A mixture of chemicals is flowing in a pipe (k = 14 W/m ∙ K, D_i = 2.5 cm, D_o = 3 cm, and L = 10 m). 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 thermal 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 W/m2∙K. 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.