Heat Flow in a Finite Cylinder having Variable Surface Temperature

Abstract

Equations of heat flow into finite circular cylinders when the surface temperature is changed either suddenly or at a uniform rate, are derived. In the first case the surface temperature of a cylinder whose temperature is initially uniform throughout is suddenly changed from 0 to $V_0$, kept there for a certain time and then suddenly changed to $V_2$ and kept there indefinitely. In the second case the surface temperature is changed to $V_0$, then is increased at a uniform rate from $V_0$ to $V_2$ and then is kept constant indefinitely. These two cases correspond roughly to the changes occurring in two canning processes and the theoretical curve for case two is found to agree roughly with an experimental curve obtained with a pint Mason jar filled with spinach by the "cold-pack" method.