Useful heat gain when collector efficiency factor is present Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
qu = (m*Cp molar)*(((C*Sflux)/Ul)+(Ta-Tfi))*(1-e^(-(F′*pi*Do*Ul*L)/(m*Cp molar)))
This formula uses 2 Constants, 11 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Variables Used
Useful heat gain - (Measured in Watt) - Useful heat gain is defined as the rate of heat transfer to the working fluid.
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.
Concentration ratio - Concentration ratio is defined as the ratio of the effective area of aperture to the surface area of the absorber.
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.
Ambient Air Temperature - (Measured in Kelvin) - Ambient Air Temperature is the temperature of the surrounding medium.
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.
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.
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.
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
Concentration ratio: 0.8 --> 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
Ambient Air Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Inlet fluid temperature flat plate collector: 10 Kelvin --> 10 Kelvin No Conversion Required
Collector Efficiency Factor: 0.3 --> 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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
qu = (m*Cp molar)*(((C*Sflux)/Ul)+(Ta-Tfi))*(1-e^(-(F′*pi*Do*Ul*L)/(m*Cp molar))) --> (12*122)*(((0.8*98)/1.25)+(300-10))*(1-e^(-(0.3*pi*2*1.25*15)/(12*122)))
Evaluating ... ...
qu = 12316.8826134102
STEP 3: Convert Result to Output's Unit
12316.8826134102 Watt --> No Conversion Required
FINAL ANSWER
12316.8826134102 12316.88 Watt <-- Useful heat gain
(Calculation completed in 00.019 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 collector efficiency factor is present Formula

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)))
qu = (m*Cp molar)*(((C*Sflux)/Ul)+(Ta-Tfi))*(1-e^(-(F′*pi*Do*Ul*L)/(m*Cp molar)))

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 when collector efficiency factor is present?

Useful heat gain when collector efficiency factor is present calculator uses 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))) to calculate the Useful heat gain, The Useful heat gain when collector efficiency factor 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 qu symbol.

How to calculate Useful heat gain when collector efficiency factor is present using this online calculator? To use this online calculator for Useful heat gain when collector efficiency factor is present, enter Mass Flowrate (m), Molar Specific Heat Capacity at Constant Pressure (Cp molar), Concentration ratio (C), Flux absorbed by plate (Sflux), Overall loss coefficient (Ul), Ambient Air Temperature (Ta), Inlet fluid temperature flat plate collector (Tfi), Collector Efficiency Factor (F′), Outer diameter of absorber tube (Do) & Length of Concentrator (L) and hit the calculate button. Here is how the Useful heat gain when collector efficiency factor is present calculation can be explained with given input values -> 12316.88 = (12*122)*(((0.8*98)/1.25)+(300-10))*(1-e^(-(0.3*pi*2*1.25*15)/(12*122))).

FAQ

What is Useful heat gain when collector efficiency factor is present?
The Useful heat gain when collector efficiency factor 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 qu = (m*Cp molar)*(((C*Sflux)/Ul)+(Ta-Tfi))*(1-e^(-(F′*pi*Do*Ul*L)/(m*Cp molar))) or 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))). 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, Concentration ratio is defined as the ratio of the effective area of aperture to the surface area of the absorber, 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, Ambient Air Temperature is the temperature of the surrounding medium, Inlet fluid temperature flat plate collector is defined as the temperature at which the liquid enters the liquid flat plate collector, 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, 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.
How to calculate Useful heat gain when collector efficiency factor is present?
The Useful heat gain when collector efficiency factor 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 = (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))). To calculate Useful heat gain when collector efficiency factor is present, you need Mass Flowrate (m), Molar Specific Heat Capacity at Constant Pressure (Cp molar), Concentration ratio (C), Flux absorbed by plate (Sflux), Overall loss coefficient (Ul), Ambient Air Temperature (Ta), Inlet fluid temperature flat plate collector (Tfi), Collector Efficiency Factor (F′), Outer diameter of absorber tube (Do) & Length of Concentrator (L). With our tool, you need to enter the respective value for 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, Collector Efficiency Factor, Outer diameter of absorber tube & 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 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, Collector Efficiency Factor, Outer diameter of absorber tube & 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 = 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 = 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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