radius R, at a distance H from centres, with hH/R. (e.g. for h=2, F12=1/4) Case View factor Plot From a small planar plate (one face or both) level to a sphere of radius R, at a distance H from centres, with hH/R. with () (e.g. for h=2, F12=0.029) Tilted Case View factor Plot From a small planar surface tilted to a sphere of radius R, at a distance H from centres, with hH/R; the tilting angle  is between the normal and the line of centres. For the facing surface: -if ||arccos(1/h) (i.e. plane not cutting the sphere), -if ||>arccos(1/h) (i.e. cutting the sphere), with For the plate (the two surfaces): -if ||arccos(1/h) (i.e. plane not cutting the sphere, hence F12=0 for the back side), -if ||>arccos(1/h) (i.e. plane cutting the sphere), F12 can be obtained as the semisum of values for the facing surface and for the opposite surface, the latter obtained as the complement angle (i.e. with → ). (e.g. for h=1.5 and =/3 (60º): F12=0.226 for the facing side, F12=0.004 for the opposite side, and F12=0.115 for the two-side plate) Patch to a spherical cap Case View factor Plot From a small planar plate facing a spherical cap subtending a half-cone angle  (or any other surface subtending the same solid angle). (e.g. for =45º, F12=1/2) Notice that the case ‘patch to frontal sphere’ above, can be recovered in our case with max=arcsin(R/H). Sphere to concentric external cylinder Case View factor Plot
From a sphere (1) to interior surface of a concentric cylinder (2) of radius R and height 2H, hH/R. Sphere radius, Rsph, is irrelevant but must be RsphH. (e.g. for H=R, i.e. h =1, F12=0.707) Disc to frontal sphere Case View factor Plot From a disc of radius R1 to a frontal sphere of radius R2 at a distance H between centres (it must be H>R1), with hH/R1 and r2R2/R1. (e.g. for h=r2=1, F12=0.586) From a sphere of radius R1 to a frontal disc of radius R2 at a distance H between centres (it must be H>R1, but does not depend on R1), with hH/R2. (e.g. for R2=H and R1≤H, F12=0.146) Cylinder to large sphere Case View factor Plot From a small cylinder (external lateral area only), at an altitude H=hR and tilted an angle , to a large sphere of radius R,  is between the cylinder axis and the line of centres). Coaxial (=0): with Perpendicular (=/2): with elliptic integrals E(x). Tilted cylinder: with (e.g. for h=1 and any , F12=1/2) Cylinder to its hemispherical closing cap Case View factor Plot From a finite cylinder (surface 1) of radius R and height H, to its hemispherical closing cap (surface 2), with r=R/H. Let surface 3 be the base, and surface 4 the virtual base of the hemisphere. , , , , , , with (e.g. for R=H, F11=0.38, F12=0.31, F21=0.31, F22=0.50, F23=0.19, F31=0.62, F32=0.38, F34=0.38)
Sphere to sphere Small to very large Case View factor Plot From a sphere of radius R1 to a much larger sphere of radius R2 at a distance H between centres (it must be H>R2, but does not depend on R1), with hH/R2. (e.g. for H=R2, F12=1/2) Concentric spheres Case View factor Plot Between concentric spheres of radii R1 and R2>R1, with rR1/R2<1. F12=1 F21=r2 F22=1r2 (e.g. for r=1/2, F12=1, F21=1/4, F22=3/4) Sphere to concentric hemisphere Case View factor Plot From a sphere of radius R1 to a larger concentric hemisphere of radius R2>R1, with RR2/R1>1. Let the enclosure be ‘3’. F12=1/2, F13=1/2, F21=1/R2, F23=1F21F22, with (e.g. for R=2, F12=1/2, F21=1/4, F13=1/2, F23=0.34,F22=0.41) Hemispheres Concentric hemispheres Case View factor Plot From a hemisphere of radius R1 to a larger concentric hemisphere of radius R2>R1, with RR2/R1>1. Let the closing planar annulus be surface 3. , , , , , , with Limit for R→∞ (=1/2): F12=3/4, F13=1/4 (e.g. for R=2, F12=0.86, F21=0.21, F13=0.14, F31=0.09, F32=0.91, F23=0.34, F22=0.41) Small hemisphere frontal to large sphere Case View factor Plot From a small hemisphere (one face) to a large frontal sphere of radius R at a distance HR between centres, with hH/R. (e.g. for H=R, F12=3/4) Hemisphere to planar surfaces Case View factor Plot
convex side, 1” the diametrical section, and 3 the enclosure. Convex side: Equal external cylinders Case View factor Plot From a of radius R to an equal cylinder at a distance H between centres (it must be H>2R), with hH/R. Note. See the method, above. (e.g. for H=2R, F12=1/21/=0.18) Equal external hemi-cylinders Case View factor Plot From a hemi-cylinder of radius R to an separated a distance W, with rR/W (wW/R=1/r). Let the strip in between be (3). (limit for r→∞: ) (limit for r→0: ) (e.g. for r=1, F12=0.11, F13=0.05) Planar strip to cylinder Case View factor Plot From frontal surface of strip (1) of width W to a cylinder (2) of radius R at a distance H between centres, with vW/(2R) and hH/R>1. with xv/h=(W/2)/H (e.g. for W=R=H, i.e. v=1/2, h=1, x=1/2, F12=0.927, F21=0.148) From frontal surface of off-centre strip of width W to a cylinder of radius R at a distance H to the strip plane. The solution is the composition of a strip of with W1 and a strip of width W2, with v1W1/R, v2W2/R, hH/R>1, x1W1/H, x2W2/H. For W=W2W1: For W=W2W1: (e.g. for W1=0 & W2=R=H, i.e. v1=0, v2=1, h=1, x1=0, x2=1, F12=0.463, F21=0.074) For W1=0 & W=W2 (with xW/H):