Liquid flows in a metal pipe with an inner diameter of D1 = 20 mm and an outer diameter of D2 = 30 mm. The thermal conductivity of the pipe wall is 10 W/m⋅K. The inner surface of the pipe is coated with a thin polyvinylidene chloride (PVDC) lining. Along a length of 95 cm, the pipe outer surface is exposed to convection heat transfer with hot gas, at T∞ = 95° C and h = 6 W/m2 ⋅K, and thermal radiation with a surrounding at Tsurr = 95° C. The emissivity at the pipe outer surface is 0.3. The liquid flowing inside the pipe has a convection heat transfer coefficient of 52 W/m2⋅K. If the outer surface of the pipe is at 86° C, determine the temperature at the PVDC lining and the temperature of the liquid.
The ASME Code for Process Piping (ASME B31.3-2014, A323) recommends a maximum temperature for PVDC lining to be 81° C. Does the PVDC lining comply with the recommendation of the code?

Liquid flows in a metal pipe with an inner diameter of D1 = 22 mm and an outer diameter of D2 = 32 mm. The thermal conductivity of the pipe wall is 12 W/m-K. The inner surface of the pipe is coated with a thin polyvinylidene chloride (PVDC) lining. Along a length of 1 m, the pipe outer surface is exposed to convection heat transfer with hot gas, at To = 100°C and h= 5 W/m².K, and thermal radiation with a surrounding at Tsurr = 100°C. The emissivity at the pipe outer surface is 0.3. The liquid flowing inside the pipe has a convection heat transfer coefficient of 50 W/m²K. If the outer surface of the pipe is at 85°C, determine the temperature at the PVDC lining and the temperature of the liquid.