Useful heat gain when collection efficiency is present Calculator

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✖Instantaneous collection efficiency is defined as ratio of useful heat gain to radiation incident on collector.ⓘ Instantaneous Collection Efficiency [η_i]			+10% -10%
✖Hourly beam component is defined as the solar radiation received from the Sun without having been scattered by the atmosphere per hour.ⓘ Hourly beam component [I_b]			+10% -10%
✖Tilt factor for beam radiation is defined as the ratio of beam radiation flux falling on a tilted surface to that falling on an horizontal surface.ⓘ Tilt Factor for Beam Radiation [r_b]			+10% -10%
✖Hourly diffuse component is defined as the part of total radiation that reaches earth's surface after a change of its directions due to scattering by the atmosphere per hour.ⓘ Hourly Diffuse Component [I_d]			+10% -10%
✖Tilt factor for diffused radiation is the ratio of the diffuse radiation flux falling on the tilted surface to that falling on a horizontal surface.ⓘ Tilt factor for diffused radiation [r_d]			+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%

✖Useful heat gain is defined as the rate of heat transfer to the working fluid.ⓘ Useful heat gain when collection efficiency is present [q_u]

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Formula

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Useful heat gain when collection efficiency is present

Formula

`"q"_{"u"} = "η"_{"i"}*("I"_{"b"}*"r"_{"b"}+"I"_{"d"}*"r"_{"d"})*"W"*"L"`

Example

`"3508.313W"="0.675"*("18J/sm²"*"0.25"+"9J/sm²"*"5")*"7m"*"15m"`

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Useful heat gain when collection efficiency is present Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
q_u = η_i*(I_b*r_b+I_d*r_d)*W*L
This formula uses 8 Variables

Variables Used

Useful heat gain - (Measured in Watt) - Useful heat gain is defined as the rate of heat transfer to the working fluid.
Instantaneous Collection Efficiency - Instantaneous collection efficiency is defined as ratio of useful heat gain to radiation incident on collector.
Hourly beam component - (Measured in Watt per Square Meter) - Hourly beam component is defined as the solar radiation received from the Sun without having been scattered by the atmosphere per hour.
Tilt Factor for Beam Radiation - Tilt factor for beam radiation is defined as the ratio of beam radiation flux falling on a tilted surface to that falling on an horizontal surface.
Hourly Diffuse Component - (Measured in Watt per Square Meter) - Hourly diffuse component is defined as the part of total radiation that reaches earth's surface after a change of its directions due to scattering by the atmosphere per hour.
Tilt factor for diffused radiation - Tilt factor for diffused radiation is the ratio of the diffuse radiation flux falling on the tilted surface to that falling on a horizontal surface.
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.

STEP 1: Convert Input(s) to Base Unit

Instantaneous Collection Efficiency: 0.675 --> No Conversion Required
Hourly beam component: 18 Joule per Second per Square Meter --> 18 Watt per Square Meter (Check conversion here)
Tilt Factor for Beam Radiation: 0.25 --> No Conversion Required
Hourly Diffuse Component: 9 Joule per Second per Square Meter --> 9 Watt per Square Meter (Check conversion here)
Tilt factor for diffused radiation: 5 --> No Conversion Required
Concentrator Aperture: 7 Meter --> 7 Meter No Conversion Required
Length of Concentrator: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q_u = η_i*(I_b*r_b+I_d*r_d)*W*L --> 0.675*(18*0.25+9*5)*7*15

Evaluating ... ...

q_u = 3508.3125

STEP 3: Convert Result to Output's Unit

3508.3125 Watt --> No Conversion Required

FINAL ANSWER

3508.3125 ≈ 3508.313 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 when collection efficiency is present Formula

What does instantaneous collection efficiency mean?

It is the amount of energy removed by the transfer fluid over a given measuring period divided by the total incident solar radiation onto the gross collector area during the measuring period.

How to Calculate Useful heat gain when collection efficiency is present?

Useful heat gain when collection efficiency is present calculator uses 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 to calculate the Useful heat gain, The Useful heat gain when collection efficiency is present 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 when collection efficiency is present using this online calculator? To use this online calculator for Useful heat gain when collection efficiency is present, enter Instantaneous Collection Efficiency (η_i), Hourly beam component (I_b), Tilt Factor for Beam Radiation (r_b), Hourly Diffuse Component (I_d), Tilt factor for diffused radiation (r_d), Concentrator Aperture (W) & Length of Concentrator (L) and hit the calculate button. Here is how the Useful heat gain when collection efficiency is present calculation can be explained with given input values -> 3508.313 = 0.675*(18*0.25+9*5)*7*15.

FAQ

What is Useful heat gain when collection efficiency is present?

The Useful heat gain when collection efficiency is present 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 = η_i*(I_b*r_b+I_d*r_d)*W*L or 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. Instantaneous collection efficiency is defined as ratio of useful heat gain to radiation incident on collector, Hourly beam component is defined as the solar radiation received from the Sun without having been scattered by the atmosphere per hour, Tilt factor for beam radiation is defined as the ratio of beam radiation flux falling on a tilted surface to that falling on an horizontal surface, Hourly diffuse component is defined as the part of total radiation that reaches earth's surface after a change of its directions due to scattering by the atmosphere per hour, Tilt factor for diffused radiation is the ratio of the diffuse radiation flux falling on the tilted surface to that falling on a horizontal surface, 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.

How to calculate Useful heat gain when collection efficiency is present?

The Useful heat gain when collection efficiency is present 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 = Instantaneous Collection Efficiency*(Hourly beam component*Tilt Factor for Beam Radiation+Hourly Diffuse Component*Tilt factor for diffused radiation)*Concentrator Aperture*Length of Concentrator. To calculate Useful heat gain when collection efficiency is present, you need Instantaneous Collection Efficiency (η_i), Hourly beam component (I_b), Tilt Factor for Beam Radiation (r_b), Hourly Diffuse Component (I_d), Tilt factor for diffused radiation (r_d), Concentrator Aperture (W) & Length of Concentrator (L). With our tool, you need to enter the respective value for Instantaneous Collection Efficiency, Hourly beam component, Tilt Factor for Beam Radiation, Hourly Diffuse Component, Tilt factor for diffused radiation, Concentrator Aperture & Length of Concentrator 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 Instantaneous Collection Efficiency, Hourly beam component, Tilt Factor for Beam Radiation, Hourly Diffuse Component, Tilt factor for diffused radiation, Concentrator Aperture & Length of Concentrator. 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 = (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)))
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)))

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