Question: The conversion of solar energy into electric
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 panel consists of a top layer of glass attached with a thin optically clear adhesive to a very thin layer of photoelectric material such as doped-silicon in which the incident solar irradiation is converted into electric energy. Experiments have shown that the solar to electric efficiency h in photovoltaic material such as silicon decrease with in- crease in temperature and is approximated by the expression, (= 0.55 - 0.001Tsilicon, where Tsilicon is the silicon temperature in K. In a typical installation where the solar irradiation is G 5 700 W/m2, 7% is reflected from the top surface of the glass, 10% is absorbed by the glass, and 83% is transmitted to the photovoltaic active layer. A part of the irradiation absorbed by the photo- voltaic material is converted to heat and the remainder is converted to electric energy. The silicon layer is attached by a 0.01-mm thick layer of solder to a 3-mm thick aluminum nitride substrate as shown in the schematic. Determine the electric power produced by this PV panel, assuming the following properties for the pertinent materials: conductivity of glass, kg = 1.4 W/m. K, conductivity of the adhesive ka = 145 W/m. K, the emissivity of glass is 0.90, heat transfer coefficient from the top of the panel to the surrounding air is 35 W/m2. K, and the surrounding air temperature is Tair = 20°C. The solar PV panel is 5 m long and 1 m wide and is situated on a roof where the bottom is considered insulated. (Hint: Start by applying the first law of thermodynamics to the photovoltaic-active layer and note that some of the irradiation will be converted to electricity and some of it transmitted thermally.) ![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 panel consists of a top layer of glass attached with a thin optically clear adhesive to a very thin layer of photoelectric material such as doped-silicon in which the incident solar irradiation is converted into electric energy. Experiments have shown that the solar to electric efficiency h in photovoltaic material such as silicon decrease with in- crease in temperature and is approximated by the expression, (= 0.55 - 0.001Tsilicon, where Tsilicon is the silicon temperature in K. In a typical installation where the solar irradiation is G 5 700 W/m2, 7% is reflected from the top surface of the glass, 10% is absorbed by the glass, and 83% is transmitted to the photovoltaic active layer. A part of the irradiation absorbed by the photo- voltaic material is converted to heat and the remainder is converted to electric energy. The silicon layer is attached by a 0.01-mm thick layer of solder to a 3-mm thick aluminum nitride substrate as shown in the schematic.
Determine the electric power produced by this PV panel, assuming the following properties for the pertinent materials: conductivity of glass,
kg = 1.4 W/m. K, conductivity of the adhesive
ka = 145 W/m. K, the emissivity of glass is 0.90, heat transfer coefficient from the top of the panel to the surrounding air is 35 W/m2. K, and the surrounding
air temperature is Tair = 20°C. The solar PV panel is 5 m long and 1 m wide and is situated on a roof where the bottom is considered insulated. (Hint: Start by applying the first law of thermodynamics to the photovoltaic-active layer and note that some of the irradiation will be converted to electricity and some of it transmitted thermally.)](../images/the-conversion-of-solar-energy-into-electric-power-by-means-of-photovoltaic-278898-1.jpg)
> 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
> 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
> 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
> 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
> 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 sketc
> 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 /
