Collector Efficiency Factor For Compound Parabolic Collector Calculator

Formula Used:

\[ F' = \left( U_l \times \left( \frac{1}{U_l} + \frac{b}{N \times \pi \times D_i \times h_f} \right) \right)^{-1} \]

Overall Loss Coefficient (U_l):

W/m²·K

Absorber Surface Width (b):

Number of Tubes (N):

Inner Diameter Absorber Tube (D_i):

Heat Transfer Coefficient Inside (h_f):

W/m²·K

Collector Efficiency Factor (F'):

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1. What is Collector Efficiency Factor?

The collector efficiency factor (F') 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. It quantifies how effectively a solar collector transfers heat from the absorber surface to the working fluid.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ F' = \left( U_l \times \left( \frac{1}{U_l} + \frac{b}{N \times \pi \times D_i \times h_f} \right) \right)^{-1} \]

Where:

\( F' \) — Collector efficiency factor
\( U_l \) — Overall loss coefficient (W/m²·K)
\( b \) — Absorber surface width (m)
\( N \) — Number of tubes
\( D_i \) — Inner diameter absorber tube (m)
\( h_f \) — Heat transfer coefficient inside (W/m²·K)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: The formula accounts for heat loss through the collector and the efficiency of heat transfer from the absorber to the fluid through the tubes.

3. Importance of Collector Efficiency Factor

Details: The collector efficiency factor is crucial for evaluating the thermal performance of solar collectors. A higher F' value indicates better heat transfer efficiency from the absorber to the working fluid, which is essential for optimizing solar thermal system performance.

4. Using the Calculator

Tips: Enter all parameters in appropriate units. Ensure all values are positive numbers. The overall loss coefficient, absorber width, tube diameter, and heat transfer coefficient should be in consistent units (W/m²·K for coefficients, meters for dimensions).

5. Frequently Asked Questions (FAQ)

Q1: What is a typical range for collector efficiency factor?
A: For most compound parabolic collectors, F' typically ranges from 0.7 to 0.95, with higher values indicating better performance.

Q2: How does tube configuration affect F'?
A: Increasing the number of tubes or their diameter generally improves F' by providing more surface area for heat transfer, but this must be balanced against increased material costs and pressure drop.

Q3: What factors influence the heat transfer coefficient?
A: The heat transfer coefficient depends on fluid properties, flow rate, tube roughness, and temperature. Turbulent flow typically provides higher coefficients than laminar flow.

Q4: How does absorber width affect collector efficiency?
A: Wider absorbers can collect more solar radiation but may have higher heat losses. The optimal width balances radiation collection with efficient heat transfer to the tubes.

Q5: Can this calculator be used for other collector types?
A: While the basic principles apply, this specific formula is optimized for compound parabolic collectors. Other collector types may require different formulations.