If heat be supplied at a constant rate to a liquid which is kept at uniform temperature throughout by stirring, and if this liquid lose heat according to Newton's law of cooling, we get dΘ/dt = β/C – αΘ for the differential equation from which to obtain the temperature, Θ, as a function of time. β/c is the rate of heat supply divided by thermal capacity and a Θ the rate of cooling. The surrounding medium is assumed to be at zero temperature. This equation is equally valid if the liquid be replaced by a solid of very high diffusivity. Equation (1) assumes the thermal capacity of the liquid to be independent of temperature.
Proceedings of the Iowa Academy of Science
©1928 Iowa Academy of Science, Inc.
Thompson, Geo. E.
"Heat Flow in the Finite Cylinder with Variable Surface Temperature,"
Proceedings of the Iowa Academy of Science, 35(1), 246-248.
Available at: https://scholarworks.uni.edu/pias/vol35/iss1/47