Chapter 2, Problem 115P

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 $k(T)=k_0(1+\beta T\text{) where }{k}_0=1.23\text{ W/m}\text{.K, }\beta =0.002{\text{K}}^{\text{-1}},andT\text{ is in K}\text{.}$ and For safety reasons and to protect workers from thermal burns, 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 low enough temperature to avoid thermal burns.