Aligned Parallel Square Plates
Computes the net radiant heat exchange between two equal, isothermal gray square plates of side W, mounted face-to-face and directly opposed, separated by a gap L.
View Factor
For a square plate both in-plane ratios are equal,
X=Y=LWand the aligned-parallel-rectangles shape factor reduces to
F12=πXY2[ln1+X2+Y2(1+X2)(1+Y2)+X1+Y2tan−11+Y2X+Y1+X2tan−11+X2Y−Xtan−1X−Ytan−1Y]Validity improves when the plate side exceeds about one fifth of the separation (W/L>0.2). For X=Y=1 the factor is F12≈0.200.
Net Radiant Exchange
Q=ε1A11−ε1+A1F121+ε2A21−ε2σ(T14−T24)with σ=5.670374×10−8 W/m2K4, A1=A2=W2, 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.