Useful Heat Gain When Collector Efficiency Factor Is Present Calculator

Useful Heat Gain Formula:

\[ q_u = (m \cdot C_{p,molar}) \cdot \left( \frac{C \cdot S_{flux}}{U_l} + (T_a - T_{fi}) \right) \cdot \left(1 - e^{-\frac{F' \cdot \pi \cdot D_o \cdot U_l \cdot L}{m \cdot C_{p,molar}}}\right) \]

Mass Flowrate (m):

kg/s

Molar Specific Heat Capacity at Constant Pressure (Cp molar):

J/K/mol

Concentration Ratio (C):

Flux Absorbed by Plate (Sflux):

W/m²

Overall Loss Coefficient (Ul):

W/m²/K

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):

Useful Heat Gain (qu):

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1. What is Useful Heat Gain When Collector Efficiency Factor Is Present?

Useful heat gain when collector efficiency factor is present represents the actual thermal energy collected by a solar thermal system, accounting for the efficiency factor that considers heat transfer characteristics between the absorber and the working fluid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ q_u = (m \cdot C_{p,molar}) \cdot \left( \frac{C \cdot S_{flux}}{U_l} + (T_a - T_{fi}) \right) \cdot \left(1 - e^{-\frac{F' \cdot \pi \cdot D_o \cdot U_l \cdot L}{m \cdot C_{p,molar}}}\right) \]

Where:

\( q_u \) — Useful heat gain (W)
\( m \) — Mass flowrate (kg/s)
\( C_{p,molar} \) — Molar specific heat capacity at constant pressure (J/K/mol)
\( C \) — Concentration ratio
\( S_{flux} \) — Flux absorbed by plate (W/m²)
\( U_l \) — Overall loss coefficient (W/m²/K)
\( T_a \) — Ambient air temperature (K)
\( T_{fi} \) — Inlet fluid temperature flat plate collector (K)
\( F' \) — Collector efficiency factor
\( D_o \) — Outer diameter of absorber tube (m)
\( L \) — Length of concentrator (m)
\( \pi \) — Archimedes' constant (3.14159)
\( e \) — Napier's constant (2.71828)

Explanation: This equation calculates the actual useful heat gain from a solar collector, considering the efficiency factor that accounts for heat transfer limitations between the absorber and the working fluid.

3. Importance of Useful Heat Gain Calculation

Details: Accurate calculation of useful heat gain is crucial for designing efficient solar thermal systems, optimizing energy collection, and evaluating system performance under various operating conditions.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure all values are positive and within reasonable physical limits for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the collector efficiency factor (F')?
A: The collector efficiency factor represents the ratio of actual useful heat gain to the heat gain that would occur if the entire absorber were at the fluid temperature.

Q2: How does concentration ratio affect heat gain?
A: Higher concentration ratios increase the solar flux on the absorber, potentially increasing useful heat gain, but also affect thermal losses.

Q3: What are typical values for overall loss coefficient?
A: Overall loss coefficients typically range from 2-10 W/m²/K for well-insulated collectors, depending on design and operating conditions.

Q4: Why is the exponential term included in the formula?
A: The exponential term accounts for the temperature distribution along the collector length and the finite heat transfer between the absorber and fluid.

Q5: When is this calculation most applicable?
A: This calculation is particularly useful for concentrated solar thermal systems where the collector efficiency factor significantly impacts overall performance.