Problem 1: Consider the composite cylinder in the figure below. Let r = 3 cm, r2...

 

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Problem 1: Consider the composite cylinder in the figure below. Let r₁ = 3 cm, r2 = 6 cm r3 = 10 cm, L = 1 m. The thermal conductivity KA = 0.05(1+0.0065 T) kB 0.04(1+0.0076 T) W/(m. °C) KA T₂ kB a) Suppose the surface temperatures T₁ = 500 °C and T3 = 20 °C are given, calculate the interface temperature between material-A and material-B, T2 and the heat transfer rate Q. (Ans: T₂ = 307 °C, Q = 316.8 W) b) Suppose the surface temperatures T₁ and T3 are not known. Instead, the inside fluid temperature is Too,i = 500 °C, hi = 1000 W/m².K and outside fluid temperature is Too,o= 20 °C, ho = 20 W/m².K are given. Calculate the unknown temperatures T₁, T2, T3 and the heat transfer rate Q. (Ans: T₁ = 498.36 °C, T2 = 311.02 °C, T3 = 44.53 °C; Q = 308.26W) Problem 1: Consider the composite cylinder in the figure below. Let r₁ = 3 cm, r2 = 6 cm r3 = 10 cm, L = 1 m. The thermal conductivity KA = 0.05(1+0.0065 T) kB 0.04(1+0.0076 T) W/(m. °C) KA T₂ kB a) Suppose the surface temperatures T₁ = 500 °C and T3 = 20 °C are given, calculate the interface temperature between material-A and material-B, T2 and the heat transfer rate Q. (Ans: T₂ = 307 °C, Q = 316.8 W) b) Suppose the surface temperatures T₁ and T3 are not known. Instead, the inside fluid temperature is Too,i = 500 °C, hi = 1000 W/m².K and outside fluid temperature is Too,o= 20 °C, ho = 20 W/m².K are given. Calculate the unknown temperatures T₁, T2, T3 and the heat transfer rate Q. (Ans: T₁ = 498.36 °C, T2 = 311.02 °C, T3 = 44.53 °C; Q = 308.26W)