A Variational Calculation of Diffusive Flux in a Mixed Boundary Value Problem

A variational solution to the transient heat flow measure above a closed conductive region of arbitrary perimeter aspect, held at constant temperature, and which is embedded in an otherwise insulating boundary plane, presented. Upon developing general formulation, full range for circular disk conductor considered as example when implementing two term trial function that comprises form based on known physical solutions problem long short times. The particular combination Lagrange density total diffusive flux functions are evidently effective dealing with difficulties often experienced mixed value transfer problems parabolic type have non-periodic time variable.