%MurNBfission000052; ]> Memorandum from Raymond L. Murray to Dr. Clifford K. Beck Machine readable transcription Murray, Raymond L. Creation of machine-readable version: Russell S. Koonts Creation of digital images: Russell S. Koonts Conversion to TEI.2-conformant markup: Russell S. Koonts ca. 9 kilobytes NCSU Libraries Raleigh, NC Modern English, MurNBfission000052

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 3 November, 2000

Nuclear Reactor Digitization Project

Raymond L. Murray Reactor Project Notebook

 Illustrations have been included from the print version. Scanned by Russell Koonts with Photoshop 5.0 software. Memorandum from Raymond L. Murray to Dr. Clifford K. Beck Raymond L. Murray

2 pp. Manuscript copy consulted UA 105.16

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Library of Congress Subject Headings English LCSH manuscript 24-bit color: 400 dpi Memorandum from Raymond L. Murray to Dr. Clifford K. Beck Typescript 2 pp. 1952 MurNBfission000052

TO: Dr. Clifford K. Beck FROM: Raymond L. Murray SUBJECT: Heat from Fission Product Radioactivity in Reactor CC: Reactor Committee

Mr. John Dee prepared the following report for our use, which appears to answer the question very nicely.

The 10 Kw water boiler operates continuously up to a shutdown. It is neces- sary to determine the power from fission product decay after this time.

Reference:1. Goodman, Vol. I, p.243 2. K. Way, Phys. Rev. 70, 115 (1946)

K. Way gives the following expression for energy dissipation from fission products by Β and γ radiation. EΒ and γ = 2.66 t-1.2 Mev/sec-fission10<t<107 seconds (goodman)(within factor of 2) Solution:

The contribution to power at time t by products produced in the interval dT is:

The total is the integral:

In terms of watts:

If the reactor has been operating for say 6 months, then To in seconds is 6 x 30 x 86,400 = 15,550,000 seconds.

Evaluating E at t = 10 seconds:
at t=100 seconds:

Conclusions:

At 100 seconds after shutdown, the maximum Β and γ power from decay of fission products is 500 watts assuming: 1. K Way's formula is incorrect adversely by a factor of 2. 2. All Β and γ's are absorbed in reactor. Since 1/2 Kw is removed from reactor by the surroundings, the solution does not boil.

That this estimate is reasonable may be seen by the following considerations. (Goodman,I, p. 240) Of the 200 Mev produced by a fission, ~ 22 Mev is due to fission product decay. "About half of this last figure is emitted as neutrino energy." Therefore, only ~11 Mev is available as γ and Β energy from fission products. That is, if equilibrium is nearly established between the fission products and a 10 Kw power level, then the steady state decay contribution will be approximately 11/200 x 10 Kw = 550 watts. This decays rapidly upon reactor shutdown and represents a maximum "decay power" in a reactor not exceeding 10 Kw.

Also, the 1/2 Kw conduction by surrounds is conservative in that an increase in fuel temperature above normal operation increases the heat removed by surround- ing almost proportionately with the change in the total temperature drop. That is, if normally the conditions are 85°-25°C removing .5 Kw of heat, then at 100°-25°C the heat removal will be ~ 75/60 x .5 = .625 Kw.

This is the maximum heat removal by surroundings if the boiling point is 100°C. However, the boiling point will be higher due to the involatile solute and may be computed by an elementary method given in "Outlines of Physical Chemistry" by Farrington Daniels, page 231, John Wiley and Sons, 1948.

If there is some question about the closeness of the power production to heat conduction shortly after shutdown it may be shown that if the contents of the water boiler is assumed to be 1 ft3 of water, then a net gain of 500 watts for a period of almost one hour is required to raise the temperature to boiling. At one hour