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Assume the sun has now set and it is night time. Under these conditions, assume there is no significant source of irradiation to the receiver (G, 0). Also assume that the molten salt inside of the receiver is very well stirred and mixed and that there is no change in air temperature or convective heat transfer coefficient at night in the desert in the summer. The receiver is still producing electricity at night from the stored thermal energy in the molten salts acquired during the day time. Because conditions have changed, the receiver is now no longer at steady-state. Assume that the molten salts have a density of 1500 kg/m³, specific heat capacity of 1300 J/kgK, and thermal conductivity of 0.45 W/mK (taken from this source and this source on properties of nitrate molten salts). What is the energy balance that now describes the receiver? O O dT, mc --A,coT-A,domu + gelec me me dT, dt dT, dt =-EOT; - goome - Gelec -A,EOT - A-domu gelec dT, -mc- cd=- A,coT$ — Arqoomu - gelec de

Assume the sun has now set and it is night time. Under these conditions, assume there is no significant source of irradiation to the receiver (G, 0). Also assume that the molten salt inside of the receiver is very well stirred and mixed and that there is no change in air temperature or convective heat transfer coefficient at night in the desert in the summer. The receiver is still producing electricity at night from the stored thermal energy in the molten salts acquired during the day time. Because conditions have changed, the receiver is now no longer at steady-state. Assume that the molten salts have a density of 1500 kg/m³, specific heat capacity of 1300 J/kgK, and thermal conductivity of 0.45 W/mK (taken from this source and this source on properties of nitrate molten salts). What is the energy balance that now describes the receiver? O O dT, mc --A,coT-A,domu + gelec me me dT, dt dT, dt =-EOT; - goome - Gelec -A,EOT - A-domu gelec dT, -mc- cd=- A,coT$ — Arqoomu - gelec de

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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b) You want to know the temperature of the receiver after 8 hours of night time have passed (in the conditions described in the previous question). What technique would you use to determine this temperature? General lumped capacitance or 1-D transient analysis? Why?

Assume the sun has now set and it is night time. Under these conditions, assume there is no significant source of irradiation to the receiver (G, ≈ 0). Also assume that the molten salt inside of the receiver is very well stirred and mixed and that there is no change in air temperature or convective heat transfer coefficient at night in the desert in the summer. The receiver is still producing electricity at night from the stored thermal energy in the molten salts acquired during the day time. Because conditions have changed, the receiver is now no longer at steady-state. Assume that the molten salts have a density of 1500 kg/m³, specific heat capacity of 1300 J/kgK, and thermal conductivity of 0.45 W/mK (taken from this source and this source on properties of nitrate molten salts). What is the energy balance that now describes the receiver? dT, mc- = me dT, dt O dT, me =-A,EOT - A-domu + gelec = -EOT Iconv gelec -A,EOT - A-domu gelec dT, -mc- = -A,EOT - Arome gelec de
Transcribed Image Text:Assume the sun has now set and it is night time. Under these conditions, assume there is no significant source of irradiation to the receiver (G, ≈ 0). Also assume that the molten salt inside of the receiver is very well stirred and mixed and that there is no change in air temperature or convective heat transfer coefficient at night in the desert in the summer. The receiver is still producing electricity at night from the stored thermal energy in the molten salts acquired during the day time. Because conditions have changed, the receiver is now no longer at steady-state. Assume that the molten salts have a density of 1500 kg/m³, specific heat capacity of 1300 J/kgK, and thermal conductivity of 0.45 W/mK (taken from this source and this source on properties of nitrate molten salts). What is the energy balance that now describes the receiver? dT, mc- = me dT, dt O dT, me =-A,EOT - A-domu + gelec = -EOT Iconv gelec -A,EOT - A-domu gelec dT, -mc- = -A,EOT - Arome gelec de
Solar power towers (also called 'central tower' power plants or 'heliostat' power plants), allow solar irradiation to be concentrated into a single receiver by a series of reflectors (mirrors) to maximize the amount of heat flux being used to make clean, renewable energy. Here's the Ivanpah Solar Power Facility pictured below (https://en.wikipedia.org/wiki/Ivanpah Solar Power Facility B). It is located in the Mojave desert by the border of California and Nevada, where irradiation from sunlight is high due 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 of thermal 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 the receiver (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 can increase this typical heat flux by "bouncing "/reflecting and concentrating this solar flux into the receiver. This is what makes this a much higher concentration of solar power than something like a solar panel would see from the sun alone. The downside is that the high magnitude of solar radiation power all being localized in this tower can be deadly for both people and wildlife if they get in the way of the concentrators - another reason to put these deep in the middle of the desert. This assignment will help us see just how much power that is!) For now, assume that the receiver at the top of the tower has a steady-state temperature of T, = 800 K. Not only is the receiver exposed to solar irradiation from the reflectors, but it also is exposed to surrounding air. Assume that the air is at an average temperature of T∞ = 300 K with a 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 of the coating at the surface of the receiver is given in the figure below: 0.9 az 0.2 λ (μm) 3 Assume that we'll be studying just the receiver at the top of the tower, which can be modeled as a very large cylinder with a diameter of 7m and a height of 12 m. Only the sides of the cylinder are exposed to the air/solar radiation, as the top/bottom have other equipment and mounting structure attached to them. This exposed surface area is represented as A,.
Transcribed Image Text:Solar power towers (also called 'central tower' power plants or 'heliostat' power plants), allow solar irradiation to be concentrated into a single receiver by a series of reflectors (mirrors) to maximize the amount of heat flux being used to make clean, renewable energy. Here's the Ivanpah Solar Power Facility pictured below (https://en.wikipedia.org/wiki/Ivanpah Solar Power Facility B). It is located in the Mojave desert by the border of California and Nevada, where irradiation from sunlight is high due 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 of thermal 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 the receiver (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 can increase this typical heat flux by "bouncing "/reflecting and concentrating this solar flux into the receiver. This is what makes this a much higher concentration of solar power than something like a solar panel would see from the sun alone. The downside is that the high magnitude of solar radiation power all being localized in this tower can be deadly for both people and wildlife if they get in the way of the concentrators - another reason to put these deep in the middle of the desert. This assignment will help us see just how much power that is!) For now, assume that the receiver at the top of the tower has a steady-state temperature of T, = 800 K. Not only is the receiver exposed to solar irradiation from the reflectors, but it also is exposed to surrounding air. Assume that the air is at an average temperature of T∞ = 300 K with a 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 of the coating at the surface of the receiver is given in the figure below: 0.9 az 0.2 λ (μm) 3 Assume that we'll be studying just the receiver at the top of the tower, which can be modeled as a very large cylinder with a diameter of 7m and a height of 12 m. Only the sides of the cylinder are exposed to the air/solar radiation, as the top/bottom have other equipment and mounting structure attached to them. This exposed surface area is represented as A,.
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