Phase field study of the tip operating state of a freely growing dendrite against convection using a novel parallel multigrid approach

Alloy dendrite growth during solidification with coupled thermal-solute-convection fields has been studied by phase field modeling and simulation. The coupled transport equations were solved using a novel parallel-multigrid numerical approach with high computational efficiency that has enabled the investigation of dendrite growth with realistic alloy values of Lewis number ∼104 and Prandtl number ∼10−2. The detailed dendrite tip shape and character were compared with widely recognized analytical approaches to show validity, and shown to be highly dependent on undercooling, solute concentration and Lewis number. In a relatively low flow velocity regime, variations in the ratio of growth selection parameter with and without convection agreed well with theory

Thermomass Theory: A Mechanical Pathway to Analyze Anomalous Heat Conduction in Nanomaterials

The synthesis and measurements of nanomaterials have yielded significant advances in the past decades. In the area of thermal conduction, the nanomaterials exhibit anomalous behavior such as size-dependent thermal conductivity, thermal rectification, and ultra-high thermoelectric properties. The theoretical understanding and modeling on these behaviors are much desired. In this chapter, we study the thermal conduction in nanomaterials through the thermomass theory, which models the heat transfer from a fluid mechanics viewpoint. The control equations of the equivalent mass of the thermal energy are formulated following the continuum mechanics principles, which give the general heat conduction law. It incorporates nonlinear effects such as spatial acceleration and boundary resistance, which can overcome the drawbacks of the traditional Fourier’s law in nanoscale systems. By the thermomass theory, we successfully model the size-dependent effective thermal conductivity in nanosystems. Furthermore, the thermal rectification as well as the thermoelectric enhancement in nanosystems is also discussed with the present framework