Question

A plate fin of length L = 1.5 cm and thickness 2 mm has efficiency of____ (if k = 210 W/m-K, h = 285 W/m²K)
1. 84.1%
2. 87.2%
3. 89.9%
4. 92.4%

Answer 1

Correct Answer - Option 3 : 89.9%

Concept:

For plate-fin; width>>>thickness

then \(\frac{P}{A}\approx\frac{2}{t}\)

Corrected length, L_c = \(L + \frac{t}{2}\)

_{\(Efficiency, \eta = \frac{\tan h(mL_c)}{mL_c}\)}

Calculation:

Given:

\(\begin{array}{l} efficiency\;\eta = \frac{{\tan h\left( {mL_C} \right)}}{{mL_C}}\\ {L_C} = L + \frac{t}{2} = 1.5+\frac{{ 0.2}}{2} = 1.6cm\\ m = \sqrt {\frac{{hP}}{{K{A_C}}}} = \sqrt {\frac{{2h}}{{Kt}}}= \sqrt {\frac{{285 \times 2}}{{210 \times 2 \times {{10}^{ - 3}}}}} \\ m{L_C} = 1.6\sqrt {\frac{{2 \times 285}}{{210 \times 2 \times {{10}^{ - 3}}}}} \times {10^{ - 2}} = 0.589\\ \eta = \frac{{\tan h\left( {0.589} \right)}}{{0.589}} = 89.9\% \end{array}\)