A pipe is used for transporting boiling water in which the inner surface is at 100C. The

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A pipe is used for transporting boiling water in which the inner surface is at 100°C. The pipe is situated in surroundings where the ambient temperature is 10°C and the convection heat transfer coefficient is 70 W/m2∙K. The wall thickness of the pipe is 3 mm and its inner diameter is 30 mm. The pipe wall has a variable thermal conductivity given as k(T) = k0 (1 + βT), where k0 = 1.23 W/m ∙ K, β = 0.002 K−1, and T is in K. For safety reasons and to prevent thermal burn to workers, the outer surface temperature of the pipe should be kept below 50°C. Determine whether the outer surface temperature of the pipe is at a safe temperature so as to avoid thermal burn.

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