GATE 2023 BT – Question 63
An evaporator has 0.15 m glass-wool insulation, inner and outer temperatures 700°C and 80°C, mean conductivity $0.29\ \mathrm{W\ m^{-1}K^{-1}}$ and wall area $1.2\ \mathrm{m^2}$. The heat loss in W, rounded to the nearest integer, is ___________.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 1438
Explanation
This is steady one-dimensional conduction through a plane wall (Fourier's law):
$$Q=\frac{k\,A\,(T_1-T_2)}{L}.$$
**Numbers.** $k=0.29$ W m⁻¹ K⁻¹, $A=1.2$ m², $\Delta T=700-80=620$ K, $L=0.15$ m:
$$Q=\frac{0.29\times1.2\times620}{0.15}=\frac{215.76}{0.15}=1438.4\text{ W}.$$
The heat loss is **1438 W**.