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+R22the shape factor from disk 1 to disk 2 is
F12=21⎩⎨⎧S−[S2−4(r1r2)2]1/2⎭⎬⎫For two equal disks with R1=R2=1 this gives F12≈0.382; as the disks grow large relative to the gap the factor approaches unity.
Net Radiant Exchange
Q=ε1A11−ε1+A1F121+ε2A21−ε2σ(T14−T24)with σ=5.670374×10−8 W/m2K4, A1=πr12, A2=πr22, and temperatures in Kelvin. When both surfaces are black this reduces to Q=σA1F12(T14−T24).
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.