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=DWthe shape factor for two aligned parallel rectangles is
F12=πxy2[ln1+x2+y2(1+x2)(1+y2)+x1+y2tan−11+y2x+y1+x2tan−11+x2y−xtan−1x−ytan−1y]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 F12≈0.200.
Net Radiant Exchange
For a two-surface gray, diffuse enclosure,
Q=ε1A11−ε1+A1F121+ε2A21−ε2σ(T14−T24)with σ=5.670374×10−8 W/m2K4, A1=A2=LW, and temperatures in Kelvin. When both surfaces are black this reduces to Q=σA1F12(T14−T24).
References
- Incropera, F.P. & DeWitt, D.P., Fundamentals of Heat and Mass Transfer, Wiley.
- Holman, J.P., Heat Transfer, 7th ed., McGraw-Hill, 1990.