GATE 2026 CH – Question 53
A pipe with outer diameter of 0.02 m, carries hot water. The temperature at the outer surface of the pipe is 70 °C. This pipe is covered with two concentric layers of insulation, each having a thickness of 0.01 m. The first layer (adjacent to the pipe) is made up of felt material (thermal conductivity $k_f = 0.12$ W m$^{-1}$ °C$^{-1}$), and the next layer is made up of asbestos (thermal conductivity $k_{as} = 0.15$ W m$^{-1}$ °C$^{-1}$). The insulated pipe is exposed to ambient air at 20 °C. The convection heat transfer coefficient at the outer insulation layer is 3 W m$^{-2}$ °C$^{-1}$. At steady state, neglecting heat transfer due to radiation, the heat loss at the outer insulation layer (in W m$^{-1}$) is _____ (rounded off to two decimal places).
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Correct answer: 15.96 to 16.12
Explanation
The radii are $r_1 = 0.01$, $r_2 = 0.02$ and $r_3 = 0.03$ m. The resistances per metre of length are: felt $\frac{\ln(2)}{2\pi \times 0.12} = 0.9193$, asbestos $\frac{\ln(1.5)}{2\pi \times 0.15} = 0.4302$ and convection $\frac{1}{2\pi \times 0.03 \times 3} = 1.7684$ m °C/W. The total is 3.1179, so $q = \frac{70 - 20}{3.1179} = 16.04$ W/m.