The diagram shows a conical section fabricated from pure aluminum It is of circular cross section having diameter D ax , where a 0 5 m The small end is located at X 1 25 mm and the large end at X 2 125 mm The end temperatures are T 1 600 K and T 2 400 K, while the lateral surface is well insulated (a) Derive an expression for the temperature distribution T(x) in symbolic form, assuming one dimensional conditions Sketch the temperature distribution (b) Calculate the heat rate q x T2

Question: The diagram shows a conical section fabricated from pure aluminum. It is of circular cross section having diameter D = ax , where a

The diagram shows a conical section fabricated from pure aluminum. It is of circular cross section having diameter D = ax^½, where a = 0.5 m^½. The small end is located at X₁ = 25 mm and the large end at X₂ = 125 mm. The end temperatures are T₁ = 600 K and T₂ = 400 K, while the lateral surface is well insulated.

(a) Derive an expression for the temperature distribution T(x) in symbolic form, assuming one-dimensional conditions. Sketch the temperature distribution.

(b) Calculate the heat rate q_x.

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