Area of Aperture given Useful Heat Gain Solution

STEP 0: Pre-Calculation Summary
Formula Used
Effective area of aperture = Useful heat gain/(Flux absorbed by plate- (Overall loss coefficient/Concentration ratio)*(Average temperature of absorber plate-Ambient Air Temperature))
Aa = qu/(Sflux- (Ul/C)*(Tpm-Ta))
This formula uses 7 Variables
Variables Used
Effective area of aperture - (Measured in Square Meter) - Effective area of aperture is defined as total area of aperture exposed to the incident radiation.
Useful heat gain - (Measured in Watt) - Useful heat gain is defined as the rate of heat transfer to the working fluid.
Flux absorbed by plate - (Measured in Watt per Square Meter) - Flux absorbed by plate is defined as the incident solar flux absorbed in the absorber plate.
Overall loss coefficient - (Measured in Watt per Square Meter per Kelvin) - Overall loss coefficient is defined as the heat loss from collector per unit area of absorber plate and temperature difference between absorber plate and surrounding air.
Concentration ratio - Concentration ratio is defined as the ratio of the effective area of aperture to the surface area of the absorber.
Average temperature of absorber plate - (Measured in Kelvin) - Average temperature of absorber plate is defined as the temperature spread across the surface area of the absorber plate.
Ambient Air Temperature - (Measured in Kelvin) - Ambient Air Temperature is the temperature of the surrounding medium.
STEP 1: Convert Input(s) to Base Unit
Useful heat gain: 20 Watt --> 20 Watt No Conversion Required
Flux absorbed by plate: 98 Joule per Second per Square Meter --> 98 Watt per Square Meter (Check conversion here)
Overall loss coefficient: 1.25 Watt per Square Meter per Kelvin --> 1.25 Watt per Square Meter per Kelvin No Conversion Required
Concentration ratio: 0.8 --> No Conversion Required
Average temperature of absorber plate: 310 Kelvin --> 310 Kelvin No Conversion Required
Ambient Air Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Aa = qu/(Sflux- (Ul/C)*(Tpm-Ta)) --> 20/(98- (1.25/0.8)*(310-300))
Evaluating ... ...
Aa = 0.242792109256449
STEP 3: Convert Result to Output's Unit
0.242792109256449 Square Meter --> No Conversion Required
FINAL ANSWER
0.242792109256449 0.242792 Square Meter <-- Effective area of aperture
(Calculation completed in 00.020 seconds)

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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 Aperture given Useful Heat Gain Formula

Effective area of aperture = Useful heat gain/(Flux absorbed by plate- (Overall loss coefficient/Concentration ratio)*(Average temperature of absorber plate-Ambient Air Temperature))
Aa = qu/(Sflux- (Ul/C)*(Tpm-Ta))

How do we get useful heat gain?

Useful heat gain is nothing but the difference between the incident (absorbed) radiation and the heat lost due to convection, re-radiation, and conduction.

How to Calculate Area of Aperture given Useful Heat Gain?

Area of Aperture given Useful Heat Gain calculator uses Effective area of aperture = Useful heat gain/(Flux absorbed by plate- (Overall loss coefficient/Concentration ratio)*(Average temperature of absorber plate-Ambient Air Temperature)) to calculate the Effective area of aperture, The Area of Aperture given Useful Heat Gain formula is defined as the total area of aperture exposed to the incident radiation. Effective area of aperture is denoted by Aa symbol.

How to calculate Area of Aperture given Useful Heat Gain using this online calculator? To use this online calculator for Area of Aperture given Useful Heat Gain, enter Useful heat gain (qu), Flux absorbed by plate (Sflux), Overall loss coefficient (Ul), Concentration ratio (C), Average temperature of absorber plate (Tpm) & Ambient Air Temperature (Ta) and hit the calculate button. Here is how the Area of Aperture given Useful Heat Gain calculation can be explained with given input values -> 0.242792 = 20/(98- (1.25/0.8)*(310-300)).

FAQ

What is Area of Aperture given Useful Heat Gain?
The Area of Aperture given Useful Heat Gain formula is defined as the total area of aperture exposed to the incident radiation and is represented as Aa = qu/(Sflux- (Ul/C)*(Tpm-Ta)) or Effective area of aperture = Useful heat gain/(Flux absorbed by plate- (Overall loss coefficient/Concentration ratio)*(Average temperature of absorber plate-Ambient Air Temperature)). Useful heat gain is defined as the rate of heat transfer to the working fluid, Flux absorbed by plate is defined as the incident solar flux absorbed in the absorber plate, Overall loss coefficient is defined as the heat loss from collector per unit area of absorber plate and temperature difference between absorber plate and surrounding air, Concentration ratio is defined as the ratio of the effective area of aperture to the surface area of the absorber, Average temperature of absorber plate is defined as the temperature spread across the surface area of the absorber plate & Ambient Air Temperature is the temperature of the surrounding medium.
How to calculate Area of Aperture given Useful Heat Gain?
The Area of Aperture given Useful Heat Gain formula is defined as the total area of aperture exposed to the incident radiation is calculated using Effective area of aperture = Useful heat gain/(Flux absorbed by plate- (Overall loss coefficient/Concentration ratio)*(Average temperature of absorber plate-Ambient Air Temperature)). To calculate Area of Aperture given Useful Heat Gain, you need Useful heat gain (qu), Flux absorbed by plate (Sflux), Overall loss coefficient (Ul), Concentration ratio (C), Average temperature of absorber plate (Tpm) & Ambient Air Temperature (Ta). With our tool, you need to enter the respective value for Useful heat gain, Flux absorbed by plate, Overall loss coefficient, Concentration ratio, Average temperature of absorber plate & Ambient Air Temperature 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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