[Radiation]

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Perpendicular Plates — Common Edge

Net radiant heat exchange between two gray rectangles meeting at a common edge.

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Inputs

Plate 1 extent (m)

Plate 2 extent (m)

Common edge width (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

Perpendicular Plates — Common Edge — schematic

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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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Computes the net radiant heat exchange between two isothermal gray surfaces that share a common edge and meet at right angles. Each plate extends a distance $L_{1}$ (or $L_{2}$ ) away from the shared edge, which has width $W$ .

View Factor

With the dimensionless ratios

x = \frac{L _{1}}{W}, y = \frac{L _{2}}{W}

the shape factor between two perpendicular rectangles with a common edge is

F_{12} = \frac{1}{π x} [x tan^{- 1} \frac{1}{x} + y tan^{- 1} \frac{1}{y} - x^{2} + y^{2} tan^{- 1} \frac{1}{x ^{2} + y ^{2}} + \frac{1}{4} ln G]

G = \frac{( 1 + x ^{2} ) ( 1 + y ^{2} )}{1 + x ^{2} + y ^{2}} [\frac{x ^{2} ( 1 + x ^{2} + y ^{2} )}{( 1 + x ^{2} ) ( x ^{2} + y ^{2} )}]^{x^{2}} [\frac{y ^{2} ( 1 + x ^{2} + y ^{2} )}{( 1 + y ^{2} ) ( x ^{2} + y ^{2} )}]^{y^{2}}

For two equal squares meeting at a common edge ( $x = y = 1$ ) this gives $F_{12} \approx 0.200$ .

Net Radiant Exchange

Treating both plates as gray, diffuse surfaces forming a two-surface enclosure, the net heat rate is

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 $σ = 5.670374 \times 1 0^{- 8} W/m^{2} K^{4}$ , $A_{1} = L_{1} W$ , $A_{2} = L_{2} W$ , and temperatures in Kelvin. When both surfaces are black ( $ε_{1} = ε_{2} = 1$ ) 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 gray rectangles meeting at a common edge. 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.