Fin Efficiency: straight#parabolic_concave

Fin efficiency (eta) vs dimensionless parameter mL for straight, annular, and pin fins — rectangular, triangular, parabolic, and conical profiles

Mechanical Engineeringpk: straight#parabolic_concave3 rows

pk	mL value	L definition	efficiency eta	fin profile	fin type	formula	geometry description	m definition	notes	tip condition
straight#parabolic_concave	0	fin length	1	parabolic_concave	straight	(-1+sqrt(1+4(mL)^2))/(2(mL)^2)	Straight fin concave parabolic profile tip thickness zero	sqrt(2h/(k*t_b)) where t_b is base half-thickness	Profile t(x)=t_b*(1-x/L)^2. Exact Euler-Cauchy ODE solution. Lowest efficiency among standard straight profiles. At mL=0.849 eta=0.6733 matches EES ref 0.6735.	insulated
straight#parabolic_concave	0.2	fin length	0.9629	parabolic_concave	straight	(-1+sqrt(1+4(mL)^2))/(2(mL)^2)	Straight fin concave parabolic profile tip thickness zero	sqrt(2h/(k*t_b)) where t_b is base half-thickness	Profile t(x)=t_b*(1-x/L)^2. Exact Euler-Cauchy ODE solution. Lowest efficiency among standard straight profiles. At mL=0.849 eta=0.6733 matches EES ref 0.6735.	insulated
straight#parabolic_concave	0.4	fin length	0.877	parabolic_concave	straight	(-1+sqrt(1+4(mL)^2))/(2(mL)^2)	Straight fin concave parabolic profile tip thickness zero	sqrt(2h/(k*t_b)) where t_b is base half-thickness	Profile t(x)=t_b*(1-x/L)^2. Exact Euler-Cauchy ODE solution. Lowest efficiency among standard straight profiles. At mL=0.849 eta=0.6733 matches EES ref 0.6735.	insulated

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