The cross section of a long circular tube, which is divided into two semi cylindrical ducts by a thin wall, is shown below. Sides 1 and 2 are maintained at temperatures of T₁ = 600 K and T₂ = 400 K, respectively, while the mean temperatures of gas flows through ducts 1 and 2 are T_{g, 1} = 571 K and T_{g, 2} = 449 K, respectively. The fore-going temperatures are invariant in the axial direction. The gases provide surface convection coefficients of h₁ = h₂ = 5 W/m₂ ? K, while all duct surfaces may be approximated as blackbodies (?₁ = ?₂ = ? _w = 1). What is the duct wall temperature, T_w? By performing an energy balance on the gas in side 1, verify that T_{g,, 1} is, in fact, equal to 571 K.

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Gas Gas T,1,