Unique Solution to a Nonlinear Ordinary Differential Equation

摘要

Numerous approaches have been employed in solving the equation governing unsteady conduction of heat along the radius of an annular cross section. One such method is described by Ozisik, in the spatial propagation of temperature is approximated by an elementary function of the penetration distance of a limiting quantity of heat. This method reduces the original problem, solving a partial differential equation for a function of two independent variables, to that of solving an ordinary differential equation for the approximate penetration distance as a function of time. Of interest here is the solution to the equation for penetration distance when, instead of heat conduction, the approximation method is applied to radial diffusion of decaying mass. 4 refs., 1 fig. (ERA citation 11:015281)