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Useful heat gain when collector efficiency factor is present Formula

GoUseful heat gain in concentrating collector Formula

GoUseful heat gain rate in concentrating collector when concentration ratio is present Formula

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The Useful Heat Gain is the amount of thermal energy collected by a solar concentrating system, contributing to the efficiency of solar energy conversion. Check FAQs

q u = (m \cdot C p molar) \cdot ((\frac{C \cdot S flux}{U l}) + (T a - T fi)) \cdot (1 - e^{- \frac{F′ \cdot π \cdot D o \cdot U l \cdot L}{m \cdot C p molar}})

q_u - Useful Heat Gain?m - Mass Flowrate?C_{p molar} - Molar Specific Heat Capacity at Constant Pressure?C - Concentration Ratio?S_flux - Flux Absorbed by Plate?U_l - Overall Loss Coefficient?T_a - Ambient Air Temperature?T_fi - Inlet fluid Temperature Flat Plate Collector?F′ - Collector Efficiency Factor?D_o - Outer Diameter of Absorber Tube?L - Length of Concentrator?π - Archimedes' constant?

Useful heat gain when collector efficiency factor is present Example

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Here is how the Useful heat gain when collector efficiency factor is present equation looks like with Values.

Here is how the Useful heat gain when collector efficiency factor is present equation looks like with Units.

Here is how the Useful heat gain when collector efficiency factor is present equation looks like.

2646.8529 = (12 \cdot 122) \cdot ((\frac{0.8 \cdot 98.0044}{1.25}) + (300 - 124.424)) \cdot (1 - e^{- \frac{0.095 \cdot 3.1416 \cdot 1.9924 \cdot 1.25 \cdot 15}{12 \cdot 122}})

2646.8529W = (12kg/s \cdot 122J/K*mol) \cdot ((\frac{0.8 \cdot 98.0044J/sm²}{1.25W/m²*K}) + (300K - 124.424K)) \cdot (1 - e^{- \frac{0.095 \cdot 3.1416 \cdot 1.9924m \cdot 1.25W/m²*K \cdot 15m}{12kg/s \cdot 122J/K*mol}})

2646.8529 = (12 \cdot 122) \cdot ((\frac{0.8 \cdot 98.0044}{1.25}) + (300 - 124.424)) \cdot (1 - e^{- \frac{0.095 \cdot 3.1416 \cdot 1.9924 \cdot 1.25 \cdot 15}{12 \cdot 122}})

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Useful heat gain when collector efficiency factor is present Solution

Follow our step by step solution on how to calculate Useful heat gain when collector efficiency factor is present?

FIRST Step Consider the formula

q u = (m \cdot C p molar) \cdot ((\frac{C \cdot S flux}{U l}) + (T a - T fi)) \cdot (1 - e^{- \frac{F′ \cdot π \cdot D o \cdot U l \cdot L}{m \cdot C p molar}})

Next Step Substitute values of Variables

∴

q u = (12kg/s \cdot 122J/K*mol) \cdot ((\frac{0.8 \cdot 98.0044J/sm²}{1.25W/m²*K}) + (300K - 124.424K)) \cdot (1 - e^{- \frac{0.095 \cdot π \cdot 1.9924m \cdot 1.25W/m²*K \cdot 15m}{12kg/s \cdot 122J/K*mol}})

Next Step Substitute values of Constants

∴

q u = (12kg/s \cdot 122J/K*mol) \cdot ((\frac{0.8 \cdot 98.0044J/sm²}{1.25W/m²*K}) + (300K - 124.424K)) \cdot (1 - e^{- \frac{0.095 \cdot 3.1416 \cdot 1.9924m \cdot 1.25W/m²*K \cdot 15m}{12kg/s \cdot 122J/K*mol}})

Next Step Convert Units

∴

q u = (12kg/s \cdot 122J/K*mol) \cdot ((\frac{0.8 \cdot 98.0044W/m²}{1.25W/m²*K}) + (300K - 124.424K)) \cdot (1 - e^{- \frac{0.095 \cdot 3.1416 \cdot 1.9924m \cdot 1.25W/m²*K \cdot 15m}{12kg/s \cdot 122J/K*mol}})

Next Step Prepare to Evaluate

∴

q u = (12 \cdot 122) \cdot ((\frac{0.8 \cdot 98.0044}{1.25}) + (300 - 124.424)) \cdot (1 - e^{- \frac{0.095 \cdot 3.1416 \cdot 1.9924 \cdot 1.25 \cdot 15}{12 \cdot 122}})

Next Step Evaluate

∴

q u = 2646.85287253066W

LAST Step Rounding Answer

∴

q u = 2646.8529W

Useful heat gain when collector efficiency factor is present Formula Elements

Variables

Constants

Useful Heat Gain

The Useful Heat Gain is the amount of thermal energy collected by a solar concentrating system, contributing to the efficiency of solar energy conversion.

Symbol: q_u

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Useful Heat Gain

Mass Flowrate

The Mass Flowrate is the measure of the mass of fluid passing through a given surface per unit time, essential for analyzing energy transfer in solar energy systems.

Symbol: m

Measurement: Mass Flow RateUnit: kg/s

Note: Value can be positive or negative.

Formulas to find Mass Flowrate

Molar Specific Heat Capacity at Constant Pressure

The Molar Specific Heat Capacity at Constant Pressure is the amount of heat required to raise the temperature of one mole of a substance at constant pressure.

Symbol: C_{p molar}

Measurement: Molar Specific Heat Capacity at Constant PressureUnit: J/K*mol

Note: Value should be greater than 0.

Formulas to find Molar Specific Heat Capacity at Constant Pressure

Concentration Ratio

The Concentration Ratio is the measure of how much solar energy is concentrated by a solar collector compared to the energy received from the sun.

Symbol: C

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Concentration Ratio

Flux Absorbed by Plate

The Flux Absorbed by Plate is the amount of solar energy captured by the plate of a concentrating collector, influencing its efficiency in converting sunlight to heat.

Symbol: S_flux

Measurement: Heat Flux DensityUnit: J/sm²

Note: Value can be positive or negative.

Formulas to find Flux Absorbed by Plate

Overall Loss Coefficient

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.

Symbol: U_l

Measurement: Heat Transfer CoefficientUnit: W/m²*K

Note: Value should be greater than 0.

Formulas to find Overall Loss Coefficient

Ambient Air Temperature

The Ambient Air Temperature is the measure of the air temperature surrounding a solar energy system, influencing its efficiency and performance.

Symbol: T_a

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Ambient Air Temperature

Inlet fluid Temperature Flat Plate Collector

The Inlet fluid Temperature Flat Plate Collector is the temperature of the fluid entering the flat plate collector, crucial for assessing the collector's efficiency in solar energy systems.

Symbol: T_fi

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Inlet fluid Temperature Flat Plate Collector

Collector Efficiency Factor

The Collector Efficiency Factor is a measure of how effectively a solar collector converts sunlight into usable energy, reflecting its performance in energy collection.

Symbol: F′

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Collector Efficiency Factor

Outer Diameter of Absorber Tube

The Outer Diameter of Absorber Tube is the measurement across the widest part of the tube that collects solar energy in concentrating solar collectors.

Symbol: D_o

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Outer Diameter of Absorber Tube

Length of Concentrator

The Length of Concentrator is the measurement of the physical extent of a solar concentrator, which focuses sunlight onto a receiver for energy conversion.

Symbol: L

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Length of Concentrator

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Useful Heat Gain

Go Useful heat gain in concentrating collector

q u = A a \cdot S - q l

Go Useful heat gain rate in concentrating collector when concentration ratio is present

q u = F R \cdot (W - D o) \cdot L \cdot (S flux - (\frac{U l}{C}) \cdot (T fi - T a))

Other formulas in Concentrating Collectors category

Go Maximum possible concentration ratio of 2-D concentrator

C m = \frac{1}{\sin (θ a 2d)}

Go Maximum possible concentration ratio of 3-D concentrator

C m = \frac{2}{1 - \cos (2 \cdot θ a 3d)}

How to Evaluate Useful heat gain when collector efficiency factor is present?

Useful heat gain when collector efficiency factor is present evaluator 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 evaluate 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 q_u symbol.

How to evaluate Useful heat gain when collector efficiency factor is present using this online evaluator? To use this online evaluator for Useful heat gain when collector efficiency factor is present, enter Mass Flowrate (m), Molar Specific Heat Capacity at Constant Pressure (C_{p molar}), Concentration Ratio (C), Flux Absorbed by Plate (S_flux), Overall Loss Coefficient (U_l), Ambient Air Temperature (T_a), Inlet fluid Temperature Flat Plate Collector (T_fi), Collector Efficiency Factor (F′), Outer Diameter of Absorber Tube (D_o) & Length of Concentrator (L) and hit the calculate button.

FAQs on Useful heat gain when collector efficiency factor is present

What is the formula to find Useful heat gain when collector efficiency factor is present?

The formula of Useful heat gain when collector efficiency factor is present is expressed as 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))). Here is an example- 3917.793 = (12*122)*(((0.8*98.00438)/1.25)+(300-124.424))*(1-e^(-(0.095*pi*1.992443*1.25*15)/(12*122))).

How to calculate Useful heat gain when collector efficiency factor is present?

With Mass Flowrate (m), Molar Specific Heat Capacity at Constant Pressure (C_{p molar}), Concentration Ratio (C), Flux Absorbed by Plate (S_flux), Overall Loss Coefficient (U_l), Ambient Air Temperature (T_a), Inlet fluid Temperature Flat Plate Collector (T_fi), Collector Efficiency Factor (F′), Outer Diameter of Absorber Tube (D_o) & Length of Concentrator (L) we can find Useful heat gain when collector efficiency factor is present using the 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))). This formula also uses Archimedes' constant .

What are the other ways to Calculate Useful Heat Gain?

Here are the different ways to Calculate Useful Heat Gain-

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

Can the Useful heat gain when collector efficiency factor is present be negative?

Yes, the Useful heat gain when collector efficiency factor is present, measured in Power can be negative.

Which unit is used to measure Useful heat gain when collector efficiency factor is present?

Useful heat gain when collector efficiency factor is present is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Useful heat gain when collector efficiency factor is present can be measured.

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: Unit

Useful heat gain when collector efficiency factor is present Formula

​GoUseful heat gain in concentrating collector Formula

​GoUseful heat gain rate in concentrating collector when concentration ratio is present Formula

Useful heat gain when collector efficiency factor is present Example

Useful heat gain when collector efficiency factor is present Solution

Useful heat gain when collector efficiency factor is present Formula Elements

Other Formulas to find Useful Heat Gain

Other formulas in Concentrating Collectors category

How to Evaluate Useful heat gain when collector efficiency factor is present?

FAQs on Useful heat gain when collector efficiency factor is present

Variable Name

GoUseful heat gain in concentrating collector Formula

GoUseful heat gain rate in concentrating collector when concentration ratio is present Formula