Steam at 235°C is flowing inside a steel pipe (k = 61 W/m·K) whose inner and outer diameters are 10 cm and 12 cm, respectively, in an environment at 20°C. The heat transfer coefficients inside and outside the pipe are 105 W/m²·K and 14 W/m²·K, respectively. Determine

(a) The thickness of the insulation (k = 0.038 W/m·K) needed to reduce the heat loss by 95 percent

(b) The thickness of the insulation needed to reduce the exposed surface temperature of insulated pipe to 40°C for safety reasons.