Appraisal of The Center and Mean Temperature Asymptotes for Unsteady Heat Conduction in The “Small Time” and “Large Time” Sub–Domains

The present study addresses unsteady heat conduction in a large wall with constant temperature at the surfaces and uniform temperature initially. The thermal diffusivity of the solid material is taken as nearly independent of temperature in the temperature interval of operation. A nonlinear interpolatin scheme is implemented with sole input from the Fourier one term series in the “large time” sub–domain t→∞. The goal of the study is to elaborate a center temperature asymptote, a mean temperature asymptote, as well as a heat transfer rate asymptote associated with the problematic “small time” sub–domain t→0. The obtained asymptotic thermal results exhibit excellent quality when compared against benchmark exact, analytical results that are available in the heat transfer literature.