Perpendicular Plates Sharing a Common Edge
Computes the net radiant heat exchange between two isothermal gray surfaces that share a common edge and meet at right angles. Each plate extends a distance L1 (or L2) away from the shared edge, which has width W.
View Factor
With the dimensionless ratios
x=WL1,y=WL2the shape factor between two perpendicular rectangles with a common edge is
F12=πx1[xtan−1x1+ytan−1y1−x2+y2tan−1x2+y21+41lnG] G=1+x2+y2(1+x2)(1+y2)[(1+x2)(x2+y2)x2(1+x2+y2)]x2[(1+y2)(x2+y2)y2(1+x2+y2)]y2For two equal squares meeting at a common edge (x=y=1) this gives F12≈0.200.
Net Radiant Exchange
Treating both plates as gray, diffuse surfaces forming a two-surface enclosure, the net heat rate is
Q=ε1A11−ε1+A1F121+ε2A21−ε2σ(T14−T24)with σ=5.670374×10−8 W/m2K4, A1=L1W, A2=L2W, and temperatures in Kelvin. When both surfaces are black (ε1=ε2=1) 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.