A Multiscale Thermo-Fluid Computational Model for a Two-Phase Cooling System

In this paper, we describe a mathematical model and a numerical simulation method for the condenser component of a novel two-phase thermosyphon cooling system for power electronics applications. The condenser consists of a set of roll-bonded vertically mounted fins among which air flows by either natural or forced convection. In order to deepen the understanding of the mechanisms that determine the performance of the condenser and to facilitate the further optimization of its industrial design, a multiscale approach is developed to reduce as much as possible the complexity of the simulation code while maintaining reasonable predictive accuracy. To this end, heat diffusion in the fins and its convective transport in air are modeled as 2D processes while the flow of the two-phase coolant within the fins is modeled as a 1D network of pipes. For the numerical solution of the resulting equations, a Dual Mixed-Finite Volume scheme with Exponential Fitting stabilization is used for 2D heat diffusion and convection while a Primal Mixed Finite Element discretization method with upwind stabilization is used for the 1D coolant flow. The mathematical model and the numerical method are validated through extensive simulations of realistic device structures which prove to be in excellent agreement with available experimental data

Energy Models for One-Carrier Transport in Semiconductor Devices

Moment models of carrier transport, derived from the Boltzmann equation, made possible the simulation of certain key effects through such realistic assumptions as energy dependent mobility functions. This type of global dependence permits the observation of velocity overshoot in the vicinity of device junctions, not discerned via classical drift-diffusion models, which are primarily local in nature. It was found that a critical role is played in the hydrodynamic model by the heat conduction term. When ignored, the overshoot is inappropriately damped. When the standard choice of the Wiedemann-Franz law is made for the conductivity, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regime required empirical modification of this law, or nonstandard choices. Simulations of the hydrodynamic model in one and two dimensions, as well as simulations of a newly developed energy model, the RT model, are presented. The RT model, intermediate between the hydrodynamic and drift-diffusion model, was developed to eliminate the parabolic energy band and Maxwellian distribution assumptions, and to reduce the spurious overshoot with physically consistent assumptions. The algorithms employed for both models are the essentially non-oscillatory shock capturing algorithms. Some mathematical results are presented and contrasted with the highly developed state of the drift-diffusion model

Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels

In this article we address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the well-known velocity-extended Poisson-Nernst-Planck (vPNP) electrodiffusion model. Two extensions of the vPNP system are proposed: the velocity-extended Thermo-Hydrodynamic model (vTHD) and the velocity-extended Electro-Thermal model (vET). Both formulations are based on the principles of conservation of mass, momentum and energy, and collapse into the vPNP model under thermodynamical equilibrium conditions. Upon introducing a suitable one-dimensional geometrical representation of the channel, we discuss appropriate boundary conditions that depend only on effectively accessible measurable quantities. Then, we describe the novel models, the solution map used to iteratively solve them, and the mixed-hybrid flux-conservative stabilized finite element scheme used to discretize the linearized equations. Finally, we successfully apply our computational algorithms to the simulation of two different realistic biological channels: 1) the Gramicidin-A channel considered in~\cite{JeromeBPJ}; and 2) the bipolar nanofluidic diode considered in~\cite{Siwy7}