Irradiation Power per Unit Area Calculator

1. What is an Irradiation Power per Unit Area Calculator?

Definition: This calculator computes the irradiation power per unit area (\( \frac{G}{A} \)) incident on a surface, adjusted by the surface's absorptivity, using a modified form of the Stefan-Boltzmann law.

Purpose: It is used in thermal engineering, HVAC systems, and radiative heat transfer analysis to quantify the rate of thermal radiation absorbed by a surface from its surroundings, aiding in the design of thermal management systems.

2. How Does the Calculator Work?

The calculator uses the following formula for irradiation power per unit area:

Irradiation Power: \[ \frac{G}{A} = \alpha \sigma T_{\text{sur}}^4 \]

Where:

\( \frac{G}{A} \): Irradiation power per unit area (Btu/hr-ft², W/m²)
\( \alpha \): Absorptivity (dimensionless, 0 to 1)
\( \sigma \): Stefan-Boltzmann constant (\( 0.1714 \times 10^{-8} \text{ Btu/hr-ft²-°R}^4 \))
\( T_{\text{sur}} \): Surrounding temperature (°R, °F, °C, or K)

Unit Conversions:

Surrounding Temperature (\( T_{\text{sur}} \)):
- °F to °R: °R = °F + 460
- °C to °R: °F = (°C × 9/5) + 32, then °R = °F + 460
- K to °R: °C = K - 273.15, then °F = (°C × 9/5) + 32, then °R = °F + 460
Irradiation Power per Unit Area (\( \frac{G}{A} \)): Btu/hr-ft², W/m² (1 Btu/hr-ft² = 3.154591 W/m²)

Steps:

Enter the absorptivity (\( \alpha \)) and surrounding temperature (\( T_{\text{sur}} \)), and select the temperature unit.
Convert the surrounding temperature to °R.
Calculate the irradiation power per unit area using the formula, with \( \sigma = 0.1714 \times 10^{-8} \text{ Btu/hr-ft²-°R}^4 \).
Convert the result to the selected unit (Btu/hr-ft² or W/m²).
Display the result with 5 decimal places, or in scientific notation if the value is greater than 10,000 or less than 0.00001.

3. Importance of Irradiation Power Calculation

Calculating the irradiation power per unit area is crucial for:

Thermal Engineering: Quantifies the radiative heat absorbed by surfaces, aiding in the design of thermal management systems.
HVAC Systems: Helps evaluate radiative heat gains in buildings, improving energy efficiency.
Solar Energy Systems: Assists in analyzing the absorption of solar radiation by surfaces for energy harvesting applications.

4. Using the Calculator

Examples:

Example 1: For \( \alpha = 0.80 \), \( T_{\text{sur}} = 75 \, \text{°F} \), irradiation power in Btu/hr-ft²:
- Convert: \( T_{\text{sur}} = 75 + 460 = 535 \, \text{°R} \)
- \( \frac{G}{A} = 0.80 \times 0.1714 \times 10^{-8} \times 535^4 \)
- \( 535^4 \approx 8.1943 \times 10^{10} \)
- \( \frac{G}{A} \approx 0.80 \times 0.1714 \times 10^{-8} \times 8.1943 \times 10^{10} \approx 11.245 \)
- Since 11.245 < 10000 and > 0.00001, display with 5 decimal places: \( 11.24500 \)
Example 2: For \( \alpha = 0.90 \), \( T_{\text{sur}} = 300 \, \text{°C} \), irradiation power in W/m²:
- Convert: \( T_{\text{sur}} = (300 \times 9/5) + 32 + 460 = 540 + 32 + 460 = 1032 \, \text{°R} \)
- \( \frac{G}{A} = 0.90 \times 0.1714 \times 10^{-8} \times 1032^4 \)
- \( 1032^4 \approx 1.1356 \times 10^{12} \)
- \( \frac{G}{A} \approx 0.90 \times 0.1714 \times 10^{-8} \times 1.1356 \times 10^{12} \approx 1751.719 \, \text{Btu/hr-ft²} \)
- Convert to W/m²: \( 1751.719 \times 3.154591 \approx 5525.865 \)
- Since 5525.865 < 10000 and > 0.00001, display with 5 decimal places: \( 5525.86500 \)
Example 3: For \( \alpha = 0.60 \), \( T_{\text{sur}} = 573.15 \, \text{K} \), irradiation power in Btu/hr-ft²:
- Convert: \( T_{\text{sur}} = (573.15 - 273.15) = 300 \, \text{°C} \), then \( (300 \times 9/5) + 32 + 460 = 1032 \, \text{°R} \)
- \( \frac{G}{A} = 0.60 \times 0.1714 \times 10^{-8} \times 1032^4 \)
- \( \frac{G}{A} \approx 0.60 \times 0.1714 \times 10^{-8} \times 1.1356 \times 10^{12} \approx 1167.813 \)
- Since 1167.813 < 10000 and > 0.00001, display with 5 decimal places: \( 1167.81300 \)

5. Frequently Asked Questions (FAQ)

Q: What does irradiation power per unit area represent?
A: Irradiation power per unit area (\( \frac{G}{A} \)) quantifies the rate of thermal radiation incident on a surface from its surroundings, adjusted by the surface's absorptivity.

Q: Why is absorptivity important in this calculation?
A: Absorptivity (\( \alpha \)) indicates how much of the incident radiation is absorbed by a surface. Values range from 0 to 1, with higher values indicating greater absorption.

Q: How can I determine the absorptivity of a surface?
A: Absorptivity can be found in material property tables, manufacturer specifications, or through experimental measurements for materials like metals, paints, or coatings.