Questions and Answers of Sustainable Engineering

Referring to Figure 5.19, prove Equation 5.46 for the angle of incidence. Use direction cosines of the sun-ray vector and a vector normal to the tilted surface to find the angle between them. Dot
Show that the hourly averaged, extraterrestrial radiation for a given hour is the same, to within $1 \%$, as instantaneous radiation at the hour's midpoint. This is equivalent to deriving Equation
Derive Equation 5.33 relating profile angle $\gamma$ to azimuth angle $\alpha$ and altitude angle $\alpha$.Equation 5.33 tany sec a tan
Based on Equation 5.46, what value of $\beta$ would result in the annual minimum value of the incidence angle $i$ ? Note that this tilt angle would result in maximum collection of beam radiation
Equation 5.53 is based on an early solar constant value of $1394 \mathrm{~W} / \mathrm{m}^{2}$. Derive a modified form of Equation 5.53 based on the presently accepted value for the solar constant
Find the wavelength of radiation whose photons have energy equal to the band gap of GaAs.
What is the theoretical maximum efficiency of conversion if blue light of wavelength $0.45 \mu \mathrm{m}$ is incident on a GaAs solar cell?
Find the theoretical maximum overall efficiency of GaAs solar cells in space.
The reverse saturation current $I_{o}$ of a silicon cell at $40^{\circ} \mathrm{C}$ is $1.8 \times 10^{-7} \mathrm{~A}$. The short circuit current when exposed to sunlight is $5 \mathrm{~A}$.
At what efficiency is a photovoltaic array running if insolation on the collector is $650 \mathrm{~W} / \mathrm{m}^{2}$, the total collector area is $10 \mathrm{~m}^{2}$, the voltage across the
If a PV array has a maximum power output of $10 \mathrm{~W}$ under an insolation level of $600 \mathrm{~W} / \mathrm{m}^{2}$, what must the insolation be to achieve a power output of \(17
A PV battery system has an end-to-end efficiency of $77 \%$. The system is used to run an all-AC load that is run only at night. The charge controller efficiency is $96 \%$ and the inverter
If the average output of the PV system in Problem 6.7 is $200 \mathrm{~W}$, the load is changed to run during the day, how much PV output energy is needed for the same load conditions? Assume that
For the system in Problem 6.7, how many hours of sunlight are needed to ensure that the battery bank is at $100 \%$ charge at the end of the day assuming the same load?Problem 6.7A PV battery
a. What is the homeowner's daily energy requirement as measured from the load?b. If she replaces her alarm clock with a wind-up clock, how much energy per day will she avoid using?c. What would you
How many $50 \mathrm{~W}$ panels will the owner require assuming battery storage is $75 \%$ efficient and all loads are DC (no inverter)?a. For a stationary system "seeing" $5 \mathrm{~h}$ of
For the loads listed:c. What size inverter (peak watts) should she purchase?d. If the inverter is $88 \%$ efficient, how much more daily energy is required from the $\mathrm{PV}$ array as
The homeowner decides to hire you to design a system for her. She has arranged with a local solar supplier for the following equipment. Specify the system and provide a line diagram.The owner of a
Redesign the system in Problem 6.14 with the following equipment:The owner of a small cabin would like to convert her home to PV power. She has the following equipment and associated run times: PV
A flashing beacon is mounted on a navigation buoy in the shipping channel at a port at $30^{\circ} \mathrm{N}$ latitude. The load consists of a single lamp operating $1.0 \mathrm{~s}$ on and
Design a PV system for the following application: A refrigerator/freezer unit for vaccine storage in a remote island of Roatan, Honduras $\left(16^{\circ} \mathrm{N}\right.$ latitude, \(86^{\circ}
A homeowner in Santa Fe, New Mexico, is interested in having a solar PV system installed at his house. He would like the system to be able to cover all of his annual energy needs. The following is a
A village in Antigua $\left(17^{\circ} \mathrm{N}, 61^{\circ} \mathrm{W}, 15^{\circ} \mathrm{C}-30^{\circ} \mathrm{C}\right.$ temperature, range), West Indies, requires $5000 \mathrm{gal}$ of
Prepare a preliminary design for a solar PV system to provide $1 \mathrm{~kW}$ of stand-alone $24 \mathrm{~h} /$ day power to a travel trailer. Make a schematic diagram of the overall system, a
Calculate the heat-removal factor for a collector having an overall heat loss coefficient of $6 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}$ and constructed of aluminum fins and tubes. Tube-to-tube
Calculate the efficiency of the collector described in Problem 7.1 on March 1 at a latitude of $40^{\circ} \mathrm{N}$ between 11 and 12 a.m. Assume that the total horizontal insolation is \(450
Calculate the plate temperature in Example 7.3 at 10 a.m., if the insolation during the first $3 \mathrm{~h}$ is 0,150 , and $270 \mathrm{~W} / \mathrm{m}^{2}$, respectively, and the air
Calculate the overall heat-transfer coefficient, neglecting edge losses, for a collector with a double glass cover, with the following specifications: Plate-to-cover spacing Plate emittance Ambient
The graph in Figure 7.18 gives the results of an ASHRAE standard performance test for a single-glazed flat-plate collector. If the transmittance for the glass is 0.90 and the absorptance of the
Calculate the overall heat loss coefficient for a solar collector with a single glass cover having the following specifications:The solution to this problem requires trial and error. Start by
Standard tests on a commercially available flat-plate collector gave a thermal efficiency of\[ \begin{gathered} \eta=0.7512-\frac{0.138\left(T_{f, i n}-T_{\alpha}\right)}{I_{c}} \\ K_{\tau
The heat-removal factor $F_{R}$ permits solar collector delivery to be written as a function of collector fluid inlet temperature $T_{f}$ in Equation 7.46. Derive the expression for a factor
In nearly all practical situations, the argument of the exponential term in Equation 7.43 for $F_{R}$ is quite small. Use this fact along with Taylor's series expansion to derive an alternate
What is the operating temperature for an evacuated tube collector operating at $50 \%$ efficiency if the insolation is $800 \mathrm{~W} / \mathrm{m}^{2}$ ? Use data from Figure 7.19.Figure 7.19
Derive an expression for the heat loss conductance $U_{c}$ for a flat-plate collector in which convection and conductance are completely eliminated in the air layers by use of a hard vacuum.
Calculate the optical efficiency on November 13 of an evacuated tube collector array at noon and $2 \mathrm{p} . \mathrm{m}$. if the direct normal insolation is $600 \mathrm{~W} / \mathrm{m}^{2}$
The no-load temperature of a building with internal heat sources is given by Equation 7.72. How would this equation be modified to account for heat losses through the surface of an unheated slab, the
An unheated garage is placed on the north wall of a building to act as a thermal buffer zone. If the garage has roof area $A_{p}$, window area $A_{w i}$ door area $A_{d}$, and wall area \(A_{w
What is the annual energy demand for a building in Denver, Colorado, if the peak heat load is $150,000 \mathrm{Btu} / \mathrm{h}$ based on a design temperature difference of \(75^{\circ}
What is the January solar load fraction for a water-heating system in Washington, DC, using $100 \mathrm{~m}^{2}$ of solar collector if the water demand is $4 \mathrm{~m}^{3} /$ day at
Repeat Problem 7.16 for Albuquerque, $\mathrm{NM}$, in July if the water source temperature is $17^{\circ} \mathrm{C}$.Problem 7.16What is the January solar load fraction for a water-heating
Explain how the $f$-chart (Figure 7.32) can be used graphically to determine the solar load fraction for a range of collector sizes once the solar and loss parameters have been evaluated for only
In an attempt to reduce cost, a solar designer has proposed replacing the shell-and-tube heat exchanger in Figure 7.27 with a tube coil immersed in the storage tank. The shelland-tube heat exchanger
If a solar system delivers $2500 \mathrm{MJ} / \mathrm{m}^{2} \cdot$ year with a water flow rate of $30 \mathrm{~kg} / \mathrm{m}_{c}{ }^{2}$ and a plate efficiency factor $F^{\prime}=0.93$,
How large (MJ/h) should a heat-rejection system be if it must dump the entire heat production of a $1000 \mathrm{~m}^{2}$ solar collector array in Denver, CO, on August 21 if the collector is at
Use the $f$-chart to determine the amount of solar energy that can be delivered in Little Rock, AR, in January for the following solar and building conditions:BuildingLoad: 40 million
Estimate the electric power requirement, in $\mathrm{kW}$, of a $1400 \mathrm{ft}^{2}$ floor area (three-bedroom home) with three occupants. Using your home power estimate, predict the power
The $f$-chart is based on $F_{R}(\tau \alpha)$ and $F_{R} U_{c}$ values, which can be deduced from a plot of collector efficiency versus $\left(T_{\text {fin }}-T_{a}\right) / I$. If such a
The following schematic diagrams illustrate the operation of a solar-assisted heatpump system and a solar system augmented with a heat pump. Discuss the advantages and disadvantages of each system
The following table gives the characteristics of a building in Houston, TX. Determine the cooling load for July 30 at solar noon. Any information regarding the load not given may be assumed or
An air-conditioning system working in a vapor-compression cycle is used to manage the load for the building in Problem 7.26. If the high and low pressures in the cycle are 915 and \(290
Consider the absorption refrigeration cycle, shown in the following line diagram, which uses lithium bromide as carrier and water as refrigerant to provide $1 \mathrm{~kW}$ of cooling. By using
Make a preliminary design for a solar-driven Rankine refrigeration machine to provide the temperature environment required below the surface of a $20 \times 40 \mathrm{~m}$ iceskating rink that is
The following table shows data from a dehumidification process using aqueous solution of lithium chloride ( $\mathrm{LiCl}$ ) in a packed tower. The desiccant leaving the dehumidifier is passed
Repeat Example 8.1 for a parabolic collector with an evacuated tube receiver (case E in Figure 8.18a).Example 8.1Figure 8.18a Derive a relationship for the efficiency of a parabolic collector with a
Repeat Example 8.3, but for a collector located in Washington, DC.Example 8.3 Find the thermal energy delivery of a polar-mounted parabolic trough collector oper- ated for 8 h per day (At = 8) during
Consider a Stirling cycle from Example 8.10 with imperfect regenerator $\left(T_{R}=230^{\circ} \mathrm{C}\right)$. Assume ideal gas.a. Compute the efficiency from\[ \eta=\frac{\text { Work
A solar electric engine operating between $5^{\circ} \mathrm{C}$ and $95^{\circ} \mathrm{C}$ has an efficiency equal to one-half the Carnot efficiency. This engine is to drive a \(4
Prepare a thermal analysis matching a line focusing collector, a paraboloid dish collector, and a CPC collector with a CR of 3:1 to a suitable working fluid in Washington, DC, and Albuquerque, New
The following schematic diagram for a solar-driven irrigation pump was developed by Battelle Memorial Institute and uses tracking PTCs. Solar energy is used to heat the water in the collectors to
Write a closed-form expression for the work output of a solar-powered heat engine if the energy delivery of the solar collector at high temperature is given approximately by the expression\[
Calculate the maximum power and LCOE for a parabolic collector similar to that in Example 8.1, but assume that an evacuated tube receiver is used (case E in Figure 8.18a).Example 8.1Figure 8.18
Prepare a preliminary design for a CRS with a power capacity of $50 \mathrm{MW}$ similar to Solar 2 for a location in Nevada.
It has been estimated that a 400 MW expansion of the existing SEGS solar plant in California would cost $\$ 2.4$ billion. Estimate the expected capital costs of the generation facility in dollars/
Using SAM, estimate the levelized cost for a $50 \mathrm{MW}_{\mathrm{e}}$ parabolic trough solar power plant in San Diego, CA, similar to the one shown in Figure 8.26. Also determine the thermal
Using SAM, estimate the levelized cost for a central receiver solar power plant with $10 \mathrm{~h}$ of storage in Phoenix, AZ, similar to the one shown in Figure 8.30. Assume that the receiver is
Explain how window placement in a building could be defined as(a) a passive solar feature,(b) an energy conservation technique,(c) both of these.
Write an equation for calculating the cost of savings life cycle economics of a proposed passive solar system. Explain why it is important to be able to determine the auxiliary energy required for
Referring to the thermal circuit diagram of Figure 9.7 for the thermal storage (Trombe) wall building, construct appropriate thermal circuits for(a) attached sunspace,(b) thermal storage, (c) direct
Using rules of thumb for a $200 \mathrm{~m}^{2}$ floor area Denver residence, determine(a) the auxiliary heating energy required,(b) the solar projected area, (c) the concrete storage mass needed
A $2000 \mathrm{ft}^{2}$ house in Boston is being designed with NLC-12,000 Btu/F-day and $150 \mathrm{ft}^{2}$ of direct gain. The direct gain system includes double glazing, nighttime
Compare the annual SSF for $150 \mathrm{ft}^{2}$ of the following passive systems for the house in Problem 9.5:(a) direct gain (DGA3),(b) vented. Trombe wall (TWD4),(c) unvented Trombe wall
A design modification to the house in Problem 9.5 is desired. A $200 \mathrm{ft}^{2}$, vented, $12 \mathrm{in}$. thick Trombe wall is to be added to the direct gain system. Assuming the same
Using the SLR method, calculate the auxiliary energy required in March for a $2000 \mathrm{ft}^{2}$, NLC 12,000 Btu/F-day house in Boston with a $150 \mathrm{ft}^{2}$, night-insulated
Calculate the heating season auxiliary energy required for the Boston house in Problem 9.8.Problem 9.8Using the SLR method, calculate the auxiliary energy required in March for a \(2000
Determine the length of the overhang needed to shade a south-facing $2 \mathrm{~m}$ high window in Dallas, TX (latitude 32 ${ }^{\circ} 51^{\prime}$ ), to allow for both winter heating and summer
A $10 \mathrm{mph}$ wind is blowing directly into an open $3 \mathrm{ft} \times 5 \mathrm{ft}$ window, which is mounted in a room's $8 \mathrm{ft}$ high by $12 \mathrm{ft}$ wide wall. If the
Design a stack effect/solar chimney (vented Trombe wall) to produce an average velocity of $0.3 \mathrm{~m} / \mathrm{s}$ within a $4 \mathrm{~m}$ wide by $5 \mathrm{~m}$ long by \(3
Estimate the overnight radiant cooling possible from an open, $30^{\circ} \mathrm{C}, 8 \mathrm{~m}$ diameter water tank during July in Chicago. What would you expect for convective and evaporative
For the buried pipe example (9.8) in the text, determine which of the three flow rate cases leads to the least expensive installation.Example (9.8)Provide the necessary 12 in. diameter pipe length(s)
Using data from Figure 9.14, design a $9 \mathrm{ft}$ deep ground-pipe system for Dallas in June to deliver $1000 \mathrm{cfm}$ at $75^{\circ} \mathrm{F}$ when the outside air temperature is
A $30 \mathrm{ft} \times 20 \mathrm{ft}$ office space has a photosensor dimmer control working with installed lighting of $2 \mathrm{~W} / \mathrm{ft}^{2}$. The required workplace illuminance is
Determine the illuminances (sun, sky, and ground-reflected) on a vertical, south-facing window at solar noon at $36^{\circ} \mathrm{N}$ latitude on June 21 and December 21 for(a) a clear day (b)
Determine the sidelighting workplace illuminances for a $20 \mathrm{ft}$ long, $15 \mathrm{ft}$ wide (deep), $8 \mathrm{ft}$ high light-colored room with a $15 \mathrm{ft}$ long by \(5
Determine the clear sky day and the cloudy day work-plane illuminances for a $30 \mathrm{ft}$ long, $30 \mathrm{ft}$ wide, $10 \mathrm{ft}$ high light-colored room. A $20 \mathrm{ft}$ long by
Determine the clear day and cloudy day illuminances on a horizontal skylight at noon on June 21 and December 21 in(a) Miami,(b) Los Angeles,(c) Denver,(d) Boston, (e) Seattle.
A $3 \mathrm{ft} \times 5 \mathrm{ft}$ double-domed skylight has outer and inner fat-plate plastic transmittances of 0.8 and 0.7, respectively; a $2 \mathrm{ft}$ deep well with $80 \%$
Determine the number and roof placement of $10 \mathrm{ft} \times 4 \mathrm{ft}$ skylights needed for a $50 \mathrm{ft} \times$ $50 \mathrm{ft} \times 10 \mathrm{ft}$ high office when the
What would be the procedure for producing uniform workplace illuminance when both sidelighting and skylighting are used simultaneously?
Design a compressed air energy storage system for a wind turbine. Assume that a cavity in an abandoned salt mine was available adjacent to the wind turbine. Use all the power generated above \(5
A hydrogen/oxygen fuel cell stack produces $100 \mathrm{~kW}$ of DC power at an efficiency of $60 \%$ with water vapor as the product. Determine the hydrogen mass flow rate in \(\mathrm{g} /
Derive an expression for the electric energy generation per unit of air volume stored in a cavity for a CAES system. Assume that there are two expansion stages and express the work output as the sum
Supposing you own some land next to a $50 \mathrm{MW}$ wind farm located on Colorado's Front Range. Your land has a fantastic cliff/ridgeline with an elevation difference of $250 \mathrm{~m}$.
It has been proposed that the United States should strive toward a hydrogen economy. At present, the United States uses about 100 quads $\left(10^{17} \mathrm{Btu}\right)$ of energy per year.
a. Design a compressed air energy storage system for a wind turbine you analyzed previously. Assume that a cavity in an abandoned salt mine is available adjacent to the wind turbine. Use all the
Derive an expression for the linear battery model power output as a function of the internal-to-external resistance ratio. Nondimensionalize the power output by dividing it by $E^{2} / R_{i}$.
Design a battery electric storage system for a power plant with $20 \mathrm{MW}$ peak power delivery for a duration of $4 \mathrm{~h}$ and estimate the minimum number of batteries and the current
A hydrogen/oxygen fuel cell operates with a voltage of $0.7 \mathrm{~V}$ with water vapor production. Calculate the $\mathrm{kW} / \mathrm{h}$ of work per $\mathrm{kg}$-mol of hydrogen and
You are asked to estimate the amount of heat that can be stored overnight in a solarheated building, which has a storage space of $6 \mathrm{~m}^{3}$. The solar system uses water with antifreeze in
A neighborhood fuel cell power plant is to be designed for an electric power output of $2000 \mathrm{~kW}$ with liquid-water product. Estimate the flow rates of hydrogen and oxygen during peak

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