[Radiation]

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Coaxial Parallel Disks

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

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Inputs

Disk 1 radius (m)

Disk 2 radius (m)

Disk separation (m)

Disk 1 temperature (°C)

Disk 2 temperature (°C)

Disk 1 surface

Disk 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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Coaxial Parallel Disks

Computes the net radiant heat exchange between two isothermal gray disks of radii $r_{1}$ and $r_{2}$ , mounted coaxially and directly opposed, separated by a gap $D$ .

View Factor

With the dimensionless radii

R_{1} = \frac{r _{1}}{D}, R_{2} = \frac{r _{2}}{D}, S = 1 + \frac{1 + R _{2}^{2}}{R _{1}^{2}}

the shape factor from disk 1 to disk 2 is

F_{12} = \frac{1}{2} ⎩ ⎨ ⎧ S - [S^{2} - 4 (\frac{r _{2}}{r _{1}})^{2}]^{1/2} ⎭ ⎬ ⎫

For two equal disks with $R_{1} = R_{2} = 1$ this gives $F_{12} \approx 0.382$ ; as the disks grow large relative to the gap the factor approaches unity.

Net Radiant Exchange

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

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.