Useful heat gain in compound parabolic collector Calculator

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✖Collector heat removal factor is the ratio of the actual heat transfer to the maximum possible heat transfer through the collector plate.ⓘ Collector heat removal factor [F_R]			+10% -10%
✖Concentrator aperture is defined as the opening through which sun rays pass .ⓘ Concentrator Aperture [W]			+10% -10%
✖Length of concentrator is the length of concentrator from one end to other end.ⓘ Length of Concentrator [L]			+10% -10%
✖Flux absorbed by plate is defined as the incident solar flux absorbed in the absorber plate.ⓘ Flux absorbed by plate [S_flux]			+10% -10%
✖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.ⓘ Overall loss coefficient [U_l]			+10% -10%
✖Concentration ratio is defined as the ratio of the effective area of aperture to the surface area of the absorber.ⓘ Concentration ratio [C]			+10% -10%
✖Inlet fluid temperature flat plate collector is defined as the temperature at which the liquid enters the liquid flat plate collector.ⓘ Inlet fluid temperature flat plate collector [T_fi]			+10% -10%
✖Ambient Air Temperature is the temperature of the surrounding medium.ⓘ Ambient Air Temperature [T_a]			+10% -10%

✖Useful heat gain is defined as the rate of heat transfer to the working fluid.ⓘ Useful heat gain in compound parabolic collector [q_u]

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Formula

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Useful heat gain in compound parabolic collector

Formula

`"q"_{"u"} = "F"_{"R"}*"W"*"L"*("S"_{"flux"}-(("U"_{"l"}/"C")*("T"_{"fi"}-"T"_{"a"})))`

Example

`"5786.813W"="0.1"*"7m"*"15m"*("98J/sm²"-(("1.25W/m²*K"/"0.8")*("10K"-"300K")))`

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Useful heat gain in compound parabolic collector Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
q_u = F_R*W*L*(S_flux-((U_l/C)*(T_fi-T_a)))
This formula uses 9 Variables

Variables Used

Useful heat gain - (Measured in Watt) - Useful heat gain is defined as the rate of heat transfer to the working fluid.
Collector heat removal factor - Collector heat removal factor is the ratio of the actual heat transfer to the maximum possible heat transfer through the collector plate.
Concentrator Aperture - (Measured in Meter) - Concentrator aperture is defined as the opening through which sun rays pass .
Length of Concentrator - (Measured in Meter) - Length of concentrator is the length of concentrator from one end to other end.
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.
Inlet fluid temperature flat plate collector - (Measured in Kelvin) - Inlet fluid temperature flat plate collector is defined as the temperature at which the liquid enters the liquid flat plate collector.
Ambient Air Temperature - (Measured in Kelvin) - Ambient Air Temperature is the temperature of the surrounding medium.

STEP 1: Convert Input(s) to Base Unit

Collector heat removal factor: 0.1 --> No Conversion Required
Concentrator Aperture: 7 Meter --> 7 Meter No Conversion Required
Length of Concentrator: 15 Meter --> 15 Meter 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
Inlet fluid temperature flat plate collector: 10 Kelvin --> 10 Kelvin No Conversion Required
Ambient Air Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q_u = F_R*W*L*(S_flux-((U_l/C)*(T_fi-T_a))) --> 0.1*7*15*(98-((1.25/0.8)*(10-300)))

Evaluating ... ...

q_u = 5786.8125

STEP 3: Convert Result to Output's Unit

5786.8125 Watt --> No Conversion Required

FINAL ANSWER

5786.8125 ≈ 5786.813 Watt <-- Useful heat gain

(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)

Useful heat gain in compound parabolic collector Formula

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 Useful heat gain in compound parabolic collector?

Useful heat gain in compound parabolic collector calculator uses 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))) to calculate the Useful heat gain, The Useful heat gain in compound parabolic collector formula is defined as the amount of heat absorbed from the incident radiation from the sun which has further applications. Useful heat gain is denoted by q_u symbol.

How to calculate Useful heat gain in compound parabolic collector using this online calculator? To use this online calculator for Useful heat gain in compound parabolic collector, enter Collector heat removal factor (F_R), Concentrator Aperture (W), Length of Concentrator (L), Flux absorbed by plate (S_flux), Overall loss coefficient (U_l), Concentration ratio (C), Inlet fluid temperature flat plate collector (T_fi) & Ambient Air Temperature (T_a) and hit the calculate button. Here is how the Useful heat gain in compound parabolic collector calculation can be explained with given input values -> 5786.813 = 0.1*7*15*(98-((1.25/0.8)*(10-300))).

FAQ

What is Useful heat gain in compound parabolic collector?

The Useful heat gain in compound parabolic collector formula is defined as the amount of heat absorbed from the incident radiation from the sun which has further applications and is represented as q_u = F_R*W*L*(S_flux-((U_l/C)*(T_fi-T_a))) or 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))). Collector heat removal factor is the ratio of the actual heat transfer to the maximum possible heat transfer through the collector plate, Concentrator aperture is defined as the opening through which sun rays pass , Length of concentrator is the length of concentrator from one end to other end, 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, Inlet fluid temperature flat plate collector is defined as the temperature at which the liquid enters the liquid flat plate collector & Ambient Air Temperature is the temperature of the surrounding medium.

How to calculate Useful heat gain in compound parabolic collector?

The Useful heat gain in compound parabolic collector formula is defined as the amount of heat absorbed from the incident radiation from the sun which has further applications is calculated using 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))). To calculate Useful heat gain in compound parabolic collector, you need Collector heat removal factor (F_R), Concentrator Aperture (W), Length of Concentrator (L), Flux absorbed by plate (S_flux), Overall loss coefficient (U_l), Concentration ratio (C), Inlet fluid temperature flat plate collector (T_fi) & Ambient Air Temperature (T_a). With our tool, you need to enter the respective value for 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 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Useful heat gain?

In this formula, Useful heat gain uses 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. We can use 4 other way(s) to calculate the same, which is/are as follows -

Useful heat gain = Effective area of aperture*Solar beam radiation-Heat Loss from Collector
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 = Instantaneous Collection Efficiency*(Hourly beam component*Tilt Factor for Beam Radiation+Hourly Diffuse Component*Tilt factor for diffused radiation)*Concentrator Aperture*Length of Concentrator
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)))

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