Analysis of Early-Time Transient Heat Conduction by Method of Characteristics

Abstract

The proposed equations describing early-time one-dimensional heat transfer are hyperbolic with temperature and flux being the dependent variables. The method of characteristics is applied resulting in a solution for the variables as functions of distance and time. A dimensionless parameter δ is introduced which is defined either as the inverse thermal propagation speed or relaxation time. The numerical solution yields explicitness, stability, and accuracy combined with ease of handling time-variable boundary conditions. Examples include predicted response to step inputs of flux or temperature at a surface or interface of materials and illustrate the transition from non-Fourier to Fourier-like diffusion.