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 ...

KNOWN Conduction in a conical section with prescribed diameter D as a function of x in 12 the form D ...

The diagram shows a conical section fabricated from pure aluminum. It is of circular cross section having

Question:

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.

Distribution
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