Realization of non-Fourier phenomena in heat transfer with 2D transfer function

The present mainstream realizes that non-Fourier phenomena in heat transfer are arisen from the time-delay in heat diffusion; however, in this paper we mathematically prove this realization an untruth. The analysis is based on the construction of 2D transfer function for the parabolic equation with time-delayed Laplacian that governs the assumed non-Fourier heat transfer. There, functional representation of this spatio-temporal dynamics is performed by the composite of Laplace transform and Galerkin projection. With 2D transfer function, the heat-transfer dynamics is further represented by feedback interconnection of thermal capacitance and time-delayed diffusion, which makes it possible for Nyquist to perform stability and bifurcation analyses on this spatio-temporal dynamics. It comes out that the heat-transfer dynamics under investigation is unstable no matter how small the time-delay in heat diffusion is. That is, time-delayed heat diffusion contradicts the first law of thermodynamics and thus cannot be observed. This paper continues to show that the realization of thermal inertia by thermal inductance is supported by the principle of electro-thermal analogy and compatible with experimental observations.