GATE MT 2019 Q35

Steady state radial heat conduction through a hollow, infinitely long zirconia cylinder is governed by the following ordinary differential equation:

Where, T is the temperature and r is the radial distance. The inner surface of the hollow cylinder is maintained at 1473 K and the outer surface at 973 K. The rate of heat loss per unit length through the outer surface of the hollow cylinder (in 𝑊. 𝑚⁻¹, rounded off to the nearest integer) is __________.

Given: Inner radius of cylinder = 0.05 m; outer radius of cylinder = 0.07 m and thermal conductivity of zirconia (k) = 2 𝑊. 𝑚⁻¹. 𝐾⁻¹.