Steam having a quality of 98% at a pressure of 1.37 × 105 N/m2 is flowing at a velocity of 1 m/s through a steel pipe of 2.7 cm OD and 2.1 cm ID. The heat transfer coefficient at the inner surface, where condensation occurs, is 567 W/(m2 K). A dirt film at the inner surface adds a unit thermal resistance of 0.18 (m2 K)/W. Estimate the rate of heat loss per meter length of pipe if; (a) the pipe is bare, (b) the pipe is covered with a 5 cm layer of 85% magnesia insulation. For both cases assume that the convective heat transfer coefficient at the outer surface is 11 W/(m2 K) and that the environmental temperature is 21?C. Also estimate the quality of the steam after a 3-m length of pipe in both cases.GIVENA steel pipe with steam condensing on the insideDiametersOutside (Do) = 2.7 cm = 0.027 mInside (Di) = 2.1 cm = 0.021 mVelocity of the steam (V) = 1 m/sInitial steam quality (Xi) = 98%Steam pressure = 1.37 × 105 N/m2Heat transfer coefficientsInside (hci) = 567 W/(m2 K)Outside (hco) = 11 W/(m2 K)Thermal resistance of dirt film on inside surface (Rf) = 0.18 (m2 K)/WAmbient temperature (T??) = 21?CASSUMPTIONSSteady state conditions existConstant thermal conductivitySteel is 1% carbon steelRadiative heat transfer from the pipe is negligibleNeglect the pressure drop of thesteam

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Steel Plpe T=21°C -Insulation -D,= .021 m -Do=.027 m Steam Steam Dirt Flm Dirt Film L = 0.05 m Case (b) Case (a)