[Radiation]

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Aligned Parallel Plates

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

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Inputs

Plate length (m)

Plate width (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

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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.

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Aligned Parallel Plates

Computes the net radiant heat exchange between two equal, isothermal gray rectangles ( $L \times W$ ) mounted face-to-face and directly opposed, separated by a gap $D$ .

View Factor

With the dimensionless ratios

x = \frac{L}{D}, y = \frac{W}{D}

the shape factor for two aligned parallel rectangles is

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]

As the plates become large compared with the gap ( $x, y \to \infty$ ) the view factor approaches unity; for square plates with $x = y = 1$ it gives $F_{12} \approx 0.200$ .

Net Radiant Exchange

For a two-surface gray, diffuse enclosure,

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 $σ = 5.670374 \times 1 0^{- 8} W/m^{2} K^{4}$ , $A_{1} = A_{2} = L W$ , 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

Incropera, F.P. & DeWitt, D.P., Fundamentals of Heat and Mass Transfer, Wiley.
Holman, J.P., Heat Transfer, 7th ed., McGraw-Hill, 1990.

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Frequently asked questions

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