✖Diameter of sphere absorber is the diameter as well as the apparent height of the absorber when viewed from the outermost mirror.ⓘ Diameter of Sphere Absorber [D_p]			+10% -10%
✖Rim Angle is defined as the angle made by the line joining the absorber and the outermost mirror with the vertical.ⓘ Rim Angle [Φ_r]			+10% -10%

✖Area of absorber in central receiver collector is defined as the area exposed to the sun that absorbs incident radiation .ⓘ Area of absorber in central receiver collector [A_central]

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Formula

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Area of absorber in central receiver collector

Formula

`"A"_{"central"} = pi/2*"D"_{"p"}^2*(1+sin("Φ"_{"r"})-(cos("Φ"_{"r"})/2))`

Example

`"20.42327m²"=pi/2*("3m")^2*(1+sin("50°")-(cos("50°")/2))`

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Area of absorber in central receiver collector Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Absorber in Central Receiver Collector = pi/2*Diameter of Sphere Absorber^2*(1+sin(Rim Angle)-(cos(Rim Angle)/2))
A_central = pi/2*D_p^2*(1+sin(Φ_r)-(cos(Φ_r)/2))
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Area of Absorber in Central Receiver Collector - (Measured in Square Meter) - Area of absorber in central receiver collector is defined as the area exposed to the sun that absorbs incident radiation .
Diameter of Sphere Absorber - (Measured in Meter) - Diameter of sphere absorber is the diameter as well as the apparent height of the absorber when viewed from the outermost mirror.
Rim Angle - (Measured in Radian) - Rim Angle is defined as the angle made by the line joining the absorber and the outermost mirror with the vertical.

STEP 1: Convert Input(s) to Base Unit

Diameter of Sphere Absorber: 3 Meter --> 3 Meter No Conversion Required
Rim Angle: 50 Degree --> 0.872664625997001 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_central = pi/2*D_p^2*(1+sin(Φ_r)-(cos(Φ_r)/2)) --> pi/2*3^2*(1+sin(0.872664625997001)-(cos(0.872664625997001)/2))

Evaluating ... ...

A_central = 20.4232672449461

STEP 3: Convert Result to Output's Unit

20.4232672449461 Square Meter --> No Conversion Required

FINAL ANSWER

20.4232672449461 ≈ 20.42327 Square Meter <-- Area of Absorber in Central Receiver Collector

(Calculation completed in 00.004 seconds)

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Home » Physics » Solar Energy Systems » Mechanical » Concentrating Collectors » Area of absorber in central receiver collector

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< 23 Concentrating Collectors Calculators

Useful heat gain when collector efficiency factor is present

Go Useful heat gain = (Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)*(((Concentration ratio*Flux absorbed by plate)/Overall loss coefficient)+(Ambient Air Temperature-Inlet fluid temperature flat plate collector))*(1-e^(-(Collector Efficiency Factor*pi*Outer diameter of absorber tube*Overall loss coefficient*Length of Concentrator)/(Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)))

Heat removal factor concentrating collector

Go Collector heat removal factor = ((Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)/(pi*Outer diameter of absorber tube*Length of Concentrator*Overall loss coefficient))*(1-e^(-(Collector Efficiency Factor*pi*Outer diameter of absorber tube*Overall loss coefficient*Length of Concentrator)/(Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)))

Heat removal factor in compound parabolic collector

Go Collector heat removal factor = ((Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)/(Absorber Surface Width*Overall loss coefficient*Length of Concentrator))*(1-e^(-(Collector Efficiency Factor*Absorber Surface Width*Overall loss coefficient*Length of Concentrator)/(Mass Flowrate*Molar Specific Heat Capacity at Constant Pressure)))

Useful heat gain rate in concentrating collector when concentration ratio is present

Go Useful heat gain = Collector heat removal factor*(Concentrator Aperture-Outer diameter of absorber tube)*Length of Concentrator*(Flux absorbed by plate-(Overall loss coefficient/Concentration ratio)*(Inlet fluid temperature flat plate collector-Ambient Air Temperature))

Useful heat gain in compound parabolic collector

Go Useful heat gain = Collector heat removal factor*Concentrator Aperture*Length of Concentrator*(Flux absorbed by plate-((Overall loss coefficient/Concentration ratio)*(Inlet fluid temperature flat plate collector-Ambient Air Temperature)))

Flux absorbed in compound parabolic collector

Go Flux absorbed by plate = ((Hourly beam component*Tilt Factor for Beam Radiation)+(Hourly Diffuse Component/Concentration ratio))*Transmissivity of Cover*Effective reflectivity of concentrator*Absorptivity of Absorber Surface

Instantaneous collection efficiency of concentrating collector

Go Instantaneous Collection Efficiency = Useful heat gain/((Hourly beam component*Tilt Factor for Beam Radiation+Hourly Diffuse Component*Tilt factor for diffused radiation)*Concentrator Aperture*Length of Concentrator)

Useful heat gain when collection efficiency is present

Go Useful heat gain = Instantaneous Collection Efficiency*(Hourly beam component*Tilt Factor for Beam Radiation+Hourly Diffuse Component*Tilt factor for diffused radiation)*Concentrator Aperture*Length of Concentrator

Collector efficiency factor for compound parabolic collector

Go Collector Efficiency Factor = (Overall loss coefficient*(1/Overall loss coefficient+(Absorber Surface Width/(Number of Tubes*pi*Inner diameter absorber tube*Heat Transfer Coefficient Inside))))^-1

Area of Aperture given Useful Heat Gain

Go Effective area of aperture = Useful heat gain/(Flux absorbed by plate-(Overall loss coefficient/Concentration ratio)*(Average temperature of absorber plate-Ambient Air Temperature))

Collector efficiency factor concentrating collector

Go Collector Efficiency Factor = 1/(Overall loss coefficient*(1/Overall loss coefficient+Outer diameter of absorber tube/(Inner diameter absorber tube*Heat Transfer Coefficient Inside)))

Instantaneous collection efficiency of concentrating collector on basis of beam radiation

Go Instantaneous Collection Efficiency = Useful heat gain/(Hourly beam component*Tilt Factor for Beam Radiation*Concentrator Aperture*Length of Concentrator)

Area of absorber in central receiver collector

Go Area of Absorber in Central Receiver Collector = pi/2*Diameter of Sphere Absorber^2*(1+sin(Rim Angle)-(cos(Rim Angle)/2))

Area of Absorber given Heat Loss from Absorber

Go Area of absorber plate = Heat Loss from Collector/(Overall loss coefficient*(Average temperature of absorber plate-Ambient Air Temperature))

Concentration ratio of collector

Go Concentration ratio = (Concentrator Aperture-Outer diameter of absorber tube)/(pi*Outer diameter of absorber tube)

Inclination of reflectors

Go Inclination of Reflector = (pi-Tilt Angle-2*Latitude Angle+2*Declination Angle)/3

Solar Beam Radiation given Useful Heat Gain Rate and Heat Loss Rate from Absorber

Go Solar beam radiation = (Useful heat gain+Heat Loss from Collector)/Effective area of aperture

Useful heat gain in concentrating collector

Go Useful heat gain = Effective area of aperture*Solar beam radiation-Heat Loss from Collector

Outer Diameter of Absorber Tube given Concentration Ratio

Go Outer diameter of absorber tube = Concentrator Aperture/(Concentration ratio*pi+1)

Acceptance Angle of 3-D Concentrator given Maximum Concentration Ratio

Go Acceptance Angle = (acos(1-2/Maximum concentration ratio))/2

Maximum possible concentration ratio of 3-D concentrator

Go Maximum concentration ratio = 2/(1-cos(2*Acceptance Angle))

Acceptance Angle of 2-D Concentrator given Maximum Concentration Ratio

Go Acceptance Angle = asin(1/Maximum concentration ratio)

Maximum possible concentration ratio of 2-D concentrator

Go Maximum concentration ratio = 1/sin(Acceptance Angle)

Area of absorber in central receiver collector Formula

Area of Absorber in Central Receiver Collector = pi/2*Diameter of Sphere Absorber^2*(1+sin(Rim Angle)-(cos(Rim Angle)/2))
A_central = pi/2*D_p^2*(1+sin(Φ_r)-(cos(Φ_r)/2))

What is central receiver?

The central receiver (or power tower) systems use a field of distributed mirrors – heliostats – that individually track the sun and focus the sunlight on the top of a tower.

How to Calculate Area of absorber in central receiver collector?

Area of absorber in central receiver collector calculator uses Area of Absorber in Central Receiver Collector = pi/2*Diameter of Sphere Absorber^2*(1+sin(Rim Angle)-(cos(Rim Angle)/2)) to calculate the Area of Absorber in Central Receiver Collector, The Area of absorber in central receiver collector formula is defined as the area exposed to the sun that absorbs incident radiation. Area of Absorber in Central Receiver Collector is denoted by A_central symbol.

How to calculate Area of absorber in central receiver collector using this online calculator? To use this online calculator for Area of absorber in central receiver collector, enter Diameter of Sphere Absorber (D_p) & Rim Angle (Φ_r) and hit the calculate button. Here is how the Area of absorber in central receiver collector calculation can be explained with given input values -> 20.42327 = pi/2*3^2*(1+sin(0.872664625997001)-(cos(0.872664625997001)/2)).

FAQ

What is Area of absorber in central receiver collector?

The Area of absorber in central receiver collector formula is defined as the area exposed to the sun that absorbs incident radiation and is represented as A_central = pi/2*D_p^2*(1+sin(Φ_r)-(cos(Φ_r)/2)) or Area of Absorber in Central Receiver Collector = pi/2*Diameter of Sphere Absorber^2*(1+sin(Rim Angle)-(cos(Rim Angle)/2)). Diameter of sphere absorber is the diameter as well as the apparent height of the absorber when viewed from the outermost mirror & Rim Angle is defined as the angle made by the line joining the absorber and the outermost mirror with the vertical.

How to calculate Area of absorber in central receiver collector?

The Area of absorber in central receiver collector formula is defined as the area exposed to the sun that absorbs incident radiation is calculated using Area of Absorber in Central Receiver Collector = pi/2*Diameter of Sphere Absorber^2*(1+sin(Rim Angle)-(cos(Rim Angle)/2)). To calculate Area of absorber in central receiver collector, you need Diameter of Sphere Absorber (D_p) & Rim Angle (Φ_r). With our tool, you need to enter the respective value for Diameter of Sphere Absorber & Rim Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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