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Coaxial Parallel Disks

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

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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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Coaxial Parallel Disks

Computes the net radiant heat exchange between two isothermal gray disks of radii r1 and r2, mounted coaxially and directly opposed, separated by a gap D.

View Factor

With the dimensionless radii

R1=Dr1,R2=Dr2,S=1+R121+R22

the shape factor from disk 1 to disk 2 is

F12=21S[S24(r1r2)2]1/2

For two equal disks with R1=R2=1 this gives F120.382; as the disks grow large relative to the gap the factor approaches unity.

Net Radiant Exchange

Q=ε1A11ε1+A1F121+ε2A21ε2σ(T14T24)

with σ=5.670374×108 W/m2K4, A1=πr12, A2=πr22, 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 coaxial, directly-opposed gray disks. 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.