Mean temperature of absorber plate Solution

STEP 0: Pre-Calculation Summary
Formula Used
Average temperature of absorber plate = (Flux absorbed by plate+Overall loss coefficient*Ambient Air Temperature+Effective heat transfer coefficient*Average of Inlet and Outlet Temperature of fluid)/(Overall loss coefficient+Effective heat transfer coefficient)
Tpm = (Sflux+Ul*Ta+he*Tf)/(Ul+he)
This formula uses 6 Variables
Variables Used
Average temperature of absorber plate - (Measured in Kelvin) - Average temperature of absorber plate is defined as the temperature spread across the surface area of the absorber plate.
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 where the ramming process starts.
Effective heat transfer coefficient - (Measured in Watt per Square Meter per Kelvin) - Effective heat transfer coefficient is defined as the heat transfer coefficient between the absorber plate and the air stream.
Average of Inlet and Outlet Temperature of fluid - (Measured in Kelvin) - Average of inlet and outlet temperature of fluid is defined as the arithmetic mean of inlet and outlet temperatures of fluid entering collector plate.
STEP 1: Convert Input(s) to Base Unit
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
Effective heat transfer coefficient: 0.95 Watt per Square Meter per Kelvin --> 0.95 Watt per Square Meter per Kelvin No Conversion Required
Average of Inlet and Outlet Temperature of fluid: 14 Kelvin --> 14 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tpm = (Sflux+Ul*Ta+he*Tf)/(Ul+he) --> (98+1.25*300+0.95*14)/(1.25+0.95)
Evaluating ... ...
Tpm = 221.045454545455
STEP 3: Convert Result to Output's Unit
221.045454545455 Kelvin --> No Conversion Required
FINAL ANSWER
221.045454545455 221.0455 Kelvin <-- Average temperature of absorber plate
(Calculation completed in 00.004 seconds)

Credits

Created by ADITYA RAWAT
DIT UNIVERSITY (DITU), Dehradun
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Verified by Ravi Khiyani
Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore
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8 Solar Air Heater Calculators

Effective heat transfer coefficient for variation
Go Effective heat transfer coefficient = Convective heat transfer Coeff of solar*(1+(2*Fin height*Fin effectiveness*Convective heat transfer Coeff of solar fin)/(Distance between fins*Convective heat transfer Coeff of solar))+(Equivalent radiative heat transfer coefficient*Convective heat transfer Coeff of solar bottom)/(Equivalent radiative heat transfer coefficient+Convective heat transfer Coeff of solar bottom)
Incident flux when flow is between Cover and Absorber plate
Go Flux absorbed by plate = Convective heat transfer Coeff of solar*(Average temperature of absorber plate-Inlet fluid temperature flat plate collector)+(Equivalent radiative heat transfer coefficient*(Average temperature of absorber plate-Temperature of Cover))+(Bottom Loss Coefficient*(Average temperature of absorber plate-Ambient Air Temperature))
Mean temperature of plate below
Go Mean Temperature of Plate below = (Equivalent radiative heat transfer coefficient*Average temperature of absorber plate+Convective heat transfer Coeff of solar bottom*Average of Inlet and Outlet Temperature of fluid)/(Equivalent radiative heat transfer coefficient+Convective heat transfer Coeff of solar bottom)
Mean temperature of absorber plate
Go Average temperature of absorber plate = (Flux absorbed by plate+Overall loss coefficient*Ambient Air Temperature+Effective heat transfer coefficient*Average of Inlet and Outlet Temperature of fluid)/(Overall loss coefficient+Effective heat transfer coefficient)
Effective heat transfer coefficient
Go Effective heat transfer coefficient = Convective heat transfer Coeff of solar+(Equivalent radiative heat transfer coefficient*Convective heat transfer Coeff of solar bottom)/ (Equivalent radiative heat transfer coefficient+Convective heat transfer Coeff of solar bottom)
Equivalent radiative heat transfer coefficient
Go Equivalent radiative heat transfer coefficient = (4*[Stefan-BoltZ]*(Average temperature of absorber plate+Mean Temperature of Plate below)^3)/((1/Emissivity of absorber plate surface)+(1/Emissivity of bottom plate surface)-1*8)
Equivalent Diameter of fin channel
Go Equivalent diameter of fin channel = (4*(Distance between fins*Distance between absorber and bottom plate-Thickness of fin*Fin height))/(2*(Distance between fins+Fin height))
Collector efficiency factor
Go Collector Efficiency Factor = (1+Overall loss coefficient/Effective heat transfer coefficient)^-1

Mean temperature of absorber plate Formula

Average temperature of absorber plate = (Flux absorbed by plate+Overall loss coefficient*Ambient Air Temperature+Effective heat transfer coefficient*Average of Inlet and Outlet Temperature of fluid)/(Overall loss coefficient+Effective heat transfer coefficient)
Tpm = (Sflux+Ul*Ta+he*Tf)/(Ul+he)

What is the purpose of the absorber plate in a flat plate collector?

Flat-plate collectors are equipped with an absorber plate characterized by a high absorptivity (achieved through black paint or special coatings) which is exposed to solar radiation. This plate absorbs a large portion of the incoming energy and transfers it to the circulating fluid going through internal passageways.

How to Calculate Mean temperature of absorber plate?

Mean temperature of absorber plate calculator uses Average temperature of absorber plate = (Flux absorbed by plate+Overall loss coefficient*Ambient Air Temperature+Effective heat transfer coefficient*Average of Inlet and Outlet Temperature of fluid)/(Overall loss coefficient+Effective heat transfer coefficient) to calculate the Average temperature of absorber plate, The Mean temperature of absorber plate formula is defined as the average temperature of the surface of absorber plate. Average temperature of absorber plate is denoted by Tpm symbol.

How to calculate Mean temperature of absorber plate using this online calculator? To use this online calculator for Mean temperature of absorber plate, enter Flux absorbed by plate (Sflux), Overall loss coefficient (Ul), Ambient Air Temperature (Ta), Effective heat transfer coefficient (he) & Average of Inlet and Outlet Temperature of fluid (Tf) and hit the calculate button. Here is how the Mean temperature of absorber plate calculation can be explained with given input values -> 221.0455 = (98+1.25*300+0.95*14)/(1.25+0.95).

FAQ

What is Mean temperature of absorber plate?
The Mean temperature of absorber plate formula is defined as the average temperature of the surface of absorber plate and is represented as Tpm = (Sflux+Ul*Ta+he*Tf)/(Ul+he) or Average temperature of absorber plate = (Flux absorbed by plate+Overall loss coefficient*Ambient Air Temperature+Effective heat transfer coefficient*Average of Inlet and Outlet Temperature of fluid)/(Overall loss coefficient+Effective heat transfer coefficient). 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 where the ramming process starts, Effective heat transfer coefficient is defined as the heat transfer coefficient between the absorber plate and the air stream & Average of inlet and outlet temperature of fluid is defined as the arithmetic mean of inlet and outlet temperatures of fluid entering collector plate.
How to calculate Mean temperature of absorber plate?
The Mean temperature of absorber plate formula is defined as the average temperature of the surface of absorber plate is calculated using Average temperature of absorber plate = (Flux absorbed by plate+Overall loss coefficient*Ambient Air Temperature+Effective heat transfer coefficient*Average of Inlet and Outlet Temperature of fluid)/(Overall loss coefficient+Effective heat transfer coefficient). To calculate Mean temperature of absorber plate, you need Flux absorbed by plate (Sflux), Overall loss coefficient (Ul), Ambient Air Temperature (Ta), Effective heat transfer coefficient (he) & Average of Inlet and Outlet Temperature of fluid (Tf). With our tool, you need to enter the respective value for Flux absorbed by plate, Overall loss coefficient, Ambient Air Temperature, Effective heat transfer coefficient & Average of Inlet and Outlet Temperature of fluid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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