Bifurcation analysis of time-delayed parabolic heat-transferwith 2D transfer function

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. With this newly developed functional representation, the heat-transfer dynamics is further realized as a 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 from the stability analysis that the dynamics is unstable, no matter how small the time-delay in heat diffusion is. This instability specifically implies that the hypothesis of time delay happened in heat diffusion contradicts the first law of thermodynamics, and thus must not be true.