Two Surface Thermal Radiation Exchange Calculator

The Two-Surface Thermal Radiation Exchange Calculator computes the signed net radiative heat transfer between two opaque, diffuse-gray, isothermal surfaces separated by a medium that neither absorbs nor emits. It runs in two modes: a complete two-surface enclosure network, where you supply both areas, both emissivities and the view factor between them, and the limiting case of a small surface inside a large isothermal enclosure, where only the small surface's own area and emissivity are read.

It reports the net heat rate and the flux referenced to surface 1, the effective gray-body exchange factor, the equivalent network resistance, the reciprocal view factor from surface 2 back to surface 1, the blackbody heat rate for the same geometry, and what fraction of that blackbody limit the gray surfaces reach. The heat rate is signed, so a colder surface 1 correctly reports exchange in the other direction.

It works in SI only: square metres, degrees Celsius internally converted to kelvin, and watts. There is no unit-system selector.

Two things are worth knowing before you start. The calculator supplies no view factor and no emissivity, holds no chart or table for either, and takes both entirely on trust. And an emissivity of exactly zero, though inside the declared range of 0 to 1, is refused by the model rather than treated as a perfect reflector.

It is a screening calculation for surface-to-surface exchange, not a furnace, fire or enclosure design.

Purpose and model boundary

This model calculates signed diffuse-gray radiative heat exchange for either a two-surface enclosure network or a small surface inside a large isothermal enclosure. It reports net heat rate, flux, direction, and comparison with the blackbody geometry limit. It does not derive view factors, model participating gases, or include convection, conduction, solar load, or transient behavior.

Inputs and units

Temperatures are entered in degrees Celsius and converted to kelvin before fourth-power calculations. Areas are in square metres, emissivities and view factors are dimensionless, and heat rate is reported in watts. Two-surface mode uses both areas, emissivities, temperatures, and F_12. Large-enclosure mode uses surface 1, the enclosure temperature, and surface-1 emissivity while applying the limiting geometry internally.

Governing relationships

Blackbody emissive power is:

E_b = σ T⁴

For the two-surface enclosure, reciprocity gives:

A_1 F_12 = A_2 F_21

The diffuse-gray network resistances are:

R_surface,1 = (1 - ε_1) / (A_1 ε_1)

R_space = 1 / (A_1 F_12)

R_surface,2 = (1 - ε_2) / (A_2 ε_2)

R_total = R_surface,1 + R_space + R_surface,2

The signed exchange is:

Q = σ (T_1⁴ - T_2⁴) / R_total

In the large-isothermal-enclosure limit:

Q = A_1 ε_1 σ (T_1⁴ - T_2⁴)

The blackbody geometry limit is computed with the same temperatures and geometry but without the gray-surface resistance penalty. Heat flux on surface 1 is q''_1 = Q / A_1.

Calculation sequence

1. Validate mode, temperatures, active areas, emissivities, and view-factor geometry.
2. Convert temperatures to absolute kelvin.
3. In enclosure mode, calculate reciprocal F_21 and both surface plus space resistances; in large-enclosure mode, apply the limiting relationship.
4. Calculate signed gray-surface heat rate, surface-1 flux, direction, effective exchange factor, and blackbody limit.
5. Compare gray and blackbody rates and evaluate workbook status.
6. Generate the temperature-sweep chart from workbook-named series.

Outputs and interpretation

Net radiative heat rate is the headline result. Supporting outputs include heat flux on surface 1, implied reciprocal view factor, total network resistance, exchange direction, effective exchange factor, blackbody limit, and the fraction of that limit achieved by the gray surfaces. A positive result follows the workbook convention of net radiation leaving surface 1.

Validation and status logic

This is the complete named RAD_Model_Status logic. Invalid states return protected zero numeric outputs; they must not be read as a valid no-exchange condition.

Assumptions and limitations

• Both surfaces are opaque, diffuse-gray, isothermal, and have temperature-independent emissivity.
• The intervening medium is nonparticipating and does not absorb, emit, or scatter radiation.
• In two-surface mode, the entered surfaces form the complete enclosure; closure and reciprocity govern the remaining view factors.
• Large-enclosure mode treats surface 1 as small relative to an isothermal surrounding enclosure.
• The workbook does not derive F_12; geometry-specific view-factor analysis remains the user's responsibility.
• Participating gases, spectral/directional effects, semitransparent media, solar irradiation, convection, conduction, and transient temperatures are outside scope.

Restrictions and non-computing states

Active areas, emissivities, and view factors must form a finite supported network. Emissivity is physically bounded from zero to one, but this finite-resistance implementation requires a positive emissivity. Temperatures must be above absolute zero. Values outside the published limits or undeclared options are rejected before the calculation runs.

Errors and warnings

NOT VALID blocks interpretation of every computed output. The workbook has no separate CHECK state; OK confirms only that the declared diffuse-gray model evaluated. Connection, publishing, and calculation-service errors are operational failures, not zero radiation.

The resistance network, reciprocity rule, large-enclosure limit, sign convention, named output formulas, and status logic were verified against the delivered workbook, its published input rules, tests, and reviewer packet. The workbook identifies these technical sources:

• DOE Fundamentals Handbook: Thermodynamics, Heat Transfer, and Fluid Flow, Volume 2 — Blackbody exchange, gray-body emissivity, configuration-factor meaning, and signed net exchange.
• NASA Free Molecular Heat Transfer Programs for Setup and Thermal Analysis — Two-surface enclosure emissivity factor and large-enclosure limiting form.
• CODATA Recommended Values of the Fundamental Physical Constants: 2022 — Stefan-Boltzmann constant.
• NASA Thermal Radiation View Factor Calculation — Diffuse view-factor definition and medium assumptions.