[Radiation]

Free tool

Aligned Parallel Square Plates (Equal Size)

Net radiant heat exchange between two equal, directly-opposed gray square plates.

[FREE_TOOLS]

Built by our engineers

Part of EnerTherm's free calculator suite — the same methods we use on live industrial projects.

[EXPLORE]

More tools, always free

Instant results in your browser, no sign-up. New calculators added regularly.

Browse all calculators→

[CALCULATOR]

Inputs

Plate side (m)

Plate separation (m)

Plate 1 temperature (°C)

Plate 2 temperature (°C)

Plate 1 surface

Plate 2 surface

Results

View factor F₁₂

——

Net heat rate

—W

Net flux (per A₁)

—W/m²

Aligned Parallel Square Plates (Equal Size) — schematic

[READ_THE_NUMBERS]

Results are indicative

Figures assume typical conditions and the stated method. For measured, guaranteed numbers on your plant, our engineers run site surveys, heat loss audits, and full process models.

[NEXT_STEP]

Send us the result — we'll tell you what it means for your plant.

[ABOUT_THIS_TOOL]

Aligned Parallel Square Plates

Computes the net radiant heat exchange between two equal, isothermal gray square plates of side $W$ , mounted face-to-face and directly opposed, separated by a gap $L$ .

View Factor

For a square plate both in-plane ratios are equal,

X = Y = \frac{W}{L}

and the aligned-parallel-rectangles shape factor reduces to

F_{12} = \frac{2}{π X Y} [ln \frac{( 1 + X ^{2} ) ( 1 + Y ^{2} )}{1 + X ^{2} + Y ^{2}} + X 1 + Y^{2} tan^{- 1} \frac{X}{1 + Y ^{2}} + Y 1 + X^{2} tan^{- 1} \frac{Y}{1 + X ^{2}} - X tan^{- 1} X - Y tan^{- 1} Y]

Validity improves when the plate side exceeds about one fifth of the separation ( $W / L > 0.2$ ). For $X = Y = 1$ the factor is $F_{12} \approx 0.200$ .

Net Radiant Exchange

Q = \frac{σ ( T _{1}^{4} - T _{2}^{4} )}{\frac{1 - ε _{1}}{ε _{1} A _{1}} + \frac{1}{A _{1} F _{12}} + \frac{1 - ε _{2}}{ε _{2} A _{2}}}

with $σ = 5.670374 \times 1 0^{- 8} W/m^{2} K^{4}$ , $A_{1} = A_{2} = W^{2}$ , and temperatures in Kelvin. When both surfaces are black this reduces to $Q = σ A_{1} F_{12} (T_{1}^{4} - T_{2}^{4})$ .

References

Rohsenow, W.M., Hartnett, J.P. & Cho, Y.I., Handbook of Heat Transfer, 3rd ed., McGraw-Hill, 1998.
Incropera, F.P. & DeWitt, D.P., Fundamentals of Heat and Mass Transfer, Wiley.

[UPGRADE]

Need this tool, but deeper?

We build advanced versions on request — your fluids, your geometry, your standards, validated against plant data.

[REQUEST]

Missing a calculator?

Tell us what you're sizing or estimating — we build the calculators engineers actually ask for.

[FAQ]

Frequently asked questions

Net radiant heat exchange between two equal, directly-opposed gray square plates. Enter your inputs and press Calculate — the worked solution shows every step of the method with your numbers substituted in.

A gray surface has an emissivity that is constant across wavelength, so one number ε between 0 and 1 characterises how it emits and absorbs. It is the standard engineering idealisation; real oxidised metals and painted surfaces follow it closely enough for plant calculations.

Use the built-in table as a starting point: polished aluminium is around 0.05, oxidised steel around 0.8, painted or anodised surfaces around 0.9. Surface condition dominates — use the in-service condition, not the as-machined one.