Question

The fin parameters are as follows Dia. of
the fin 2 cm. thermal conductivity = 200 W/
mK, convective heat transfer coefficient =
12 W/m-K base temperature of the fin =
500 °C, Air temperature = 50 °C. The rate
of heat transfer from the fin is
(A) 119.7 watts (B) 97.93 watts
(C) 57.7 watts (D) 4.62 watts​

Answer 1

Given info : thermal conductivity, k = 20 W/mK , convection heat transfer coefficient, h = 12 W/mK

Base temperature of fin, T_f = 500°C

Air temperature, T_i = 50°C

Perimeter of fin, P = πd = 2π cm

Cross sectional area of fin , A = πd²/4 = π(2)²/4 = π cm²

To find : the rate of heat transfer from the fin

Solution : using formula, R = √(hpkA) (T_f - T_i)

= √(12 × 2π × 10¯² × 200 × π × 10¯⁴) (500 - 50)

= √(48π² × 10¯⁴) × 450

≈ 97.93 watt

Therefore the rate of heat transfer from the fin is 97.93 watt