Various mathematical approaches undertaken to model all stages of droplet freezing are
reviewed. The literature is rife with theoretical, experimental, and numerical treatments of the …

During the last ten years, the miniaturization of nanoscale field-effect transistors (FETs)
predicted by Moore's law has confronted an aggressive scaling down of the FET architecture …

The dispersion relation in ω-k space has been derived and analyzed for discrete heat
conduction equation (DE). The DE is inherently nonlocal both in time and space and can be …

Stefan problems provide one of the most fundamental frameworks to capture phase change
processes. The problem in cylindrical coordinates can model outward solidification, which …

The non-Fourier effects, such as wave-like temperature propagation and boundary
temperature jumps, arise in nanosized systems due to the multiple time and space scales …

Phase-change is an important phenomenon and usually it causes a concomitant change in
the density of the underlying materials. As applications of phase-change grow, it is important …

In this paper we formulate a Stefan problem appropriate when the thermophysical properties
are distinct in each phase and the phase-change temperature is size or velocity dependent …

We analyze the short scale effects on the 1D steady-state heat conduction across a nano
film using discrete variable model (DVM). The DVM allows for both diffusive and ballistic …

In this work, a modified form of Taylor series is proposed which we call the moving Taylor
series. We prove theorems that formulate coefficients of the proposed series along with the …

Discrete heat equations for the multilayered periodic systems with allowance for the thermal
resistance between the layers and corresponding dispersion relations in ω− k space have …