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Aligned Parallel Square Plates (Equal Size)

Net radiant heat exchange between two equal, directly-opposed gray square 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 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=LW

and the aligned-parallel-rectangles shape factor reduces to

F12=πXY2[ln1+X2+Y2(1+X2)(1+Y2)+X1+Y2tan11+Y2X+Y1+X2tan11+X2YXtan1XYtan1Y]

Validity improves when the plate side exceeds about one fifth of the separation (W/L>0.2). For X=Y=1 the factor is F120.200.

Net Radiant Exchange

Q=ε1A11ε1+A1F121+ε2A21ε2σ(T14T24)

with σ=5.670374×108 W/m2K4, A1=A2=W2, and temperatures in Kelvin. When both surfaces are black this reduces to Q=σA1F12(T14T24).

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.
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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.