a)b) Find the overall emissivity of the receiver's surface at its steady-state temperature. What is true about the relationship between the emissivity and absorptivity of the receiver'ssurface?○ It can only be said that e(0, 0, X) = a(0, 0, X) since this is the only relationship that is always true.The overall emissivity and absorptivity are equal to each other because the irradiation source is diffuse.They are equal only spectrally, because the surface of the receiver is diffuse and the source of irradiation isdiffuse. BOTH of these MUST be true for the spectral emissivity and absorptivity to be equal to one another.The overall emissivity and absorptivity are equal to each other because the receiver surface is diffuse.O It can only be said that c(0, 0, X) = a(0, 0, X) since the surface of the receiver is diffuse but the source ofirradiation is not specifically stated to be a diffuse source.They are equal only spectrally, because the surface of the receiver is diffuse and the source of irradiation isdiffuse. Only one of these needs to be true for the spectral emissivity and absorptivity to be equal to oneanother. Solar power towers (also called 'central tower' power plants or 'heliostat' power plants), allow solarirradiation to be concentrated into a single receiver by a series of reflectors (mirrors) to maximize theamount of heat flux being used to make clean, renewable energy. Here's the Ivanpah Solar PowerFacility pictured below (https://en.wikipedia.org/wiki/Ivanpah Solar Power Facility B). It is locatedin the Mojave desert by the border of California and Nevada, where irradiation from sunlight is highdue to lack of cloud cover and interference from moisture in the air.In this problem, we'll study a simplified solar power plant model to understand how the properties ofthermal radiation affect its ability to take in and use energy from the sun.Let's assume that the solar reflectors provide G = 80,000 W/m² of solar heat flux to thereceiver (white glowing cylinder at the top of the tower).(Keep in mind that solar irradiation onto the Earth's surface is typically around 1400W/m². The reflectors are what canincrease this typical heat flux by "bouncing "/reflecting and concentrating this solar flux into the receiver. This is what makes thisa much higher concentration of solar power than something like a solar panel would see from the sun alone. The downside isthat the high magnitude of solar radiation power all being localized in this tower can be deadly for both people and wildlife ifthey get in the way of the concentrators - another reason to put these deep in the middle of the desert. This assignment will helpus see just how much power that is!)For now, assume that the receiver at the top of the tower has a steady-state temperature ofT, = 800 K. Not only is the receiver exposed to solar irradiation from the reflectors, but it also isexposed to surrounding air. Assume that the air is at an average temperature of T∞ = 300 K witha convective heat transfer coefficient of 7 W/m² K due to natural convection (no wind).The outer surface of the receiver can be treated as diffuse and opaque. The spectral absorptivity ofthe coating at the surface of the receiver is given in the figure below:0.9az0.2λ (μm)3Assume that we'll be studying just the receiver at the top of the tower, which can be modeled as avery large cylinder with a diameter of 7m and a height of 12 m. Only the sides of the cylinder areexposed to the air/solar radiation, as the top/bottom have other equipment and mounting structureattached to them. This exposed surface area is represented as A,.

Question

a)b) Find the overall emissivity of the receiver's surface at its steady-state temperature. What is true about the relationship between the emissivity and absorptivity of the receiver'ssurface?○ It can only be said that e(0, 0, X) = a(0, 0, X) since this is the only relationship that is always true.The overall emissivity and absorptivity are equal to each other because the irradiation source is diffuse.They are equal only spectrally, because the surface of the receiver is diffuse and the source of irradiation isdiffuse. BOTH of these MUST be true for the spectral emissivity and absorptivity to be equal to one another.The overall emissivity and absorptivity are equal to each other because the receiver surface is diffuse.O It can only be said that c(0, 0, X) = a(0, 0, X) since the surface of the receiver is diffuse but the source ofirradiation is not specifically stated to be a diffuse source.They are equal only spectrally, because the surface of the receiver is diffuse and the source of irradiation isdiffuse. Only one of these needs to be true for the spectral emissivity and absorptivity to be equal to oneanother. Solar power towers (also called 'central tower' power plants or 'heliostat' power plants), allow solarirradiation to be concentrated into a single receiver by a series of reflectors (mirrors) to maximize theamount of heat flux being used to make clean, renewable energy. Here's the Ivanpah Solar PowerFacility pictured below (https://en.wikipedia.org/wiki/Ivanpah Solar Power Facility B). It is locatedin the Mojave desert by the border of California and Nevada, where irradiation from sunlight is highdue to lack of cloud cover and interference from moisture in the air.In this problem, we'll study a simplified solar power plant model to understand how the properties ofthermal radiation affect its ability to take in and use energy from the sun.Let's assume that the solar reflectors provide G = 80,000 W/m² of solar heat flux to thereceiver (white glowing cylinder at the top of the tower).(Keep in mind that solar irradiation onto the Earth's surface is typically around 1400W/m². The reflectors are what canincrease this typical heat flux by &#34;bouncing &#34;/reflecting and concentrating this solar flux into the receiver. This is what makes thisa much higher concentration of solar power than something like a solar panel would see from the sun alone. The downside isthat the high magnitude of solar radiation power all being localized in this tower can be deadly for both people and wildlife ifthey get in the way of the concentrators - another reason to put these deep in the middle of the desert. This assignment will helpus see just how much power that is!)For now, assume that the receiver at the top of the tower has a steady-state temperature ofT, = 800 K. Not only is the receiver exposed to solar irradiation from the reflectors, but it also isexposed to surrounding air. Assume that the air is at an average temperature of T∞ = 300 K witha convective heat transfer coefficient of 7 W/m² K due to natural convection (no wind).The outer surface of the receiver can be treated as diffuse and opaque. The spectral absorptivity ofthe coating at the surface of the receiver is given in the figure below:0.9az0.2λ (μm)3Assume that we'll be studying just the receiver at the top of the tower, which can be modeled as avery large cylinder with a diameter of 7m and a height of 12 m. Only the sides of the cylinder areexposed to the air/solar radiation, as the top/bottom have other equipment and mounting structureattached to them. This exposed surface area is represented as A,.

Accepted Answer

Given Data:
Receiver Solar radiation Gs=80000 W/m2
Receiver Steady state Temperature Tr=800 K…