Heat conduction and finite measures for transition times between steady states

Abstract

A finite time, the mean action time associated with the conductive transition from a constant initial temperature to thermal equilibrium at a constant ambient temperature, is related to time lag constants, mean energy residence times, mean first passage times, and Green's function properties for linear equations, and to freezing times and finite transition times for problems with phase transitions. When the boundary conditions are linear of mixed type and the conductivity is constant, or when they are of Dirichlet type and the conductivity perhaps temperature dependent, the mean action time is given by the solution of a linear Poisson problem. It is then easily found and is a useful finite comparative time for the thermal transition process, giving a measure of its dependence on size and other geometric factors. © 1991 Oxford University Press.