Fin Efficiency: pin#conical
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 | tip condition |
|---|---|---|---|---|---|---|---|---|---|---|
| pin#conical | 0 | pin length | 1 | conical | pin | (1/mL)*I1(2mL)/I0(2mL) | Pin spine fin conical diameter tapers linearly to zero at tip | sqrt(4h/(k*D_b)) where D_b is base diameter | D(x)=D_b*(1-x/L). Same Bessel form as triangular straight fin due to equivalent ODE. Tip naturally insulated (zero area). | insulated |
| pin#conical | 0.2 | pin length | 0.9805 | conical | pin | (1/mL)*I1(2mL)/I0(2mL) | Pin spine fin conical diameter tapers linearly to zero at tip | sqrt(4h/(k*D_b)) where D_b is base diameter | D(x)=D_b*(1-x/L). Same Bessel form as triangular straight fin due to equivalent ODE. Tip naturally insulated (zero area). | insulated |
| pin#conical | 0.4 | pin length | 0.9277 | conical | pin | (1/mL)*I1(2mL)/I0(2mL) | Pin spine fin conical diameter tapers linearly to zero at tip | sqrt(4h/(k*D_b)) where D_b is base diameter | D(x)=D_b*(1-x/L). Same Bessel form as triangular straight fin due to equivalent ODE. Tip naturally insulated (zero area). | insulated |
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