Chapter 3, Problem 99P

A mixture of chemicals is flowing in a pipe $(k=14\text{ W/m}\text{.K,}\text{}{\text{ D}}_{\text{i}}\text{ =2}{\text{.5 cm, D}}_{\text{o}}\text{=3 cm and L= 10 m)}\text{.}$ and During the transport. the mixture undergoes an exothermic reaction having an average temperature of 135°C and a convection heat transfer coefficient of 150 W/m² K. To prevent any incident of thennal burn, the pipe needs to be insulated. However, due to the vicinity of the pipe, there is only enough room to fit a 2.5-cm-thick layer of insulation over the pipe. The pipe is situated in a plant where the average ambient air temperature is 20°C and the convection heat transfer coefficient is 25 Win2K. Determine the insulation for the pipe such that the thermal conductivity of the insulation is sufficient to maintain the outside surface temperature at 45°C or lower.