Consider the fin of section 9.2.1 and its solution given by equation (9.21).

a. Develop expressions for the effectiveness and efficiency of such a fin.

b. Estimate the effectiveness for the following data:

\[\begin{array}{ll}k=10 \mathrm{~W} / \mathrm{m} \mathrm{K} & h=500 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K} \quad y_{o}=0.005 \mathrm{~m} \\L=40 \mathrm{~mm} & T_{b}=100^{\circ} \mathrm{C} \quad T_{\infty}=25^{\circ} \mathrm{C}\end{array}\]

c. How does your calculated value compare to the 1-D approximation?

Transcribed Image Text:

9.2.1 REVISITING THE FIN PROBLEM We presume that the fin shown in Figure 9.2 is not constructed well so that there are temperature gradients in the x- and y-directions. Our first task is to look for symmetry points, lines, or planes that Symmetry Plane T h Symmetry Plane X k conv FIGURE 9.2 Fin with two-dimensional control volume. Qy+Ay Ayi qx 9x+Ax Ax qy