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Solved: The diagram shows a conical section fabricated
Chapter , Problem 3.39(choose chapter or problem)
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. (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 qx.
Questions & Answers
QUESTION:
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. (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 qx.
ANSWER:(a) The temperature distribution T(x) of conical section can be expressed using the one-dimensional heat equation:
T(x) = (T1-T2)*(x2-x)/(x2-x1) + T2
The temperature distribution can also be expressed as:
T(x) = (600K-400K)*(125m