Estimate the time required to freeze vegetables in thin, tin cylindrical containers 15 cm in diameter. Air at 212°C is blowing at 4 m/s over the cans, which are stacked to form one long cylinder. The physical properties of the vegetables before and after freezing are taken as those of water and ice respectively.
> Determine the shape factor F1–2 for the geometrical configuration shown in the figure.
> A tungsten filament is heated to 2700 K. At what wavelength is the maximum amount of radiation emitted? What fraction of the total energy is in the visible range (0.4 to 0.75 m)? Assume that the filament radiates as a graybody.
> Determine the shape factor F1–4 for the geometrical configuration shown in the figure.
> Derive an expression for the geometric shape factor F1–2 for the rectangular surface A1 shown in the figure. A1 is 1-m * 20-m and is placed parallel to and centered 5 m above a 20-m square surface A2.
> Estimate the rate at which heat needs to be supplied to an astronaut repairing the Hubble telescope in space. Assume that the emissivity of the spacesuit is 0.5. Describe your model with a simple sketch and clearly state your assumptions.
> On a rainy Monday afternoon, a wealthy banker calls Sherlock Holmes to arrange a breakfast appointment for the following day to discuss the collection of a loan from farmer Joe. When Holmes arrives at the home of the banker at 9 a.m. Tuesday, he finds th
> The ceiling of a tract house is constructed of wooden studs with fiberglass insulation between them. On the interior of the ceiling is plaster and on the exterior is a thin layer of sheet metal. A cross section of the ceiling with dimensions is shown bel
> A hypothetical PV solar cell in space can utilize solar radiation between 0.8 and 1.1 mm in wavelength. Estimate the maximum theoretical efficiency for this solar cell facing the sun using the ideal black- body curve of the sun as the source. Supposing t
> As a result of the atmosphere surrounding the Earth trapping some of the incoming solar radiation, the average temperature of the Earth is approximately 15°C. Estimate the amount of radiation that is trapped by the atmosphere, including CO2 and methane,
> The diameter of the sun is 1.39 * 109 m. Estimate the percentage of the total radiation emitted by the sun, which approximates a blackbody at 5760 K, that is actually intercepted by the Earth. Of the total radiation falling on the Earth, about 70% f
> The glass cover for a flat plate solar collector has a spectral transmissivity that may be approximated as shown in the figure. Determine the total effective transmissivity of the glass cover to solar radiation assuming the sun emits that of a blackbody
> For an ideal radiator (hohlraum) with a 10-cm- diameter opening, located in black surroundings at 16°C, calculate (a) the net radiant heat transfer rate for hohlraum temperatures of 100°C and 560°C, (b) the wavelength at which the emission is a maxi- mu
> In a shell-and-tube heat exchanger with /W/M2 K and negligible wall resistance, by what percent would the overall heat transfer coefficient (based on the outside area) change if the number of tubes were doubled? The tubes have an outside diameter of 2.5
> The heat transfer coefficient of a copper tube (1.9-cm ID and 2.3-cm OD) is 500 W/m2 K on the inside and 120 W/m2 K on the outside, but a deposit with a fouling factor of 0.009 m2 K/W (based on the tube outside diameter) has built up over time. Estimate
> Repeat Problem 10.6, but assume that a fouling factor of 0.173 m2 K/kW based on the tube outside diameter has developed over time.
> Hot water is used to heat air in a double-pipe heat exchanger as shown in the following sketch. If the heat transfer coefficients on the water side and on the air side are 550 W/m2 K and 55 W/m2 K respectively, calculate the overall heat transfer coeffi
> The temperature of a 100-m-diameter cooling pond is 7oC on a winter day. If the air temperature suddenly drops to -7 °C, calculate the thickness of ice formed after three hours.
> Microchannel compact heat exchangers can be used to cool high heat flux microelectronic devices. The accompanying sketch on the next page shows a schematic view of a typical microchannel heat sink. Microfabrication techniques can be used to mass produce
> Draw the thermal circuit for heat transfer through a double-glazed or a double-paned window. Identify each of the circuit elements. Include solar radiation to the window and interior space.
> An air-to-water compact heat exchanger is to be designed to serve as an intercooler for a 3.7 MW gas turbine plant. The exchanger is to meet the following heat transfer and pressure drop performance specifications: Air-side operating conditions: The exch
> Calculate the water-side heat transfer coefficient and the coolant pressure drop per unit length of tube for the core of a compact air-to-water inter- cooler for a 3.7 MW gas turbine plant. The water flows inside a flattened aluminum tube having the cros
> Saturated steam at 137 kPa condenses on the outside of a 2.6-m length of copper tubing, heating 5 kg/h of water flowing in the tube. The water temperatures measured at 10 equally spaced stations along the tube length (see the sketch) are: Calculate (a)
> While flowing at the rate of 1.25 kg/s in a simple counterflow heat exchanger, dry air is cooled from 65°C to 38°C by means of cold air that enters at 15°C and flows at a rate of 1.6 kg/s. It is planned to lengthen the heat exchanger so that 1.25 kg/s of
> Water flowing in a long, aluminum tube is to be heated by air flowing perpendicular to the exterior of the tube. The ID of the tube is 1.85 cm, and its OD is 2.3 cm. The mass flow rate of the water through the tube is 0.65 kg/s, and the temperature of th
> An oil having a specific heat of 2100 J/kg K enters an oil cooler at 82°C at the rate of 2.5 kg/s. The cooler is a counterflow unit with water as the cool- ant; the transfer area is 28 m2, and the overall heat transfer coefficient is 570 W/m2 K. The wate
> Calculate the overall heat transfer coefficient and the rate of heat flow from the hot gases to the cold air in the cross-flow tube bank of the heat exchanger shown in the accompanying illustration on the next page. The following operating conditions are
> Liquid benzene 1 specific gravity 5 0.862 is to be heated in a counterflow concentric-pipe heat exchanger from 30°C to 90°C. For a tentative design, the velocity of the benzene through the inside pipe (ID = 2.7 cm, OD = 3.3 cm ) can be taken as 8
> Determine the excess temperature at one-half of the maximum heat flux for the fluid-surface combinations in Problem 9.3.
> In an industrial plant a shell-and-tube heat exchanger is heating pressurized dirty water at the rate of 38 kg/s from 60°C to 110°C by means of steam condensing at 115°C on the outside of the tubes. The heat exchanger has 500 steel tubes (ID = 1.6 cm, OD
> A shell-and-tube heat exchanger in an ammonia plant is preheating 1132 m3 of atmospheric pressure nitrogen per hour from 21°C to 65°C using steam condensing at 138,000 N/m2. The tubes in the heat exchanger have an inside diameter of 2.5 cm. In order to c
> The walls of a typical industrial furnace used for the heat treating of metals are usually a composite structure made up of layers of firebrick, high-temperature insulation, steel plates, and outer surface cladding. Radiant tubes/beams and/or combustion
> A shell-and-tube counterflow heat exchanger is to be designed for heating an oil from 27°C to 82°C. The heat exchanger has two tube passes and one shell pass. The oil is to pass through 3.8 cm schedule 40 pipes at a velocity of 1 m/
> A one-tube pass cross-flow heat exchanger is being considered for recovering energy from the exhaust gases of a turbine-driven engine. The heat exchanger is constructed of flat plates forming an egg-crate pattern as shown in the following sketch. The ve
> A small space heater is constructed of 1.25 cm, 18-gauge brass tubes that are 60 cm. The tubes are arranged in equilateral, staggered triangles on 3.6 cm centers with four rows of 15 tubes each. A fan blows 0.95 m3/s of atmospheric pressure air at 21
> Determine the heat-transfer area requirements of Problem 10.41 if (a) a 1–2 shell-and-tube, (b) an unmixed cross-flow, and (c) a parallel flow heat exchanger are used.
> A counterflow regenerator is used in a gas tur- bine power plant to preheat the air before it enters the combustor. The air leaves the compressor at a temperature of 350°C. Exhaust gas leaves the turbine at 700°C. The mass flow rates of air and gas ar
> Repeat Problem 10.3, but assume that fouling factors of 0.0009 m2 K/W and 0.0004 m2 K/W have developed on the inside and on the outside, respectively.
> Determine the appropriate size of a shell-and-tube heat exchanger with two tube passes and one shell pass to heat 8.82 kg/s of pure ethanol from 15.6°C to 60°C. The heating medium is saturated steam at 152 kPa condensing on the outside of the tubes with
> Estimate the time required for nocturnal radiation to freeze a 3-cm thickness of water with ambient air and initial water temperatures at 4oC. Neglect evaporation effects.
> A shell-and-tube heat exchanger with the characteristics given below is to be used to heat 27,000 kg/h of water before it is sent to a reaction system. Saturated steam at 239 kPa absolute pressure is available as the heating medium and will be condensed
> A shell-and-tube heat exchanger is to be used to cool 25.2 kg/s of water from 38°C to 32°C. The exchanger has one shell-side pass and two tube-side passes. The hot water flows through the tubes, and the cooling water flows through the shell. The cooling
> A horizontal shell-and-tube heat exchanger is used to condense organic vapors. The organic vapors condense on the outside of the tubes, while water is used as the cooling medium on the inside of the tubes. The condenser tubes are 1.9-cm OD, 1.6-cm- ID co
> A pipe carrying superheated steam in a basement at 10°C has a surface temperature of 150°C. Heat loss from the pipe occurs by radiation and natural convection / Determine the percentage of the total heat loss by these two
> Two engineers are having an argument about the efficiency of a tube-side multipass heat exchanger compared to a similar exchanger with a single tube- side pass. Smith claims that for a given number of tubes and rate of heat transfer, more area is require
> Design (i.e., determine the overall area and a suit- able arrangement of shell and tube passes) a tubular feed-water heater capable of heating 2300 kg/h of water from 21°C to 90°C. The following specifications are given: (a) saturated steam at 920 kPa a
> An air-cooled low-pressure steam condenser is shown in the following figure. The tube bank is four rows deep in the direction of air flow, and there are a total of 80 tubes. The tubes have a 2.2-cm ID and a 2.5-cm OD and are 9 m long with circular fins o
> Water flowing at a rate of 10 kg/s through a 50-tube double-pass shell-and-tube heat exchanger heats air that flows through the shell side. The length of the brass tubes is 6.7 m, and they have an outside diameter of 2.6 cm and an inside diameter of 2.3
> Water flowing at a rate of 12.6 kg/s is to be cooled from 90°C to 65°C by means of an equal flow rate of cold water entering at 40°C. The water velocity will be such that the overall coefficient of heat transfer U is 2300 W/m2 K. Calculate the heat-excha
> Hot water is to be heated from 10°C to 30°C at the rate of 300 kg/s by atmospheric pressure steam in a single-pass shell-and-tube heat exchanger consisting of 1-in. schedule 40 steel pipe. The surface coefficient on the steam side is estimated to be 11,3
> A light oil flows through a copper tube of 2.6-cm ID and 3.2-cm OD. Air flows perpendicular over the exterior of the tube as shown in the following sketch. The convection heat transfer coefficient for the oil is 120 W/m2 K and for the air is 35 W/m2 K. C
> It is proposed to preheat the water for a boiler using flue gases from the boiler stack. The flue gases are available at the rate of 0.25 kg/s at 150°C, with a specific heat of 1000 J/kg K. The water entering the exchanger at 15°C at the rate of 0.05 kg/
> Water at a rate of 0.32 L/s and a temperature of 27°C enters a No. 18 BWG 1.6 cm condenser tube made of nickel chromium steel (k = 26 W/m K ) . The tube is 3 m long, and its outside is heated by steam condensing at 50°C. Under these conditions the avera
> Water flowing through a pipe is heated by steam condensing on the outside of the pipe. (a) Assuming a uniform overall heat transfer coefficient along the pipe, derive an expression for the water temperature as a function of distance from the entrance.
> Some automobile manufacturers are currently working on a ceramic engine block that could operate without a cooling system. Idealize such an engine as a rectangular solid, 45 cm * 30 cm * 30 cm. Suppose that under maximum power output the engine consumes
> An economizer is to be purchased for a power plant. The unit is to be large enough to heat 7.5 kg/s of pressurized water from 71°C to 182°C. There are 26 kg/s of flue gases (cp = 1000 J/kg K ) available at 426°C. Estimate (a) the outlet temperature of t
> Carbon dioxide at 427°C is to be used to heat 12.6 kg/s of pressurized water from 37°C to 148°C while the gas temperature drops 204°C. For an overall heat transfer coefficient of 57 W/m2 K, compute the required area of the exchanger in square feet for (a
> Determine the outlet temperature of the oil in Problem 10.24 for the same initial fluid temperatures if the flow arrangement is one shell pass and two tube passes. The total area and average overall heat transfer coefficient are the same as those for the
> In a single-pass counterflow heat exchanger, 1.25 kg/s of water enters at 15°C and cools 2.5 kg/s of an oil having a specific heat of 2093 J/kg K from 95°C to 65°C. If the overall heat transfer coefficient is 280 W/m2 K, determine the surface area requir
> For safety reasons, a heat exchanger performs as shown in (a) of the accompanying figure. An engineer suggests that it would be wise to double the heat transfer area so as to double the heat transfer rate. The suggestion is made to add a second, identic
> In the manufacture of can ice, cans having inside dimensions of 27.5 * 55 * 125 cm with 2.5 cm inside taper are filled with water and immersed in brine at a temperature of –12oC. For the purpose of a preliminary analysis, the actual ice can be considered
> A steam-heated, single-pass tubular preheater is designed to raise 5.6 kg/s of air from 20°C to 75°C, using saturated steam at 2.6 MPa (abs). It is pro- posed to double the flow rate of air, and in order to be able to use the same heat exchanger and achi
> In a single-pass counter flow heat exchanger, 4536 kg/h of water enter at 15°C and cool 9071 kg/h of an oil having a specific heat of 2093 J/kg K from 93°C to 65°C. If the overall heat transfer coefficient is 284 W/m2 K, determine the surface area requ
> Repeat Problem 10.1 but assume that a fouling factor of 0.00018 m2 K/W has developed on the inside of the tube during operation.
> In gas turbine recuperators the exhaust gases are used to heat the incoming air and Cmin/Cmax is therefore approximately equal to unity. Show that for this case / for counter- flow and / for parallel flow.
> In the shell of a shell-and-tube heat exchanger with two shell passes and eight tube passes, 12.6 kg/s of water is heated from 80°C to 150°C. Hot exhaust gases having roughly the same physical properties as air enter the tubes at 340°C and leave at 180°C
> The soldering iron tip in Problem 1.53 becomes oxidized with age and its gray-body emittance increases to 0.8. Assuming that the surroundings are at 20°C, determine the power requirement for the soldering iron.
> Starting with a heat balance, show that the heat exchanger effectiveness for a counterflow arrangement is
> Water entering a shell-and-tube heat exchanger at 35°C is to be heated to 75°C by an oil. The oil enters at 110°C and leaves at 75°C. The heat exchanger is arranged for counterflow with the water making one shell pass and the oil making two tube passes.
> Benzene flowing at 12.5 kg/s is to be cooled continuously from 82°C to 54°C by 10 kg/s of water avail- able at 15.5°C. Using Table 10.6, estimate the surface area required for (a) cross-flow with six tube passes and one shell pass, with neither of the f
> A shell-and-tube heat exchanger with two tube passes and a single shell pass is used to heat water by condensing steam in the shell. The flow rate of the water is 15 kg/s, and it is heated from 60°C to 80°C. The steam condenses at 140°C, and the over- al
> A flat roof of a house absorbs a solar radiation flux of 600 W/m2. The backside of the roof is well insulated, while the outside loses heat by radiation and convection to ambient air at 20°C. If the emittance of the roof is 0.80 and the convection heat t
> Oil / is used to heat water in a shell-and-tube heat exchanger with a single shell pass and two tube passes. The overall heat transfer coefficient is 525 W/m2 K. The mass flow rates are 7 kg/s for the oil and 10 kg/s for the water. The oil and water ente
> A standard 10-cm steel pipe (ID = 10.066 cm, OD = 11.25 cm) carries superheated steam at 650oC in an enclosed space where a fire hazard exists, limiting the outer surface temperature to 38oC. To minimize the insulation cost, two materials are to be used:
> The addition of insulation to a cylindrical surface such as a wire, may increase the rate of heat dissipation to the surroundings (see Problem 2.15). (a) For a No. 10 wire (0.26 cm in diameter), what is the thick- ness of rubber insulation 1 k 5 0.16 W/
> A cylindrical liquid oxygen (LOX) tank has a diameter of 1.22 m, a length of 6.1 m, and hemispherical ends. The boiling point of LOX is 2179.4oC. An insulation is sought that will reduce the boil-off rate in the steady state to no more than 11.3 kg/h. Th
> A salesperson for insulation material claims that insulating exposed steam pipes in the basement of a large hotel will be cost-effective. Suppose saturated steam at 5.7 bar flows through a 30-cm-OD steel pipe with a 3-cm wall thickness. The pipe is surro
> A shell-and-tube heat exchanger having one shell pass and four tube passes is shown schematically in the following sketch. The fluid in the tubes enters at 200°C and leaves at 100°C. The temperature of the fluid is 20°C e
> A 2.5-cm-OD, 2-cm-ID copper pipe carries liquid oxy- gen to the storage site of a space shuttle at 213°C and 0.04 m3/min. The ambient air is at 21oC and has a dew point of 10oC. How much insulation with a thermal conductivity of 0.02 W/m K is
> 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
