Analytic temperature distributions are obtained for the fuel and coolant regions of a heterogeneous, convection-cooled reactor with axial power variation ewt sin (πz/H). The fundamental assumption in the governing differential equations is that the temperature distribution in the fuel region does not vary in the direction transverse to the coolant flow. The solutions involve two and three-parameter integrals encountered and numerically evaluated previously which are integrated herein and arranged in a form suitable for desk calculations. Closed-form expressions are developed for the final steady-state axial distributions which are applicable at times long in comparison with the characteristic temperature-response times.
Axial Temperature Distribution for a Nuclear Reactor With Sinusoidal Space and Exponential Time-Varying Power Generation
Doggett, W. O., and Arnold, E. L. (November 1, 1961). "Axial Temperature Distribution for a Nuclear Reactor With Sinusoidal Space and Exponential Time-Varying Power Generation." ASME. J. Heat Transfer. November 1961; 83(4): 423–431. https://doi.org/10.1115/1.3683661
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