wall of the chest is 5-cm thick, calculate its R-value in (m2 K)/(W cm).
> The thermal conductivity of silver at 212°F is 238 Btu/h ft °F. What is the conductivity in SI units?
> The thermal conductivity of fiberglass insulation at 68°F is 0.02 Btu/h ft °F. What is its value in SI units?
> A cooling system is to be designed for a food storage warehouse for keeping perishable foods cool prior to transportation to grocery stores. The warehouse has an effective surface area of 1860 m2 exposed to an ambient air temperature of 32°C. The warehou
> The heat transfer coefficient between a surface and a liquid is 57 W/ ( m2 K ) . How many watts per square meter will be transferred in this system if the temperature difference is 10°C?
> In a heat exchanger, as shown in the accompanying figure, air flows over brass tubes of 1.8-cm 1D and 2.1-cm OD containing steam. The convection heat transfer coefficients on the air and steam sides of the tubes are 70 W/m2 K and 210 W/m2 K, respectively
> In Problem 1.67, the heat loss from the hairdryer duct enclosure was neglected. To a designer, while this may appear to be a reasonable assumption, it should really be checked by order-of-magnitude calculations even if all the parameters are not known. I
> In beauty salons and in homes, a ubiquitous device is the hairdryer. The front end of a typical hairdryer is idealized as a thin-walled cylindrical duct with a 6-cm diameter with a fan at the inlet that blows air over an electric heating coil as schemati
> At the present time, radioactive waste from nuclear power plants is placed in long, thin-walled cylindrical containers that are submerged in a water bath for cooling. The radioactive waste generates heat non-uniformly across the radial direction
> Many specialized applications (ranging from advanced gas-turbine blades to medical devices and implants) require metal components that are coated with a protective material layer. In a manufacturing plant for such coatings, an infrared lamp is used for c
> Determine the ratio of the total hemispherical emissivity to the normal emissivity for a nondiffuse sur- face if the intensity of emission varies as the cosine of the angle measured from the normal.
> By substituting / and performing the integration over the entire spectrum, derive a relationship between and constants C1 and C2 in Eq. (11.1).
> A flat plate is in a solar orbit 150,000,000 km from the sun. It is always oriented normal to the rays of the sun, and both sides of the plate have a finish that has a spectral absorptivity of 0.95 at wavelengths shorter than 3 mm and 0.06 at wavelengt
> Two infinitely large, black, plane surfaces are 0.3 m apart, and the space between them is filled by an isothermal gas mixture at 811 K and atmospheric pressure. The gas mixture consists of 25% CO2, 25% H2O, and 50% N2 by volume. If one of the surfaces i
> A 0.61-m-radius hemisphere (811 K in surface temperature) is filled with a gas mixture containing 6.67% CO2 and water vapor at 0.5% relative humidity at 533 K and 2 atm pressure. Determine the emissivity and absorptivity of the gas and the net rate of ra
> A small sphere (2.5 cm in diameter) is placed in a heating oven. The oven cavity is a 30 cm cube filled with air at 101 kPa (abs); it contains 3% water vapor at 810 K, and its walls are at 1370 K. The emissivity of the sphere is equal to 0.44 – 0.00018 T
> Prepare a graph showing the effect of subcooling between 0oC and 50oC on the maximum heat flux calculated in Problem 9.8.
> A 10-cm-square, electrically-heated plate is placed in a horizontal position 5 cm below a second plate of the same size, as shown schematically. The heating surface is gray (emissivity = 0.8) , while the receiver has a black surface. The lower plate is h
> A spherical satellite circling the sun is to be maintained at a temperature of 25°C. The satellite rotates continuously and is partly covered with solar cells having a gray surface with an absorptivity of 0.1. The rest of the sphere is to be covered by a
> A 2.5-cm-diameter cylindrical-refractory crucible for melting lead is to be built for thermocouple calibration. An electrical heater immersed in the metal is shut off at some temperature above the melting point. The fusion-cooling curve is obtained by ob
> Mercury is to be evaporated at 317°C in a furnace. The mercury flows through a 25.4-m BWG no. 18 gauge 304 stainless-steel tube that is placed in the center of the furnace. The furnace cross section perpendicular to the tube axis is a square 20
> The interior wall of a large, commercial walk-in type meat freezer is covered under normal operating conditions with a 2-cm thick layer of ice. One day, a power outage cuts electricity to the refrigeration system of the freezer. Estimate the time require
> A rectangular, flat water tank is placed on the roof of a house with its lower portion perfectly insulated. A sheet of glass, whose transmission characteristics are tabulated here, is placed 1 cm above the water surface. Assuming that the average inciden
> A large body of nonluminous gas at a temperature of 1100°C has emission bands between 2.5 and 3.5 m and between 5 and 8 m. At 1100°C the effective emissivity in the first band is 0.8 and in the second 0.6. Determine the emissive power of this gas in W/
> A hydrogen bomb is approximated by a fireball at a temperature of 7200 K, according to a report published in 1950 by the Atomic Energy Commission. (a) Calculate the total rate of radiant-energy emission in watts, assuming that the gas radiates as a black
> Forty five kilograms of carbon dioxide is stored in a high-pressure cylinder that is 25 cm in diameter (OD), 1.2 m long, and 1.2 cm thick. The cylinder is fitted with a safety rupture diaphragm designed to fail at 14 MPa (with the specified charge, this
> Determine the power requirement of a soldering iron in which the tip is maintained at 400°C. The tip is a cylinder 3 mm in diameter and 10 mm long. The surrounding air temperature is 20°C, and the average convection heat transfer co
> In a manufacturing process, a fluid is transported through a cellar maintained at a temperature of 300 K. The fluid is contained in a pipe having an external diameter of 0.4 m. The pipe surface has an emissivity of 0.5. To reduce heat losses, the pipe is
> A 60-cm-square section of panel heater is installed in the corner of the ceiling of a room having a 2.7-m * 3.6-m floor area with an 2.4-m ceiling. If the surface of the heater, made from oxidized iron, is at 147°C and the walls and the air of the room
> A metal plate is placed in the sunlight. The incident radiant energy G is 780 W/m2. The air and the surroundings are at 10°C. The heat transfer coefficient by natural convection from the upper surface of the plate is 17 W/m2 K. The plate has an average e
> A thermocouple is used to measure the temperature of a flame in a combustion chamber. If the thermocouple temperature is 1033 K and the walls of the chamber are at 700 K, what is the error in the thermocouple reading due to radiation to the walls? Assume
> Repeat Problem 11.52 with the addition of a radiation shield with emissivity /
> Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Tec
> Calculate the equilibrium temperature of a thermo- couple in a large air duct (see the figure) if the air temperature is 1367 K, the duct-wall temperature is 533 K, the emissivity of the thermocouple is 0.5, and the convection heat transfer coefficient,
> A 6-mm-thick sheet of polished 304 stainless steel is suspended in a comparatively large vacuum-drying oven with black walls. The dimensions of the sheet are 30 cm * 30 cm, and its specific heat is 565 J/kg K. If the walls of the oven are uniformly at 15
> An 0.2-m-OD oxidized steel pipe at a surface temperature of 756 K passes through a large room in which the air and the walls are at 38°C. If the heat transfer coefficient by convection from the surface of the pipe to the air in the room is 28 W/m2 K, est
> Compute the average emissivity of anodized aluminum at 100°C and 650°C from the spectral curve in Fig. 11.17. Assume /
> For establishing an experimental station that carries out mineral prospecting on the Moon and also houses periodic human visits for space-based explorations, a cooling (or thermal management) system is to be designed for the high-powered electronic sys
> Liquid nitrogen is stored in a dewar (see the sketch) made of two concentric spheres with the space between them evacuated. The inner sphere has an outside diameter of 1 m, and the space between the two spheres is 0.1 m. The surfaces of both spheres are
> A package of electronic equipment is enclosed in a sheet-metal box that has a 0.3-m-square base and is 0.15 m high. The equipment uses 1200 W of electrical power and is placed on the floor of a large room. The emissivity of the walls of the box is 0.80,
> A thin layer of water is placed in a pan 1 m in diameter in the desert. The upper surface is exposed to 300 K air, and the convection heat transfer coefficient between the upper surface of the water and the air is estimated to be 10 W/m2 K. The effective
> A 1-m * 1-m-square solar collector is placed on the roof of a house. The collector receives a solar radiation flux of 800 W/m2. Assuming that the surroundings act as a blackbody at an effective sky temperature of 30°C, calculate the equilibrium temperatu
> A manned spacecraft capsule has a shape of a cylinder 2.5 m in diameter and 9 m long (see the sketch). The air inside the capsule is maintained at 20°C, and the convection heat transfer coefficient on the interior surface is 17 W/m2 K. Between
> An inventor claims that a solar collector consisting of two absorber plates connected by a glass sur- face configured in an equilateral triangle (shown in the sketch) is superior to a collector consisting of two parallel plates (also shown in the sketch)
> A homeowner wants to replace an electric hot-water heater. There are two models in the store. The inexpensive model costs $280 and has no insulation between the inner and outer walls. Due to natural convection, the space between the inner and outer walls
> For each of the following situations, determine the rate of heat transfer between two 1-m * 1-m parallel flat plates placed 0.2 m apart and connected by reradiating walls. Assume that plate 1 is maintained at 1500K and plate 2 at 500 K. (a) Plate 1 has
> Three thin sheets of polished aluminum are placed parallel to each other so that the distance between them is very small compared to the size of the sheets. If one of the outer sheets is at 280°C and the other outer sheet is at 60°C, calculate the temper
> Determine the steady-state temperatures of two radiation shields placed in the evacuated space between two infinite planes at temperatures of 555 K and 278 K. The emissivity of all surfaces is 0.8.
> For saturated pool boiling of water on a horizontal plate, calculate the peak heat flux at pressures of 10, 20, 40, 60, and 80% of the critical pressure pc. Plot your Where ( is in newtons per meter and T in degrees Centigrade. The critical pressure of w
> Two concentric spheres 0.2 m and 0.3 m in diameter are to be used to store liquid air (133 K). The space between the spheres is evacuated. If the surfaces of the spheres have been flashed with aluminum and the liquid air has a latent heat of vaporization
> (a) Show that / only. (b) For T = 5000 m K, calculate /
> In order to conserve energy, the inner surface of double-glazed windows are treated with a low emissivity coating that reduces the emissivity of the uncoated surface from 0.95 to 0.5 for the coated surface. If the temperatures of the two glass panes are
> Two 1.5-m-square, parallel flat plates are 30 cm apart. Plate A1 is maintained at a temperature of 1100 K and A2 at 500 K. The emissivities of the plates are 0.5 and 0.8, respectively. Considering the surroundings that are black at 0 K and including mult
> Derive an equation for the net rate of radiant heat transfer from surface 1 in the system shown in the accompanying sketch. Assume that each surface is at a uniform temperature and that the geometrical shape factor F1–2 is 0.1.
> The wedge-shaped cavity shown in the accompanying sketch consists of two long strips joined along one edge. Surface 1 is 1 m wide, has an emissivity of 0.4, and has a temperature of 1000 K. The other wall has a temperature of 600 K. Assuming gray diffuse
> A black sphere (2.5 cm in diameter) is placed in a large infrared heating oven whose walls are maintained at 370°C. The temperature of the air in the oven is 90°C, and the heat transfer coefficient for convection between the surface of the sphere and the
> In Problem 1.60, instead of diffusive heating (or by conduction), consider that the water is heated by natural convection from the surface of the heaters. The heat transfer coefficient, /, in W/m2 K, is expressed in the form / where Ts is the s
> Calculate the net radiant-heat-transfer rate if the two surfaces in Problem 11.18 are black and are connected by a refractory surface with an area of 500 m2. A1 is at 555 K, and A2 is at 278 K. What is the refractory surface temperature?
> Show that the effective conductance, / for two black, parallel plates of equal area connected by reradiating walls at a constant temperature is
> Compare the critical heat flux for a flat horizontal surface with that for a submerged horizontal wire of 3-mm diameter in water at saturation temperature and pressure.
> Show that the dimensionless equation for ice formation on the outside of a tube of radius r0 is Assume that the water is originally at the freezing temperature Tf, that the cooling medium inside the tube surface is just below the freezing temperature at
> Compare the axial heat flux achievable by a heat pipe using water as the working fluid with that of a solid silver rod. Assume that both are 20 cm long, that the temperature difference for the rod from end to end is 100oC, and that the heat pipe operates
> Design a heat pipe cooling system for a spherical satellite that dissipates 5000 W/m3, has a surface area of 5 m2, and cannot exceed a temperature of 120oC. All the heat must be dissipated by radiation into space. State all your assumptions.
> Estimate the cross-sectional area required for a 30-cm-long methanol-nickel heat pipe to transport 30 W at atmospheric pressure.
> The one-pass condenser, heat exchanger shown in the sketch has 64 tubes arranged in a square array with 8 tubes per line. The tubes are 1.22 m long and are made of copper with an outside diameter of 1.27 cm. They are contained in a shell at atmospheric p
> The 1-m-long, tube-within-a-tube, heat exchanger shown in the sketch is used to condense steam at 2 atm in the annulus. Water flows in the inner tube, entering at 90oC. The inner tube is made of copper with a 1.27-cm-OD and 1.0-cm-ID. (a) Estimate the w
> A vertical, rectangular water duct 1 m high and 0.10 m deep shown in the sketch is placed in an environment of saturated steam at atmospheric pressure. If the outer surface of the duct is about 50oC, estimate the rate of steam condensation per unit lengt
> Estimate the maximum heat flux obtainable with nucleate pool boiling on a clean surface for (a) water at 100 kPa on brass, (b) water at 1 MPa on brass.
> Saturated methyl chloride at 430 kPa (abs) condenses on a horizontal 10 * 10 bank of tubes. The 5-cm- OD tubes are equally spaced and are 10 cm apart center-to-center on rows and columns. If the surface temperature of the tubes is maintained at 7oC by p
> Problem 9.11 indicated that the Nusselt number for condensation depends on the Prandtl number and four other dimensionless groups including the Jakob number (Ja), the Bond number (Bo), and a nameless group resembling the Grashof number / Give
> The inner wall of a rocket motor combustion chamber receives 160 kW/m2 by radiation from a gas at 2760°C. The convection heat transfer coefficient between the gas and the wall is 110 W/ ( m2 K ) . If the inner wall of the combustion chamber is
> Repeat Problem 9.26 (b) and (c) but assume that condensation occurs on a 5-cm-OD, horizontal tube.
> At a pressure of 490 kPa, the saturation temperature of sulfur dioxide ( SO2) is 32oC, the density is 1350 kg/m3, the latent heat of vaporization is 343 kJ/kg, the absolute viscosity is 3.2 * 10-4 kg/m s, the spe-ific heat is 1445 J/kg K and the thermal
> Saturated steam at 34 kPa condenses on a 1-m-tall vertical plate whose surface temperature is uniform at 608C. Compare the average heat transfer coefficient and the value of the coefficient 1/3 m, 2/3 m, and 1 m from the top. Also, find the maximum heigh
