Realization of Thermal Inertia in Frequency Domain

Abstract

Abstract:To realize the lagging behavior in heat conduction observed in these two decades, this paper firstly theoretically excludes the possibility that the underlying thermal inertia is a result of the time delay in heat diffusion. Instead, we verify in experiments the electro-thermal analogy, wherein the thermal inertial is parameterized by thermal inductance that formulates hyperbolic heat-conduction. The thermal hyperbolicity exhibits a special frequency response in Bode plot, wherein the amplitude ratios is kept flat after crossing some certain frequency, as opposed to Fourier heat-conduction. We apply this specialty to design an instrument that reliably identifies thermal inductances of some materials in frequency domain. The instrument is embedded with a DSP-based frequency synthesizer capable of modulating frequencies in utmost high-resolution. Thermal inertia implies a new possibility for energy storage in analogy to inductive energy storage in electricity or mechanics.

Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism

“…arising from insufficient information of thermal inductance is distributed in high-frequency domain, so 1 W is high-passed. Thus 2 W allows only for low-pass, meaning that the closed-loop system is unable to guarantee tracking of fast-time reference temperatures to some extent.…”

“…Firstly, a µ-plate tends to disappear as the robustness weighting 1 W and the performance weighting 2 W are simultaneously magnified. This reflects the trade-off between robust stability and nominal performance.…”

“…where the thermal inductance L is included to fulfill the electro-thermal analogy [1]. Apart from thermal inductance L , a differential volume of Ω is of thermal resistance R and thermal capacitance…”

“…In the works [1,2] and the references cited therein, we learned that many materials possess measurable entropy-flow storage, and that heat conduction in these thermally inductive materials behaves as a standing wave whenever the heat conduction region is small enough to some extent of engineering practice. Known from modal decomposition of standing waves, modes of larger (smaller) variations in space have faster (slower) motions in time.…”

“…Therein, the Double Laplace transform, for example in [36,37], and Double Fourier transform, for example in [15,17,19], were always applied for signal processing and feedback control in semi-infinite and infinite space regions, respectively. The Laplace-Galerkin transform [1,[38][39][40] or Fourier-Galerkin transform [41,42] is justified to model the non-Fourier heat conduction and its controllers for bounded space regions that are of real concern in heat conduction practice. Such an integral transform is obtained through the composite of Laplace transform in time and modal decomposition in space.…”