Many-body Green?s function approach to lattice thermal transport

Recent progress in understanding thermal transport in complex crystals has highlighted the prominent role of heat conduction mediated by interband tunneling processes, which emerge between overlapping phonon bands (i.e., with energy differences smaller than their broadenings). These processes have recently been described in different ways, relying on the Wigner or Green-Kubo formalism, leading to apparently different results, which question the definition of the heat-current operator. Here, we implement a full quantum approach based on the Kubo formula, elucidating analogies and differences with the recently introduced Wigner or Green-Kubo formulations, and extending the description of thermal transport to the overdamped regime of atomic vibrations, where the phonon quasiparticle picture breaks down. We rely on first-principles calculations on complex crystals with ultralow conductivity to compare numerically the thermal conductivity obtained within the aforementioned approaches, showing that at least in the quasiparticle regime the differences are negligible for practical applica-tions.

Numerical Modeling of Annular Laminar Film Condensation in Circular and Non-Circular Micro-Channels under Normal and Micro-Gravity

Stefano Nebuloni

A theoretical and numerical model to predict film condensation heat transfer in mini, micro and ultra micro-channels of different internal shapes is presented in this thesis. The model is based on a finite volume formulation of the Navier-Stokes and energy equations and it includes the contributions of the unsteady terms, surface tension, axial shear stresses, gravitational forces and wall thermal conduction. Notably, interphase mass transfer and near-to-wall effects (disjoining pressure) are also included. This model has been validated versus various benchmark cases and versus published experimental results from three different laboratories, predicting micro-channel heat transfer data with an average error of 20 % or better. The conjugate heat transfer problem arising from the coupling between the thin film fluid dynamics, the heat transfer in the condensing fluid and the heat conduction in the channel wall has been studied and analyzed. The work has focused on the effects of three external wall boundary conditions: a uniform wall temperature, a non uniform wall heat flux and single-phase convective cooling. The thermal axial and peripheral conduction occurring in the wall of the channel can affect the behavior of the condensate film, not only because it redistributes the heat, but also because the annular laminar film condensation process is dependent on the local saturation to wall temperature difference. When moving from mini to micro and ultra-micro channels, the results shows that the axial conduction effects can become very important in the prediction of the wall temperature profile and they can not be ignored. Under these conditions, the overall performances of the heat exchanger become dependent not only on the fluid properties and the operative conditions but also on the geometry and wall material. Results obtained for steady state conditions are presented for circular, elliptical and flattened shape cross sections for R-134a and ammonia, for hydraulic diameters between 10 µm and 3 mm. Microscale condensation finds applications in heat pipes and compact heat exchangers for electronic equipment or spacecraft thermal control, in automotive condensers, in residential air conditioning and in refrigeration applications: the influence of the steady or unsteady gravitational field and of the inertia forces on the flow field and consequently on the heat transfer performances is investigated allowing the model to be applied as a design and optimization tool for enhanced heat exchangers.

EPFL2010

Numerical Modeling of Annular Laminar Film Condensation in Circular and Non-Circular Micro-Channels under Normal and Micro-Gravity

Stefano Nebuloni

EPFL2010