Among the many problems of heat flow which are of importance to the physicist and the engineer, the question of a heat-evolving medium, i.e ., a medium evolving heat everywhere in its mass, has only recently found a place, and consequently it has as yet been but little considered from the theoretical standpoint. As exceptions to this general statement may be cited the astrophysical problem of heat generation in the interior of a star which has been considered by EDDINGTON, MILNE, and others, and the geophysical problem, treated by JEFFREYS and others, of the effect on the earth ’s cooling of the heat generated by radioactive substances in the earth ’s crust. The increasing use, in engineering construction, of rapid hardening cement with its accompanying rapid heat evolution has caused the temperature rise due to heat of reaction to be no longer a negligible quantity, and it has thus become of considerable practical importance to obtain some means of estimating the magnitude of the temperature rise in large masses of concrete. The theoretical problem thus presented of heat conduction in a chemically reacting mass in which the rate of heat evolution is a function of time, forms the subject of the present paper and, so far as the author is aware, no systematic treatment of this problem has hitherto been published.
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