Heat removal factor concentrating collector Calculator

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Concentrating Collectors

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✖Mass flowrate is the mass moved in unit amount of time.ⓘ Mass Flowrate [m]			+10% -10%
✖Molar Specific Heat Capacity at Constant Pressure, (of a gas) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure.ⓘ Molar Specific Heat Capacity at Constant Pressure [C_{p molar}]			+10% -10%
✖Outer diameter of absorber tube is the measurement of the outside edges of the tube passing through its center.ⓘ Outer diameter of absorber tube [D_o]			+10% -10%
✖Length of concentrator is the length of concentrator from one end to other end.ⓘ Length of Concentrator [L]			+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%
✖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 [F′]			+10% -10%

✖Collector heat removal factor is the ratio of the actual heat transfer to the maximum possible heat transfer through the collector plate.ⓘ Heat removal factor concentrating collector [F_R]

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Formula

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Heat removal factor concentrating collector

Formula

`"F"_{"R"} = (("m"*"C"_{"p molar"})/(pi*"D"_{"o"}*"L"*"U"_{"l"}))*(1-e^(-("F′"*pi*"D"_{"o"}*"U"_{"l"}*"L")/("m"*"C"_{"p molar"})))`

Example

`"0.296408"=(("12kg/s"*"122J/K*mol")/(pi*"2m"*"15m"*"1.25W/m²*K"))*(1-e^(-("0.3"*pi*"2m"*"1.25W/m²*K"*"15m")/("12kg/s"*"122J/K*mol")))`

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Heat removal factor concentrating collector Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
F_R = ((m*C_{p molar})/(pi*D_o*L*U_l))*(1-e^(-(F′*pi*D_o*U_l*L)/(m*C_{p molar})))
This formula uses 2 Constants, 7 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Variables Used

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.
Mass Flowrate - (Measured in Kilogram per Second) - Mass flowrate is the mass moved in unit amount of time.
Molar Specific Heat Capacity at Constant Pressure - (Measured in Joule Per Kelvin Per Mole) - Molar Specific Heat Capacity at Constant Pressure, (of a gas) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure.
Outer diameter of absorber tube - (Measured in Meter) - Outer diameter of absorber tube is the measurement of the outside edges of the tube passing through its center.
Length of Concentrator - (Measured in Meter) - Length of concentrator is the length of concentrator from one end to other end.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Mass Flowrate: 12 Kilogram per Second --> 12 Kilogram per Second No Conversion Required
Molar Specific Heat Capacity at Constant Pressure: 122 Joule Per Kelvin Per Mole --> 122 Joule Per Kelvin Per Mole No Conversion Required
Outer diameter of absorber tube: 2 Meter --> 2 Meter No Conversion Required
Length of Concentrator: 15 Meter --> 15 Meter No Conversion Required
Overall loss coefficient: 1.25 Watt per Square Meter per Kelvin --> 1.25 Watt per Square Meter per Kelvin No Conversion Required
Collector Efficiency Factor: 0.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_R = ((m*C_{p molar})/(pi*D_o*L*U_l))*(1-e^(-(F′*pi*D_o*U_l*L)/(m*C_{p molar}))) --> ((12*122)/(pi*2*15*1.25))*(1-e^(-(0.3*pi*2*1.25*15)/(12*122)))

Evaluating ... ...

F_R = 0.296407764633985

STEP 3: Convert Result to Output's Unit

0.296407764633985 --> No Conversion Required

FINAL ANSWER

0.296407764633985 ≈ 0.296408 <-- Collector heat removal factor

(Calculation completed in 00.005 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)

Heat removal factor concentrating collector Formula

Why is collector heat removal factor important?

It is an important design parameter since it is a measure of the thermal resistance encountered by the absorbed solar radiation in reaching the collector fluid.

How to Calculate Heat removal factor concentrating collector?

Heat removal factor concentrating collector calculator uses 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))) to calculate the Collector heat removal factor, The Heat removal factor concentrating collector formula is defined as the ratio of the actual heat transfer to the maximum possible heat transfer through the collector plate. Collector heat removal factor is denoted by F_R symbol.

How to calculate Heat removal factor concentrating collector using this online calculator? To use this online calculator for Heat removal factor concentrating collector, enter Mass Flowrate (m), Molar Specific Heat Capacity at Constant Pressure (C_{p molar}), Outer diameter of absorber tube (D_o), Length of Concentrator (L), Overall loss coefficient (U_l) & Collector Efficiency Factor (F′) and hit the calculate button. Here is how the Heat removal factor concentrating collector calculation can be explained with given input values -> 0.296408 = ((12*122)/(pi*2*15*1.25))*(1-e^(-(0.3*pi*2*1.25*15)/(12*122))).

FAQ

What is Heat removal factor concentrating collector?

The Heat removal factor concentrating collector formula is defined as the ratio of the actual heat transfer to the maximum possible heat transfer through the collector plate and is represented as F_R = ((m*C_{p molar})/(pi*D_o*L*U_l))*(1-e^(-(F′*pi*D_o*U_l*L)/(m*C_{p molar}))) or 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))). Mass flowrate is the mass moved in unit amount of time, Molar Specific Heat Capacity at Constant Pressure, (of a gas) is the amount of heat required to raise the temperature of 1 mol of the gas by 1 °C at the constant pressure, Outer diameter of absorber tube is the measurement of the outside edges of the tube passing through its center, Length of concentrator is the length of concentrator from one end to other end, 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 & 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.

How to calculate Heat removal factor concentrating collector?

The Heat removal factor concentrating collector formula is defined as the ratio of the actual heat transfer to the maximum possible heat transfer through the collector plate is calculated using 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))). To calculate Heat removal factor concentrating collector, you need Mass Flowrate (m), Molar Specific Heat Capacity at Constant Pressure (C_{p molar}), Outer diameter of absorber tube (D_o), Length of Concentrator (L), Overall loss coefficient (U_l) & Collector Efficiency Factor (F′). With our tool, you need to enter the respective value for Mass Flowrate, Molar Specific Heat Capacity at Constant Pressure, Outer diameter of absorber tube, Length of Concentrator, Overall loss coefficient & Collector Efficiency Factor 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 heat removal factor?

In this formula, Collector heat removal factor uses Mass Flowrate, Molar Specific Heat Capacity at Constant Pressure, Outer diameter of absorber tube, Length of Concentrator, Overall loss coefficient & Collector Efficiency Factor. We can use 1 other way(s) to calculate the same, which is/are as follows -

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)))

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