Collector efficiency factor for compound parabolic collector Calculator

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✖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%
✖Absorber surface width is the measurement or extent of the surface from side to side.ⓘ Absorber Surface Width [b]			+10% -10%
✖Number of tubes are the total tubes through which the fluid flows and takes heat from the absorber surface.ⓘ Number of Tubes [N]			+10% -10%
✖Inner diameter absorber tube is defined as the inside diameter of absorber tube.ⓘ Inner diameter absorber tube [D_i]			+10% -10%
✖Heat transfer coefficient inside is the heat transfer coefficient on the inside surface of the tube.ⓘ Heat Transfer Coefficient Inside [h_f]			+10% -10%

✖Collector efficiency factor is defined as the ratio of the actual thermal collector power to the power of an ideal collector whose absorber temperature is equal to the fluid temperature.ⓘ Collector efficiency factor for compound parabolic collector [F′]

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Collector efficiency factor for compound parabolic collector

Formula

`"F′" = ("U"_{"l"}*(1/"U"_{"l"}+("b"/("N"*pi*"D"_{"i"}*"h"_{"f"}))))^-1`

Example

`"0.84071"=("1.25W/m²*K"*(1/"1.25W/m²*K"+("0.75m"/("6"*pi*"0.15m"*"1.75W/m²*K"))))^-1`

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Collector efficiency factor for compound parabolic collector Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
F′ = (U_l*(1/U_l+(b/(N*pi*D_i*h_f))))^-1
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Collector Efficiency Factor - Collector efficiency factor is defined as the ratio of the actual thermal collector power to the power of an ideal collector whose absorber temperature is equal to the fluid temperature.
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.
Absorber Surface Width - (Measured in Meter) - Absorber surface width is the measurement or extent of the surface from side to side.
Number of Tubes - Number of tubes are the total tubes through which the fluid flows and takes heat from the absorber surface.
Inner diameter absorber tube - (Measured in Meter) - Inner diameter absorber tube is defined as the inside diameter of absorber tube.
Heat Transfer Coefficient Inside - (Measured in Watt per Square Meter per Kelvin) - Heat transfer coefficient inside is the heat transfer coefficient on the inside surface of the tube.

STEP 1: Convert Input(s) to Base Unit

Overall loss coefficient: 1.25 Watt per Square Meter per Kelvin --> 1.25 Watt per Square Meter per Kelvin No Conversion Required
Absorber Surface Width: 0.75 Meter --> 0.75 Meter No Conversion Required
Number of Tubes: 6 --> No Conversion Required
Inner diameter absorber tube: 0.15 Meter --> 0.15 Meter No Conversion Required
Heat Transfer Coefficient Inside: 1.75 Watt per Square Meter per Kelvin --> 1.75 Watt per Square Meter per Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F′ = (U_l*(1/U_l+(b/(N*pi*D_i*h_f))))^-1 --> (1.25*(1/1.25+(0.75/(6*pi*0.15*1.75))))^-1

Evaluating ... ...

F′ = 0.840710448171943

STEP 3: Convert Result to Output's Unit

0.840710448171943 --> No Conversion Required

FINAL ANSWER

0.840710448171943 ≈ 0.84071 <-- Collector Efficiency Factor

(Calculation completed in 00.004 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)

Collector efficiency factor for compound parabolic collector Formula

What does collector efficiency factor specify?

The collector efficiency factor F′ conveys information about the variation in temperature over a segment . It is is essentially a constant factor for any collector design and fluid flow rate.

How to Calculate Collector efficiency factor for compound parabolic collector?

Collector efficiency factor for compound parabolic collector calculator uses 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 to calculate the Collector Efficiency Factor, The Collector efficiency factor for compound parabolic collector formula is defined as the ratio of the actual thermal collector power to the power of an ideal collector whose absorber temperature is equal to the fluid temperature. Collector Efficiency Factor is denoted by F′ symbol.

How to calculate Collector efficiency factor for compound parabolic collector using this online calculator? To use this online calculator for Collector efficiency factor for compound parabolic collector, enter Overall loss coefficient (U_l), Absorber Surface Width (b), Number of Tubes (N), Inner diameter absorber tube (D_i) & Heat Transfer Coefficient Inside (h_f) and hit the calculate button. Here is how the Collector efficiency factor for compound parabolic collector calculation can be explained with given input values -> 0.84071 = (1.25*(1/1.25+(0.75/(6*pi*0.15*1.75))))^-1.

FAQ

What is Collector efficiency factor for compound parabolic collector?

The Collector efficiency factor for compound parabolic collector formula is defined as the ratio of the actual thermal collector power to the power of an ideal collector whose absorber temperature is equal to the fluid temperature and is represented as F′ = (U_l*(1/U_l+(b/(N*pi*D_i*h_f))))^-1 or 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. 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, Absorber surface width is the measurement or extent of the surface from side to side, Number of tubes are the total tubes through which the fluid flows and takes heat from the absorber surface, Inner diameter absorber tube is defined as the inside diameter of absorber tube & Heat transfer coefficient inside is the heat transfer coefficient on the inside surface of the tube.

How to calculate Collector efficiency factor for compound parabolic collector?

The Collector efficiency factor for compound parabolic collector formula is defined as the ratio of the actual thermal collector power to the power of an ideal collector whose absorber temperature is equal to the fluid temperature is calculated using 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. To calculate Collector efficiency factor for compound parabolic collector, you need Overall loss coefficient (U_l), Absorber Surface Width (b), Number of Tubes (N), Inner diameter absorber tube (D_i) & Heat Transfer Coefficient Inside (h_f). With our tool, you need to enter the respective value for Overall loss coefficient, Absorber Surface Width, Number of Tubes, Inner diameter absorber tube & Heat Transfer Coefficient Inside 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 Collector Efficiency Factor?

In this formula, Collector Efficiency Factor uses Overall loss coefficient, Absorber Surface Width, Number of Tubes, Inner diameter absorber tube & Heat Transfer Coefficient Inside. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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