A plane wall of nuclear fuel with thickness L = 0.1 m, is insulated on one side at x = 0 and covered by a steel plate on the opposite side at x = L. There is no contact resistance between the steel and the fuel and open side of the steel is exposed to convection with T = 20°C and h = 400 W/m²/K. The steel plate has thickness b = .03 m and thermal conductivity kst = 15.1 W/m/K. The nuclear fuel has thermal conductivity kf= 1.4 W/m/K and provides a uniform volumetric heat generation of q=150 kW/m³. For steady-state conditions, neatly sketch the temperature profile shape and determine the maximum temperature in the wall by: a) Use resistance analogy to determine the temperature at the fuel-steel interface TL in terms of constant parameters q, L, b, kst, T, h and/or any other necessary parameters. b) Develop an expression for the steady-state temperature distribution within the fuel in terms of constant parameters q., L, kf, T₁ and/or any other necessary parameters. Hint: Consider an isothermal boundary condition T(x=L) TL found in part a). c) For the given parameter values, calculate the maximum temperature in the wall. d) Neatly plot the temperature distribution in the wall. Nuclear fuel The general heat equation is provided for reference. ƏT pc Ət · = kV²T+q qo L Steel ↑↑↑ To, h

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Transcribed Image Text:A plane wall of nuclear fuel with thickness L = 0.1 m, is insulated on one side at x = 0 and covered by a steel plate on the opposite side at x = L. There is no contact resistance between the steel and the fuel and open side of the steel is exposed to convection with T = 20°C and h = 400 W/m²/K. The steel plate has thickness b = .03 m and thermal conductivity kst = 15.1 W/m/K. The nuclear fuel has thermal conductivity kf= 1.4 W/m/K and provides a uniform volumetric heat generation of q=150 kW/m³. For steady-state conditions, neatly sketch the temperature profile shape and determine the maximum temperature in the wall by: a) Use resistance analogy to determine the temperature at the fuel-steel interface TL in terms of constant parameters à, L, b, kst, T, h and/or any other necessary parameters. b) Develop an expression for the steady-state temperature distribution within the fuel in terms of constant parameters q., L, kf, T₁ and/or any other necessary parameters. Hint: Consider an isothermal boundary condition T(x =L) = T₁ found in part a). For the given parameter values, calculate the maximum temperature in the wall. d) Neatly plot the temperature distribution in the wall. c) Nuclear fuel The general heat equation is provided for reference. ƏT pc. == Ət = kV²T + q Steel ↑↑↑ HE b To, h

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