If, for the conditions of Problem 15.29, ho in Btu/h ft °F varies according to h₀ = 0.575/D¹₀/4, where D₀ is the outside diameter of the insulation in feet, determine the thickness of insulation that will reduce the heat flux to one-half that of the value for the bare pipe.

Data From Problem 15.29

A 1-in.-nominal-diameter steel pipe with its outside surface at 400°F is located in air at 90°F with the convective heat-transfer coefficient between the surface of the pipe and the air equal to 1.5 Btu/h ft °F. It is proposed to add insulation having a thermal conductivity of 0.06 Btu/h ft °F to the pipe to reduce the heat loss to one-half that for the bare pipe. What thickness of insulation is necessary if the surface temperature of the steel pipe and ho remain constant?