Formula used
This tool uses the diffuse-gray radiation network for two surfaces with a specified view factor. It returns the net steady heat transfer rate from Surface 1 to Surface 2.
How to use this calculator
- Enter both surface temperatures and select the correct unit.
- Enter areas for both surfaces in the same area unit.
- Provide emissivities (0 to 1) for each surface.
- Set the view factor F12 from geometry or references.
- Click Calculate to see Q12, heat flux, and resistances.
- Use CSV or PDF buttons to save your results.
Example data table
| T1 (K) | T2 (K) | A1 (m²) | A2 (m²) | ε1 | ε2 | F12 | Q12 (W) |
|---|---|---|---|---|---|---|---|
| 800 | 300 | 1.0 | 1.0 | 0.80 | 0.60 | 0.90 | ~ 1.69e+4 |
| 600 | 350 | 2.0 | 1.5 | 0.95 | 0.90 | 0.70 | ~ 1.13e+4 |
Radiative exchange overview
Thermal radiation moves energy as electromagnetic waves and grows rapidly with absolute temperature. For engineering surfaces, the Stefan–Boltzmann law scales with T4, so doubling temperature increases ideal emission by sixteen. This calculator estimates the net radiative heat transfer between two diffuse, gray surfaces using a resistance-network approach.
Where this model is used
Two-surface radiation is common in furnaces, heat shields, vacuum chambers, and building envelopes. It is especially useful when convection is small (vacuum or stagnant gas) or when surfaces “see” each other strongly. Typical view factors range from about 0.1 for partially obstructed geometries to nearly 1.0 for facing plates.
Temperature inputs and practical ranges
Enter temperatures in Kelvin, Celsius, Fahrenheit, or Rankine; the calculator converts to Kelvin for the T4 terms. Radiative transfer becomes dominant above roughly 500 K for many industrial setups. For example, a surface at 800 K radiates orders of magnitude more than one at 300 K, even with the same emissivity.
Area and geometry considerations
Areas A1 and A2 set the “size” of each node in the network and influence reciprocity through A1F12 = A2F21. If computed F21 exceeds 1, the selected areas and view factor are inconsistent. In practice, keep units consistent and use projected areas that match the view-factor definition.
Emissivity data you can start with
Emissivity depends on finish, oxidation, and wavelength. Polished aluminum or stainless steel can be as low as 0.03–0.20, while anodized or painted surfaces are often 0.80–0.95. Using realistic emissivities can change Q12 by several times compared with a blackbody assumption (ε = 1).
Interpreting the resistance breakdown
The total denominator is a sum of three resistances: Surface 1, space (view factor), and Surface 2. Low emissivity increases surface resistance, while small F12 increases space resistance. The table helps identify whether improving coating (higher ε) or improving alignment (higher F12) gives the biggest benefit.
Design insights from heat flux and hr
Heat flux (W/m²) is useful for checking material limits and insulation needs. The effective radiation coefficient hr converts radiation into a convection-like form near the operating point. Engineers often compare hr with a convection coefficient to decide which mechanism dominates.
Assumptions and validation tips
Results assume diffuse emission, gray behavior, steady state, and a known view factor. If a participating gas, spectral effects, or multiple reflections dominate, a more detailed enclosure analysis is needed. Validate with a simple energy balance, check sign (Q12 > 0 means 1 → 2), and run a sensitivity test on ε and F12.
FAQs
1) What does the view factor F12 represent?
F12 is the fraction of radiation leaving Surface 1 that directly reaches Surface 2. It depends only on geometry and relative orientation, not temperature or emissivity.
2) Why does the calculator convert everything to Kelvin?
Radiation uses absolute temperature in the T4 terms. Converting to Kelvin ensures physical correctness and prevents negative temperatures from breaking the Stefan–Boltzmann relationship.
3) How accurate are emissivity values?
Emissivity can vary with surface finish, oxidation, and temperature. If unsure, use a realistic range (for example 0.7–0.95 for coatings) and run a sensitivity check to bound Q12.
4) What does a negative Q12 mean?
A negative Q12 means net radiation flows from Surface 2 to Surface 1, usually because T2 is higher than T1. The magnitude still represents the net heat transfer rate in watts.
5) Why is there a reciprocity warning for F21?
Reciprocity requires A1F12 = A2F21. If the computed F21 is above 1, your A1, A2, or F12 combination cannot be correct for a real two-surface exchange geometry.
6) Can I use this for non-gray or specular surfaces?
This model assumes diffuse, gray behavior. Strongly spectral materials or specular reflections may need spectral properties or enclosure methods. Use this as a first-pass estimate only.
7) How do I choose between improving emissivity or changing geometry?
Compare the resistance terms. If surface resistance dominates, increasing emissivity helps most. If space resistance dominates, improving F12 through alignment, spacing, or shielding will have the biggest effect.