-
A fin has 5 mm diameter and 100 mm length. The thermal conductivity of fin material is 400 Wm–1K–1. One end of the fin is maintained at 130°C and its remaining surface is exposed to ambient air at 30°C. If the convective heat transfer coefficient is 40 Wm–2K–1, the heat loss (in W) from the fin is
-
- 0.08
- 5.0
- 7.0
- 7.8
- 0.08
Correct Option: B
Fin diameter, d = 5 mm
Fin length, L = 100 mm
k = 400 W/mK
T0 = 130°C
T∞ = 30°C
h = 40 W/m2K
∴ Heat loss from fin Q = √kAhP (T0 - T∞) tanh ml
where P = πd = 3.14 × 5 × 10– 3 = 0.015
A = | d2 = | × (5 × 10– 3)2 = 1.96 × 10– 5 m 2 | ||
4 | 4 |
∴ m = √hp / kA = √(40 × 0.0157) / (400 × 1.96 × 10– 5) = 8.949
∴ ml = 8.949 × 0.100 = 0.895
∴ Q = √40 × 0.0157 × 400 × 1.96 × 10– 5(T0 - T∞) tanh (0.895) = 5.0 W