Fin Efficiency: annular#rectangular#r2r1_3.0
Fin efficiency (eta) vs dimensionless parameter mL for straight, annular, and pin fins — rectangular, triangular, parabolic, and conical profiles
| pk | mL value | L definition | efficiency eta | fin profile | fin type | formula | geometry description | m definition | notes | r2 r1 ratio | tip condition |
|---|---|---|---|---|---|---|---|---|---|---|---|
| annular#rectangular#r2r1_3.0 | 0 | r2-r1 radial fin height; mL=m*(r2-r1) | 1 | rectangular | annular | (2*r1/(m*(r2^2-r1^2)))*(K1(mr1)*I1(mr2)-I1(mr1)*K1(mr2))/(I0(mr1)*K1(mr2)+K0(mr1)*I1(mr2)) | Annular circular fin of uniform thickness r2/r1=3.0 | sqrt(2h/(k*t)) where t is fin thickness; L=r2-r1 is radial height | r2/r1=3.0. r1=tube outer radius r2=fin tip radius. For convective tip use r2c=r2+t/2. I0 I1 K0 K1 are modified Bessel functions. | 3 | insulated |
| annular#rectangular#r2r1_3.0 | 0.2 | r2-r1 radial fin height; mL=m*(r2-r1) | 0.9775 | rectangular | annular | (2*r1/(m*(r2^2-r1^2)))*(K1(mr1)*I1(mr2)-I1(mr1)*K1(mr2))/(I0(mr1)*K1(mr2)+K0(mr1)*I1(mr2)) | Annular circular fin of uniform thickness r2/r1=3.0 | sqrt(2h/(k*t)) where t is fin thickness; L=r2-r1 is radial height | r2/r1=3.0. r1=tube outer radius r2=fin tip radius. For convective tip use r2c=r2+t/2. I0 I1 K0 K1 are modified Bessel functions. | 3 | insulated |
| annular#rectangular#r2r1_3.0 | 0.4 | r2-r1 radial fin height; mL=m*(r2-r1) | 0.9161 | rectangular | annular | (2*r1/(m*(r2^2-r1^2)))*(K1(mr1)*I1(mr2)-I1(mr1)*K1(mr2))/(I0(mr1)*K1(mr2)+K0(mr1)*I1(mr2)) | Annular circular fin of uniform thickness r2/r1=3.0 | sqrt(2h/(k*t)) where t is fin thickness; L=r2-r1 is radial height | r2/r1=3.0. r1=tube outer radius r2=fin tip radius. For convective tip use r2c=r2+t/2. I0 I1 K0 K1 are modified Bessel functions. | 3 | insulated |
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