Problem 2 [4 marks] A steel pipe has a fluid flowing through it at 100C, resulting...

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Problem 2 [4 marks] A steel pipe has a fluid flowing through it at 100°C, resulting in a convective heat transfer coeffi- cient of 200 W m2 K-¹. The steel pipe is surrounded by a very thin heater (negligible thickness). A cast iron tube surrounds the heater and insulation surrounds the cast iron tube. The dimensions and physical properties of each of these layers are provided on the diagram. The heater has an unknown heating rate per meter of pipe length. Only convection occurs on the outer surface of the insulation (neglect radiation effects). The temperature of the ambient air is 25°C and natural convection results in a convective heat transfer coefficient of 40 W m2 K-¹ on the outer surface of the insulation. At steady state the temperature of the heater is 200°C. You should assume that the system is very long and that the ends are insulated. Therefore, heat is only transferred in the radial direction. Determine the heating rate per meter of cylinder length provided by the heater (gen), the outside surface temperature of the insulation (T4), and the inside surface temperature of the steel pipe (T₁). Heater (Negligible Thickness) (w/m) T₂ T₁ T₂ - 200°C T₁ Tmz -25°C h-40 W m K T-100°C -200 W m² K¹ 4= 30 mm 23 mm 20 mm -r₁-15 mm Steel k₂= 15 Wm¹ K¹ Cast Iron K₂-60W ¹K¹ Insulation k=0.2 Wm¹K¹ Problem 2 [4 marks] A steel pipe has a fluid flowing through it at 100°C, resulting in a convective heat transfer coeffi- cient of 200 W m2 K-¹. The steel pipe is surrounded by a very thin heater (negligible thickness). A cast iron tube surrounds the heater and insulation surrounds the cast iron tube. The dimensions and physical properties of each of these layers are provided on the diagram. The heater has an unknown heating rate per meter of pipe length. Only convection occurs on the outer surface of the insulation (neglect radiation effects). The temperature of the ambient air is 25°C and natural convection results in a convective heat transfer coefficient of 40 W m2 K-¹ on the outer surface of the insulation. At steady state the temperature of the heater is 200°C. You should assume that the system is very long and that the ends are insulated. Therefore, heat is only transferred in the radial direction. Determine the heating rate per meter of cylinder length provided by the heater (gen), the outside surface temperature of the insulation (T4), and the inside surface temperature of the steel pipe (T₁). Heater (Negligible Thickness) (w/m) T₂ T₁ T₂ - 200°C T₁ Tmz -25°C h-40 W m K T-100°C -200 W m² K¹ 4= 30 mm 23 mm 20 mm -r₁-15 mm Steel k₂= 15 Wm¹ K¹ Cast Iron K₂-60W ¹K¹ Insulation k=0.2 Wm¹K¹