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Aligned Parallel Plates

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

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Radiation scales with absolute temperature to the fourth power — a surface at 600 °C radiates over five times more than the same surface at 300 °C.

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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×W) mounted face-to-face and directly opposed, separated by a gap D.

View Factor

With the dimensionless ratios

x=DL,y=DW

the shape factor for two aligned parallel rectangles is

F12=πxy2[ln1+x2+y2(1+x2)(1+y2)+x1+y2tan11+y2x+y1+x2tan11+x2yxtan1xytan1y]

As the plates become large compared with the gap (x,y) the view factor approaches unity; for square plates with x=y=1 it gives F120.200.

Net Radiant Exchange

For a two-surface gray, diffuse enclosure,

Q=ε1A11ε1+A1F121+ε2A21ε2σ(T14T24)

with σ=5.670374×108 W/m2K4, A1=A2=LW, and temperatures in Kelvin. When both surfaces are black this reduces to Q=σA1F12(T14T24).

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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.