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 can´t be observed. This paper continues to show that the realization of thermal inertia by thermal inductance is supported by the principle of electrothermal analogy and compatible with experimental observations.