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Area of absorber in central receiver collector Formula

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Area of absorber in central receiver collector is defined as the area exposed to the sun that absorbs incident radiation . Check FAQs

A central = \frac{π}{2} \cdot {D p}^{2} \cdot (1 + \sin (Φ r) - (\frac{\cos (Φ r)}{2}))

A_central - Area of Absorber in Central Receiver Collector?D_p - Diameter of Sphere Absorber?Φ_r - Rim Angle?π - Archimedes' constant?

Area of absorber in central receiver collector Example

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Here is how the Area of absorber in central receiver collector equation looks like with Values.

Here is how the Area of absorber in central receiver collector equation looks like with Units.

Here is how the Area of absorber in central receiver collector equation looks like.

20.4233 = \frac{3.1416}{2} \cdot 3^{2} \cdot (1 + \sin (50) - (\frac{\cos (50)}{2}))

20.4233m² = \frac{3.1416}{2} \cdot {3m}^{2} \cdot (1 + \sin (50°) - (\frac{\cos (50°)}{2}))

20.4233 = \frac{3.1416}{2} \cdot 3^{2} \cdot (1 + \sin (50) - (\frac{\cos (50)}{2}))

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Area of absorber in central receiver collector Solution

Follow our step by step solution on how to calculate Area of absorber in central receiver collector?

FIRST Step Consider the formula

A central = \frac{π}{2} \cdot {D p}^{2} \cdot (1 + \sin (Φ r) - (\frac{\cos (Φ r)}{2}))

Next Step Substitute values of Variables

∴

A central = \frac{π}{2} \cdot {3m}^{2} \cdot (1 + \sin (50°) - (\frac{\cos (50°)}{2}))

Next Step Substitute values of Constants

∴

A central = \frac{3.1416}{2} \cdot {3m}^{2} \cdot (1 + \sin (50°) - (\frac{\cos (50°)}{2}))

Next Step Convert Units

∴

A central = \frac{3.1416}{2} \cdot {3m}^{2} \cdot (1 + \sin (0.8727rad) - (\frac{\cos (0.8727rad)}{2}))

Next Step Prepare to Evaluate

∴

A central = \frac{3.1416}{2} \cdot 3^{2} \cdot (1 + \sin (0.8727) - (\frac{\cos (0.8727)}{2}))

Next Step Evaluate

∴

A central = 20.4232672449461m²

LAST Step Rounding Answer

∴

A central = 20.4233m²

Area of absorber in central receiver collector Formula Elements

Variables

Constants

Functions

Area of Absorber in Central Receiver Collector

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

Symbol: A_central

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Absorber in Central Receiver Collector

Diameter of Sphere Absorber

Diameter of sphere absorber is the diameter as well as the apparent height of the absorber when viewed from the outermost mirror.

Symbol: D_p

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Diameter of Sphere Absorber

Rim Angle

Rim Angle is defined as the angle made by the line joining the absorber and the outermost mirror with the vertical.

Symbol: Φ_r

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Rim Angle

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Concentrating Collectors category

Go Maximum possible concentration ratio of 2-D concentrator

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Go Maximum possible concentration ratio of 3-D concentrator

C m = \frac{2}{1 - \cos (2 \cdot θ a)}

Go Useful heat gain in concentrating collector

q u = A a \cdot S - q l

Go Inclination of reflectors

Ψ = \frac{π - β - 2 \cdot Φ + 2 \cdot δ}{3}

How to Evaluate Area of absorber in central receiver collector?

Area of absorber in central receiver collector evaluator uses Area of Absorber in Central Receiver Collector = pi/2*Diameter of Sphere Absorber^2*(1+sin(Rim Angle)-(cos(Rim Angle)/2)) to evaluate 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 evaluate Area of absorber in central receiver collector using this online evaluator? To use this online evaluator for Area of absorber in central receiver collector, enter Diameter of Sphere Absorber (D_p) & Rim Angle (Φ_r) and hit the calculate button.

FAQs on Area of absorber in central receiver collector

What is the formula to find Area of absorber in central receiver collector?

The formula of Area of absorber in central receiver collector is expressed as Area of Absorber in Central Receiver Collector = pi/2*Diameter of Sphere Absorber^2*(1+sin(Rim Angle)-(cos(Rim Angle)/2)). Here is an example- 20.42327 = pi/2*3^2*(1+sin(0.872664625997001)-(cos(0.872664625997001)/2)).

How to calculate Area of absorber in central receiver collector?

With Diameter of Sphere Absorber (D_p) & Rim Angle (Φ_r) we can find Area of absorber in central receiver collector using the formula - Area of Absorber in Central Receiver Collector = pi/2*Diameter of Sphere Absorber^2*(1+sin(Rim Angle)-(cos(Rim Angle)/2)). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) function(s).

Can the Area of absorber in central receiver collector be negative?

No, the Area of absorber in central receiver collector, measured in Area cannot be negative.

Which unit is used to measure Area of absorber in central receiver collector?

Area of absorber in central receiver collector is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of absorber in central receiver collector can be measured.

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