Heat Transfer Between Two Infinite Parallel Planes Given Temp And Emissivity Of Both Surfaces Calculator

Heat Transfer Formula:

\[ q = \frac{A \cdot \sigma \cdot (T_1^4 - T_2^4)}{(\frac{1}{\varepsilon_1} + \frac{1}{\varepsilon_2} - 1)} \]

Area (A):

m²

Temperature of Surface 1 (T₁):

Temperature of Surface 2 (T₂):

Emissivity of Body 1 (ε₁):

Emissivity of Body 2 (ε₂):

Heat Transfer (q):

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1. What is Heat Transfer Between Two Infinite Parallel Planes?

Heat transfer between two infinite parallel planes refers to the radiative heat exchange between two large, flat surfaces facing each other. This calculation is essential in thermal engineering for designing insulation systems, thermal barriers, and understanding heat exchange in confined spaces.

2. How Does the Calculator Work?

The calculator uses the heat transfer formula for infinite parallel planes:

\[ q = \frac{A \cdot \sigma \cdot (T_1^4 - T_2^4)}{(\frac{1}{\varepsilon_1} + \frac{1}{\varepsilon_2} - 1)} \]

Where:

\( q \) — Heat transfer rate (W)
\( A \) — Surface area (m²)
\( \sigma \) — Stefan-Boltzmann constant (5.670367×10⁻⁸ W/m²K⁴)
\( T_1 \) — Temperature of surface 1 (K)
\( T_2 \) — Temperature of surface 2 (K)
\( \varepsilon_1 \) — Emissivity of body 1
\( \varepsilon_2 \) — Emissivity of body 2

Explanation: The formula accounts for radiative heat exchange between two surfaces, considering their temperatures, emissivities, and the Stefan-Boltzmann law.

3. Importance of Heat Transfer Calculation

Details: Accurate heat transfer calculation is crucial for thermal system design, energy efficiency analysis, insulation performance evaluation, and predicting temperature distributions in engineering applications.

4. Using the Calculator

Tips: Enter area in square meters, temperatures in Kelvin, and emissivity values between 0 and 1. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: Why use this specific formula for parallel planes?
A: This formula is derived specifically for infinite parallel planes where view factor is 1 and radiation is confined between the two surfaces.

Q2: What is the range of emissivity values?
A: Emissivity ranges from 0 (perfect reflector) to 1 (perfect blackbody). Most real materials have emissivity between 0.1 and 0.9.

Q3: Why are temperatures in Kelvin?
A: The Stefan-Boltzmann law requires absolute temperature (Kelvin) since it involves temperature to the fourth power.

Q4: What are typical applications of this calculation?
A: Thermal insulation design, double-pane windows, spacecraft thermal control, industrial furnace design, and building energy analysis.

Q5: How accurate is this calculation for real-world applications?
A: The calculation provides good approximation for large parallel surfaces. For finite surfaces or complex geometries, additional view factor calculations may be needed.