Temperature component method for heat conduction problems

Abstract

The work includes a solving proposal for initial-boundary value 3D heat conduction problems. The proposal is based on an extension of the body model region to the whole space where the space integral as a particular solution to the initial-boundary value problem is derived. Temperature component is separated from the space integral. The component admissibility conditions are formulated. For numerical purposes the approximated integral with a discrete set of fictitious components is proposed. The fictitious component intensities are determined on an approximate way from the boundary condition. An approximate solution of the heat conduction problem is obtained by extension in time and contraction in space of the approximated integral.