The diagram shows a conical section fabricated from pure aluminum. It is of circular cross section having diameter D = ax¹/2, where a = 0.5 m²/2. The small end is located at x₁ = 25 mm and large end at x₂ = 125 mm. The end temperatures are T₁ = 600 K and 7₂ = 400 K, while the lateral surface is well insulated. (a) Derive an expression for the temperature distribution 7(x) in symbolic form, assuming one-dimensional conditions. Sketch the temperature distribution. (b) Calculate the heat rate q

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Author:Kreith, Frank; Manglik, Raj M.
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Chapter3: Transient Heat Conduction
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Problem 3.4P
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The diagram shows a conical section fabricated from pure aluminum. It is of circular cross section having diameter D = ax¹/2, where a = 0.5 m¹/2. 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.
T₂
T₁
1.x₂
(a) Derive an expression for the temperature distribution 7(x) in symbolic form, assuming one-dimensional conditions. Sketch the temperature distribution.
(b) Calculate the heat rate qx²
Transcribed Image Text:The diagram shows a conical section fabricated from pure aluminum. It is of circular cross section having diameter D = ax¹/2, where a = 0.5 m¹/2. 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. T₂ T₁ 1.x₂ (a) Derive an expression for the temperature distribution 7(x) in symbolic form, assuming one-dimensional conditions. Sketch the temperature distribution. (b) Calculate the heat rate qx²
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