Numerical Analysis in Heat Transfer of a Triangular Fin

삼각휜 열전달의 수치해석

One-dimensional approximation for fin problems is widely used in current texts and industrial practice. The errors caused by this approximation is analysed for a longitudinal triangular fin by the numerical solution of two-dimensional fin equation. Two-dimensional solution is obtained by the finite element method and com pared with the one-dimensional esact solution. The results show that total heat transfer and fin efficiency are overestimated by the one-dimensional approximation. The factors which cause these errors are the Biot number (Bi) and the ratio of fin length to half the thickness (L/a). When Bi is smaller than 1.0 these errors are smaller than $10\%$, but when Bi is larger than 5.0 they are a few ten percents. Fin efficiency obtaned by one-dimensional and long fin assumption is valid only then Bi is small and L/a is large.